Posters

QSIM 2024 POSTER SESSIONS

Instructions for poster presenters:

• Suggested poster dimensions: 4 feet by 3 feet (usually landscape)
• Please print before you come to Rhode Island.
• Poster mounting hardware will be provided by the conference venue
• Poster sessions are on Tuesday (Aug 13) and Thursday (Aug 15). Your poster number is listed below next to the title. The same poster numbers will be marked at the venue. You can mount your poster anytime after lunch.
• Poster sessions will be at the Fascitelli Center for Engineering building at 2 East Alumni Ave, Kingston, RI 02881.
• Please take down your poster after the end of the poster session of each day.

Session 1: Tuesday, August 13, 2024

[1] Co-designing Algorithms and Codes for Early Fault-tolerant Quantum Computation

Authors: Abhinav Anand (Duke University) and Kenneth Brown (Duke University)

Abstract: In recent years, various demonstrations of fault-tolerant (FT) operations on physical devices have been carried out, leading to proposals for their use in early fault-tolerant quantum computing. One line of research focuses on developing methods to reduce overhead (such as the number of logical qubits, operations, and T-count) for fault tolerant implementation of different algorithms. Although this is an important research direction, the overhead associated with these proposals can still be prohibitively high.

In this work, we explore a new direction of co-designing algorithms and error correction codes for early fault-tolerant quantum computation, with a focus on preparing approximate ground states of molecules. We first propose a fully classical algorithm to determine the best classical approximation of the ground state. The algorithm uses the geometric properties of stabilizer states to construct the optimal stabilizer state from excitations of the Hartree-Fock state.

Subsequently, we construct quantum error correction codes using codeword stabilized codes based on this stabilizer state. The resulting code is an error detection code with a single logical qubit. This code enables fault-tolerant preparation of the stabilizer states (can be used as initial states) and arbitrary superpositions of the logical codewords (better approximations to the ground state than stabilizer states) using magic state injection.

Finally, we present results from numerical simulations that approximate the ground state of various molecules. While these states do not yet reach the true ground state, this proposal represents a step in the right direction towards co-designing algorithms and codes for early fault-tolerant quantum computation.

Keywords: Early fault-tolerant protocols, Quantum algorithms, Error correction codes

[2] Efficient Hamiltonian Reconstruction from Equilibrium States

Authors: Adam Artymowicz (Caltech)

Abstract: The problem of reconstructing a local Hamiltonian from an equilibrium state is not only of theoretical interest, but also of considerable practical value. A recent series of works culminated with a proof by Bakshi et al. that in the setting of projective measurements of a Gibbs state at a fixed temperature, this problem can be solved using polynomially many copies of the state and polynomial classical resources. However, what has so far been missing is a demonstration that in this setting, the Hamiltonian learning problem can be practically solved in the regime of hundreds of qubits and realistic levels of measurement noise.

In this talk I will describe how physical considerations of thermodynamic stability lead to a new algorithm for Hamiltonian learning that is easy to implement at experimentally relevant scales. The algorithm is based on the fact that a state is thermodynamically stable against a perturbation if the perturbation increases free energy. As I will show, for a certain class of local perturbations, the change in free energy can be bounded above using only knowledge of the expectation values of local observables. This way, the parent Hamiltonian of a Gibbs state can be estimated by requiring that no local perturbation of the state visibly decreases the free energy.

Computationally, the algorithm is a semidefinite optimization of a size that scales polynomially with the number of qubits, and can be efficiently solved with interior-point methods. I will describe the performance of an open-source implementation of the algorithm on a simulated quantum system of 100 qubits with realistic levels of measurement noise.

Keywords: Hamiltonian learning, Hamiltonian reconstruction, quantum state tomography, Gibbs state, equilibrium state

[3] Quantum-Aided GRAND for Classical Channels

Authors: Alan Bidart (Brown University) and Miles Miller-Dickson (Brown University)

Abstract: We present a quantum-aided version of the \textit{guessing random additive noise decoding} (GRAND) algorithm.  GRAND receives a potentially noisy received sequence and checks it against a probability-ordered list of error sequences to identify the likeliest transmitted sequence. In contrast, our algorithm searches over the set of most likely error sequences simultaneously by making use of coherent superpositions of quantum states that encode the sequences, and use Grover’s algorithm to amplify errors consistent with the received message.  We show that a GRAND search over $2^s$ $n$-bit error sequences can be done using a quantum circuit on $n + s$ qubits. Our construction depends on the ability to design a quantum gate $A$ with the property of translating indices on $s$ qubits to error sequences on $n$ qubits. We outline cases in which the design of $A$ with depth $a_s$ is feasible and show that the resulting circuit has depth $O( \sqrt{2^s}(a_s + n))$.

Keywords: Quantum Algorithms, Quantum Error Correction, Quantum Communication

[4] Quantum Computation of Electronic Structure with Projector Augmented-Wave Method and Plane Wave Basis Set

Authors: Aleksei V. Ivanov (Riverlane), Andrew Patterson (Riverlane), Marius Bothe (Riverlane, Astex Pharmaceuticals), Christoph Suenderhauf (Riverlane), Bjorn K. Berntson (Riverlane), Jens Jørgen Mortensen (Technical University Denmark), Mikael Kuisma (Technical University Denmark), Earl Campbell (Riverlane) and Robert Iszak (Riverlane)

Abstract: Quantum simulations of materials will likely be a key application of quantum  computers. But the plane waves basis sets used for this require effective treatment of the singular potential near the nucleus to keep the number of basis functions manageable. In the quantum literature this has so far been achieved through encoding pseudo-potentials [1], but classically the gold standard is the projector-augmented wave (PAW) method, which has been proven to reduce the number of required basis states by a factor 2-3. In this work we adapt the PAW formalism for an all-electron quantum phase estimation algorithm and provide fault-tolerant costings.

Keywords: Quantum Chemistry, Quantum Phase Estimation, Fault Tolerance, Projector augmented wave method

[5] Entanglement-informed Construction of Variational Quantum Circuits

Authors: Alina Joch (German Aerospace Center (DLR)) and Benedikt Fauseweh (Technical University Dortmund)

Abstract: The Variational Quantum Eigensolver (VQE) is a promising tool for simulating ground states of quantum many-body systems. Its effectiveness relies heavily on the ansatz choice, which must be both hardware-efficient for implementation on noisy hardware and problem-specific to avoid local minima and convergence problems. We explore entanglement-informed ansatz schemes that naturally emerge from specific models, aiming to balance accuracy with minimal use of two-qubit entangling gates, allowing for efficient use of techniques like quantum circuit cutting. We focus on two models of 1D spin Hamiltonians: (i) systems with impurities acting as entanglement barriers, and (ii) systems with competing long-range and short-range interactions transitioning from a long-range singlet to a quantum critical state. For the first model, we observe a plateau in the ansatz accuracy, controlled by the number of entangling gates between the subsystems. This behavior is explained by iterative capture of the correct eigenvalues in the entanglement spectrum. In the second model, combining long-range and short-range entanglement schemes yields the best overall accuracy, leading to global convergence in the entanglement spectrum. Our work provides a new perspective on the design of ansatz schemes based on the expected entanglement structure of the approximated state.

Keywords: Variational Quantum Eigensolver, Ansatz Construction, Entanglement, Quantum Spin Chains

[6] Quasiprobabilistic Imaginary-time Evolution on Quantum Computers

Authors: Annie Ray (University of Waterloo), Esha Swaroop (University of Waterloo), Ningping Cao (Perimeter Institute and IQC (University of Waterloo)), Anirban Chowdhury (IBM) and Michael Vasmer (Perimeter Institute)

Abstract: The estimation of ground-state and thermal equilibrium properties of quantum many-body systems is an important but challenging problem in the simulation of quantum physics. In computational physics, imaginary time evolution (ITE) is a key ingredient in many algorithms for computing such properties. However, performing ITE with general quantum many-body Hamiltonians on classical computers is computationally difficult. A number of quantum algorithms have been developed for ITE, including recent proposals [1] that are aimed at intermediate to near-term quantum computers. Nevertheless, implementing these algorithms on hardware is likely to require extensive error-mitigation. In this work, we propose a new quantum algorithm to compute imaginary-time evolved expectation values which incorporates ideas from quantum error-mitigation [2]. Specifically, we use a technique inspired by probabilistic error-cancellation (PEC) [2] to implement a trotterized ITE as a probabilistic linear combination of quantum circuits followed by post-processing. Our algorithm requires no ancillary qubits, and is inherently noise-resilient since we can directly implement it as a probabilistic linear combination of native noisy gates. Our method is especially well-suited to estimating thermal expectation values using the so-called thermal pure quantum (TPQ) states [3], which can be prepared from simple start states using ITE. We demonstrate our algorithm for ITE by performing numerical (classical) simulations and by implementing it on an IBM quantum computer. The agreement of the experimental data with the theoretical value demonstrates the noise-resilience of our algorithm. In our work, we also analyze our ITE algorithm as applied to the preparation of TPQ states and classically simulate it to prepare TPQ states of the 1D Heisenberg Hamiltonian for up to 7 qubits.

[1] Mario Motta, Chong Sun, Adrian T. K. Tan, Matthew J. O’Rourke, Erika Ye, Austin J. Minnich, Fernando G. S. L. Brand ̃ao, and Garnet Kin-Lic Chan. Determining eigenstates and thermal states on a quantum computer using quantum imaginary time evolution. Nature Physics, 16:205–210, 2019.

[2] Kristan Temme, Sergey Bravyi, and Jay M. Gambetta. Error Mitigation for Short-Depth Quantum Circuits. Phys. Rev. Lett., 119(18):180509, November 2017.

[3] Luuk Coopmans, Yuta Kikuchi, and Marcello Benedetti. Predicting gibbs-state expectation values with pure thermal shadows. PRX Quantum, 4(1):010305, 2023.

Keywords: imaginary-time evolution, quasiprobability decomposition, quantum computing, quantum simulation

[7] Simulating Open-quantum System Chemical Dynamics on a Near-term Quantum Computer

Authors: Ben Stewart (University of York, University of Sydney), Vanessa Olaya-Agudelo (University of Sydney), Christophe Valahu (University of Sydney), Ryan J. MacDonell (Dalhousie University), Ting Rei Tan (University of Sydney) and Ivan Kassal (University of Sydney). 

Abstract: The interaction of molecules with their environment can trigger and control essential processes

in nature, including almost all chemical reactions and energy-transfer processes in photosynthesis or organic solar cells. Efficient simulation of these processes could contribute to the development of next-generation chemical technologies. However, classical computers struggle to accurately simulate large molecular systems interacting with their surroundings, primarily due to the steep growth of computational resources. Therefore, many chemical simulations are restricted to isolated molecules, whose dynamics can be dramatically different

to what happens in solution. We previously demonstrated that an analog quantum simulator can efficiently simulate complex molecular dynamics [1]. Here, we expand the framework to include open-molecular-system simulation by injecting controllable noise into the simulator. 

Our technique mimics realistic molecular systems undergoing dissipation in condensed phase by incorporating widely used dissipative processes within the Lindblad formalism, such as pure dephasing, electronic relaxation, and vibrational relaxation. The model can be readily implemented with available ion-trap technology to simulate a range of systems, from I₃⁻ in polar solvents experiencing fast dissipation, to O2 in argon at low temperatures with a weaker system-bath coupling. Our approach enables long-time simulations on analog simulators by exploiting the native noise as a resource, rather than seeing it as a limitation. In addition, it

shows that open quantum simulations can be easier to perform on quantum computers than corresponding closed ones, in complete reversal of the situation in classical computing.

[1] R. J. MacDonell, et al. Analog quantum simulation of chemical dynamics, Chem. Sci. 12, 9794 (2021).

Keywords: quantum simulation, chemical dynamics, open quantum systems

[8] Unveiling quantum phase transitions from traps in variational quantum algorithms

Authors: Chenfeng Cao (Phasecraft Ltd.), Filippo Maria Gambetta (Phasecraft Ltd.), Ashley Montanaro (Phasecraft Ltd. and University of Bristol) and Raul A. Santos (Phasecraft Ltd.)

Abstract: Understanding quantum phase transitions in physical systems is fundamental to characterize their behavior at small temperatures. Achieving this requires both accessing good approximations to the ground state and identifying order parameters to distinguish different phases. Addressing these challenges, our work introduces a hybrid algorithm that combines quantum optimization with classical machine learning. This approach leverages the capability of near-term quantum computers to prepare locally trapped states through finite optimization. Specifically, we utilize LASSO for identifying conventional phase transitions and the Transformer model for topological transitions, applying these with a sliding window of Hamiltonian parameters to learn appropriate order parameters and estimate the critical points accurately. We verified the effectiveness of our method with numerical simulation and real-hardware experiments on Rigetti’s Ankaa 9Q-1 quantum computer. Our protocol not only provides a robust framework for investigating quantum phase transitions using shallow quantum circuits but also significantly enhances efficiency and precision, opening new avenues in the integration of quantum computing and machine learning.

Keywords: quantum phase transitions, quantum simulation, variational quantum algorithms, machine learning

[9] Approximate Quantum Error-Correction from $SU(2)$ Irreducible Representations with Continuous Transversal Gates and a Metrological Advantage

Authors: Cheng-Ju Lin (University of Maryland), Zi-Wen Liu (Yau Mathematical Science Center, Tsinghua University), Victor V. Albert (QuICS @ NIST and UMD College Park) and Alexey Gorshkov (University of Maryland)

Abstract: We show that a subset of the basis for the irreducible representations of the total $SU(2)$ rotation forms a covariant approximate quantum error-correcting code with transversal $U(1)$ logical gates.

In particular, using the $SU(2)$ algebraic relation and Clebsch-Gordan coefficients, we obtain a universal code performance against a generic $d$-local noise and a $d$-local heralded erasure error, respectively, generalizing and improving the previous works on the “thermodynamic code” to general $s$ and different irreducible representations.

We show that this family of codes can host and protect a probe state with quantum Fisher information beyond the standard quantum limit when the sensing parameter is generated by the $U(1)$ logical gate.

Using our code performance, we discuss the parameter regime of the code where such a metrological advantage is protected against the noise models in our consideration, which we also confirmed numerically.

Keywords: Approximate quantum error correction, Quantum metrology, Group Theory

[10] Mixed Discrete Unitaries for Universal Quantum Computation

Authors: Dmitrii Khitrin (Duke University), Abhinav Anand (Duke University), Jonathan Baker (UT Austin) and Kenneth Brown (Duke University)

Abstract: General single-qubit unitaries are essential for achieving universal quantum computation. However,

real devices may only be able to implement a limited set of these operations, supporting  2p possible variations of the general single-qubit unitary, where  P  can be considered as the precision of the device.  Recently,  probabilistic   angle   interpolation  was   proposed  to  overcome   this  limitation  by randomly replacing a  single-qubit  (along a  single  axis) gate  with one  of three  discretized gate settings.

In this work, we look at the case of a general single-qubit unitary U and propose replacing these gates with a mixture of discrete gates, p1U1 + p2U2+…, where pi is the probability of choosing Ui, defined by the precision P of the device. We show that the probabilistic mixture of the discrete gates approximates the general single-qubit unitary quite well.  We then use the proposed method to replace every single-qubit gate in a quantum circuit with one of the discrete gates using the probability distribution. This is relevant for near-term algorithms, where observables are measured by averaging outputs from multiple circuit runs, and for fault-tolerant algorithms,   where probabilistic unitaries can reduce T-count.

Finally, we demonstrate the effectiveness of our method through numerical simulations, showing that it achieves accurate results without requiring additional computational resources.

Keywords: Mixed unitary channels, Discrete rotation gates, Near-term quantum algorithms

[11] The Effect of Gate Errors on Hamiltonian Simulation Quantum Circuits

Authors: Eli Chertkov (Quantinuum) and Michael Foss-Feig (Quantinuum)

Abstract: Simulating the dynamics of quantum many-body systems is one of the most promising applications of digital quantum computers. A large obstacle to realizing useful dynamics simulations on current quantum computers is the presence of errors during quantum operations such as two-qubit gates. In this work, we analyze how gate errors affect the measurements of observables in quantum circuits that represent the dynamics of a Hamiltonian under a Trotter decomposition. We illustrate with heuristic arguments, numerical evidence, and experimental demonstration that the effect of gate errors is significantly less than one would naively expect when measuring local observables and time evolving by a thermalizing energy-conserving dynamics. Moreover, we show that a two-qubit gate error probability that scales linearly with gate angle, which has been approximately demonstrated on a Quantinuum quantum computer, is particularly helpful in reaching accurate long-time dynamics simulations.

Keywords: Hamiltonian simulation, Gate errors, Experimental demonstration, Trapped-ion quantum computing

[12] Simulation of Fermionic Circuits of Molecular Systems using a Tensor Network Emulator

Authors: Emiliano Poli (University of Padova), Davide Castaldo (University of Padova) and Stefano Corni (University of Padova)

Abstract: Quantum computing is currently in the noisy intermediate-scale quantum (NISQ) era and an ever increasing effort has been put in finding application where “quantum utility” can be found before fault tolerance. In the current landscape Variational Quantum Eigensolver (VQE) is one of the most studied algorithm for applications in quantum chemistry and condensed matter. The VQE algorithm consists in taking a carefully initialized qubit register apply a parametrized quantum circuit to it to model the physics and entanglement of the electronic wavefunction and then measure the Hamiltonian expectation value from the obtained trial wave function. The parameters of the applied quantum circuit are iteratively updated, after each set of measurements, until convergence is reached. The VQE is a promising algorithm since it can theoretically find the ground state of a Hamiltonian in polynomial time and is relatively resilient to quantum hardware noise. In spite of these advantages several questions remain open in order to determine if a real quantum advantage can be reached using this approach. In particular the presence of vanishing gradients and increment of the number of iterations required to optimize the variational parameters with respect to the size of the system simulated are still relatively unexplored aspects that could be decisive in defining the final performance of the VQE.

In this work making use of a highly parallelizable Tensor Network quantum computer emulator we explore the performance of different VQE approaches such as UCCSD, ADAPT-VQE, Tetris-ADAPT-VQE on relatively extended molecules such as H2O, NH3, C2H4, considering the scaling of both the number of gradients and variational parameters calculated. We then analyze/benchmark the scalability of our emulator and evaluate its possible future use for the development of new quantum algorithm. Making use of the characteristic of our emulator we will also evaluate the entanglement production during variational optimization of large molecular systems.

Keywords: VQE, Tensor Network Emulator, Quantum chemistry

[13] Scalable Simulation of Fermionic Encoding Performance on Noisy Quantum Computers

Authors: Emiliia Dyrenkova (Institute for Quantum Computing), Raymond Laflamme (Institute for Quantum Computing) and Michael Vasmer (Perimeter Institute for Theoretical Physics)

Abstract: As we move towards the era of quantum computers with thousands of qubits, the most promising application able to harness the potential of such devices is quantum simulation. Simulating fermionic systems is both a well-formulated problem with clear real-world applications and a computationally challenging task. In order to simulate a system of fermions on a quantum computer, one often has to first map the fermionic Hamiltonian to a qubit Hamiltonian. The most popular such mapping is the Jordan-Wigner encoding, which suffers from inefficiencies caused by the non-locality of the encoded operators. As a result, alternative local encodings have been proposed that solve the problem of long encoded operators at the expense of a constant factor increase in the number of qubits. Some of these alternatives end up possessing non-trivial stabilizer structure akin to quantum error-correcting codes. A natural error mitigation approach for such an encoding is to measure the stabilizers and discard any run with non-trivial error syndrome. With the help of modern stabilizer simulation tools, we classically simulate a local encoding known as the Compact Encoding, comparing its performance with the Jordan-Wigner encoding and the ternary tree encoding. Our simulations use more complex error models and significantly larger system sizes than in previous works. We simulate both memory experiments (only encoding and decoding) and logical circuits for the Fermi-Hubbard model. We found error detection methods for certain types of measurements that could significantly improve the performance of near-term simulations. Work to extend these results to all measurements required for estimating the energy of the system is still ongoing.

Keywords: fermionic encoding, jordan-wigner, quantum simulation, error detection, error mitigation, stabilizer simulation

[14] Predicting Outputs of Digital Quantum Circuits with Neural Networks

Authors: Eric Chen (Acton-Boxborough Regional High School, Acton, MA), David Nizovsky (Vanderbilt University, Nashville, TN), Helen Zeng (Innobridge Institute, Boston MA) and Mikhail Shalaginov (Massachusetts Institute of Technology, Cambridge, MA)

Abstract: Quantum algorithms are typically graphically represented in the form of quantum logical circuits. They contain initialized qubits placed vertically on the left side, horizontal timelines filled with the gates sequence applied to the corresponding qubits and measurement gauges on the right. To compute a quantum algorithm on a classical computer, one needs to run a direct quantum solver performing a series of numerous matrix multiplications, which become computationally costly especially for the quantum circuits of increased sizes (e.g. quantum circuits containing more than 30 qubits). In this work, we investigated an opportunity to leverage neural networks to bypass direct computations. We trained deep neural nets to predict the outputs of quantum circuits based on the content of logical circuits. To synthesize training datasets, we built a generator that randomly fills in the space on a quantum circuit with a set of universal gates, i.e. T, S, H and CNOT. The outputs were collected in the form of state-vectors with complex amplitudes. Afterwards, we constructed and trained two neural nets, as fully connected layers, to predict both real and imaginary components of state-vector amplitudes. We studied the neural net predicting performance and its dependence on quantum circuit parameters, such as number of qubits, gates, and types of gates. The predicting neural net is an essential part for solving an inverse design problem of predicting a quantum circuit that yields a desired quantum state. To sum up, we explored the application of neural nets for predicting the outputs of quantum circuits and introduced a new tool enabling more efficient and faster development of quantum algorithms.

Keywords: quantum circuit, quantum algorithm, deep learning, predicting neural network

[15] Open Quantum Simulation of Chemical Dynamics with Controllable Noise Injection

Authors: F. Scuccimarra (School of Physics, University of Sydney, NSW 2006, Australia), C. H. Valahu (School of Physics, University of Sydney, NSW 2006, Australia), V. G. Matsos (School of Physics, University of Sydney, NSW 2006, Australia), M. J. Millican (School of Physics, University of Sydney, NSW 2006, Australia), V. C. Olaya-Agudelo (School of Chemistry, University of Sydney, NSW 2006, Australia), B. Stewart (School of Chemistry, University of Sydney, NSW 2006, Australia), R. J. MacDonell (Department of Chemistry, Dalhousie University, Halifax, NS B3J 4H9, Canada), P. Nagpal (School of Physics, University of Sydney, NSW 2006, Australia), I. Kassal (School of Chemistry, University of Sydney, NSW 2006, Australia) and T. R. Tan (School of Physics, University of Sydney, NSW 2006, Australia)

Abstract: Chemistry problems such as drug discovery hinge on our ability to accurately simulate the

dynamics of electronic and nuclear-vibrational degrees of freedom in molecules, whose dynamics are particularly susceptible to environmental interactions [1]. Studying such systems on classical computers, however, quickly becomes intractable due to poor resource scaling with molecular and environmental complexity, even when using state-of-the-art algorithms and making modest approximations [2, 3].

Trapped ion systems provide a computationally efficient alternative platform for analogue chemistry simulations, as we can directly map the Hamiltonian of the system of interest onto the electronic and vibrational degrees of freedom of a collection of ions [3–7]. In this work, we show that open quantum simulations with linear scaling of quantum resources can be realised using trapped ions, by exploiting the simulator’s native dissipation and injecting additional dissipation as necessary. We present a collection of schemes to controllably inject various types of noise into a trapped ion system, effectively simulating common dissipators in chemistry problems.

References

[1] A. Nitzan. Chemical Dynamics in Condensed Phases. 1st ed. Oxford University Press, 2006.

[2] G A Worth et al. “Using the MCTDH wavepacket propagation method to describe multimode non-

adiabatic dynamics”. In: Int. Rev. in Phys. Chem. 27.3 (2008), pp. 569–606. ISSN: 0144-235X. DOI:

10.1080/01442350802137656.

[3] Ryan J. MacDonell et al. “Analog quantum simulation of chemical dynamics”. In: Chem. Sci. 12.28

(2021), pp. 9794–9805. DOI: 10.1039/d1sc02142g.

[4] Ryan J. MacDonell et al. “Predicting molecular vibronic spectra using time-domain analog quantum

simulation”. In: Chem. Sci. 14.28 (2023), pp. 9439–9451. DOI: 10.1039/D3SC02453A.

[5] C. H. Valahu et al. “Direct observation of geometric-phase interference in dynamics around a coni-

cal intersection”. In: Nat. Chem. 15 (11 2023), pp. 1503–1508. DOI: 10.1038/s41557-023-01300-

3.

[6] Visal So et al. “Trapped-Ion Quantum Simulation of Electron Transfer Models with Tunable Dissipa-

tion”. 2024. arXiv: 2405.10368.

[7] Ke Sun et al. “Quantum Simulation of Spin-Boson Models with Structured Bath”. 2024. arXiv: 2405.

14624.

Keywords: trapped ions, analog mixed-qudit-boson simulator, open quantum simulation, chemical dynamics

[16] Title: Valence Bond Shadows of Quantum Spin Liquids

Authors: Gaurav Gyawali (Cornell University), Phillip Martin (Cornell University) and Michael Lawler (Binghamton University, Cornell University)

Abstract: A central challenge in the quantum simulation of quantum spin liquids is determining what observables to measure. Quantum spin liquids are enigmatic phases of matter challenging to connect microscopic simulations governed by spin operators S_i with theory governed by partons and to study in solid state experiments. We need an intermediate third set of observables and a means to estimate them to overcome these difficulties in immanent quantum advantage experiments.  Inspired by Anderson’s original resonating valence bond picture of quantum spin liquids and modern vison theories\cite{huh2011vison}, we propose two shadow tomographic techniques\cite{aaronson2018shadow}, ‘spin fusion shadows’ and ‘valence bond shadows’. We prove the first is tomographic given enough shots for rotationally invariant mixed states and that a quantum Markov chain governs the second with numerical experiments demonstrating a short mixing time. Using these two algorithms, a quantum computer can generate shots that connect either more closely to the original spin operators $S_i$ while preserving symmetry quantum numbers (spin fusion shadow case) or extend to Andersons original picture of a quantum spin liquid (valence bond shadows case) which more closely underpins parton theory.

Keywords: Quantum Spin Liquids, Shadow tomography, Quantum Algorithm

[17] Scaling of Excitation Densities on a Programmable Quantum Annealer after a First-order Quantum Phase Transition

Authors: Gregor Humar (Jožef Stefan Institute), Jaka Vodeb (Juelich Research Institute) and Dragan Mihailović (Jožef Stefan Institute)

Abstract: First order quantum phase transitions are a fundamental process in the study of non-equilibrium dynamics of many body systems, giving rise to complex behaviour such as metastability, coarsening and nucleation. Slow quenches across the transition point are well understood for second-order transitions in terms of the Kibble-Zurek mechanism [1]. Recent studies have expanded this mechanic to certain first-order transitions [2,3]. Advances in quantum technology have provided new controllable and programmable platforms for experimental explorations of first order transitions in various quantum systems. We present scaling of excitation densities in the tilted Ising model when driven across a first-order quantum phase transition on the D-Wave programmable quantum annealer. We consider a protocol where, starting in the ground state, the longitudinal field in the Ising model is slowly varied across the first order phase quantum transition. During the evolution excitations in the form of quantized bubbles form at specific parameter regions. Densities of these excitations follow scaling laws similar to the Kibble-Zurek mechanism. We utilize the D-Wave quantum annealer to access large scale systems of 2000 qubits and long simulation times. Quantum simulation results from the quantum annealer are compared to numerical simulations.

[1]  D. Rossini and E. Vicari. Coherent and dissipative dynamics at quantum

phase transitions. Physics Reports, 936:1–110  (2021).

[2]  A. Sinha et al. Nonadiabatic dynamics across a first-order quantum phase transition: Quantized bubble nucleation. Phys. Rev. B, 103:L220302 (2021).

[3]  L.-Y. Qiu et al. ,Observation of generalized Kibble-Zurek mechanism across a first-order quantum phase transition in a spinor condensate. Sci. Adv. 6, eaba7292 (2020).

Keywords: Quantum phase transitions, Non-equilibrium quantum dynamics, Tilted Ising model, Scaling of excitation densities, Quantum annealer

[18] When Can a Classical Control Transition Herald the Measurement-induced Entanglement Transition?

Authors: Haining Pan (Rutgers University), Sriram Ganeshan (City College, City University of New York), Thomas Iadecola (Iowa State University), Justin Wilson (Louisiana State University) and Jed Pixley (Rutgers University) 

Abstract: The experimental observation in the measurement-induced phase transition from the volume-law entangled state to the area-law entangled state is challenging due to post-selection issues where the ensemble-averaged density matrix always flows to the infinite-temperature Gibbs state.

One clever way to avoid it is to steer the dynamics onto a controlled phase with predetermined fixed points to herald the entanglement transition via the control transition.

However, it remains uncertain whether these two transitions always coincide.

In this work, we study both scenarios where the transitions either coincide or split.

When the two transitions coincide, the entanglement transition is dominated by the control transition.

When the two transitions split, they may belong to different universality classes at the critical point.

Our numerical results demonstrate that the topology of the phase diagram is significantly influenced by the structure of the control map— whether it is local or global— and whether there is projective measurement.

This work provides a comprehensive understanding of the interplay between the control transition and the measurement-induced entanglement transition.

Keywords: Quantum dynamics, Measurement-induced phase transition, Quantum measurements, Entanglement entropy

[19] SHARC-VQE: Simplified Hamiltonian Approach with Refinement and Correction enabled Variational Quantum Eignesolver for Molecular Simulation on Quantum Device

Authors: Harshdeep Singh (IIT Kharagpur), Sonjoy Majumder (IIT Kharagpur) and Sabyashachi Mishra (IIT Kharagpur).

Abstract: Quantum computing is increasingly utilized in quantum chemistry, particularly for simulating simple molecules and evaluating properties such as ground state energy and dipole moment. Transforming a molecular Hamiltonian from the fermionic space to the qubit space results in a series of Pauli strings. Calculating the energy then involves evaluating the expectation values of each of these strings, which presents a significant bottleneck for applying Variational Quantum Eigensolvers (VQEs) in quantum chemistry. Unlike fermionic Hamiltonians, the terms in a qubit Hamiltonian are additive. This work leverages this property to introduce a novel method for extracting information from the partial qubit Hamiltonian of simple molecules, thereby enhancing the efficiency of VQEs. This work introduces the SHARC-VQE (Simplified Hamiltonian Approximation, Refinement, and Correction-VQE) method, where the full molecular Hamiltonian is partitioned into two parts, one that is computationally easier to handle, known as the Partial Hamiltonian, and another that, while more complex, is less significant, which is approximated and added up as a correction into the partial Hamiltonian. The SHARC-VQE method involves analyzing the qubit Hamiltonian term-by-term to understand their relative contributions to the overall energy. The partial Hamiltonian is constructed with fewer Pauli strings but can still resolve the entire Hamiltonian. This truncated Hamiltonian significantly reduces computational costs for molecular simulations. Furthermore, measurement outcomes using SHARC-VQE are less prone to errors induced by noise from quantum circuits. Additionally, we demonstrate the application of SHARC-VQE as an initialization technique, where the simplified partial Hamiltonian is used to identify an optimal starting point for more complex systems. This method not only improves the efficiency of VQEs but also enhances the accuracy and reliability of quantum simulations by mitigating noise and computational challenges.

Keywords: Variational Quantum Algorithms, Quantum Chemistry, Quantum Computing, Molecular Simulation

[20] Pathwise Differentiation of Worldline Path Integrals

Authors: He Zheng (University of Oregon), Daniel Steck (University of Oregon) and Jonathan Mackrory (University of Oregon)

Abstract: The worldline method is a powerful numerical path-integral framework for computing Casimir and Casimir–Polder energies. An important challenge arises when one desires derivatives of path-integral quantities—standard finite-difference techniques, for example, yield results of poor accuracy. In this work we present methods for computing derivatives of worldline-type path integrals of scalar fields to calculate forces, energy curvatures, and torques. In Casimir–Polder-type path integrals, which require derivatives with respect to the source point of the paths, the derivatives can be computed by a simple reweighting of the path integral. However, a partial-averaging technique is necessary to render the differentiated path integral computationally efficient. We also discuss the computation of Casimir forces, curvatures, and torques between macroscopic bodies. Here a different method is used, involving summing over the derivatives of all the intersections with a body; again, a different partial-averaging method makes the path integral efficient. To demonstrate the efficiency of the techniques, we give the results of numerical implementations of these worldline methods in atom-plane and plane–plane geometries. Being quite general, the methods here should apply to path integrals outside the worldline context (e.g., financial mathematics).

Keywords: Numerical path integrals, Casimir energies, Worldline method, Monte Carlo simulation

[21] Quantum Algorithms for Nonlinear Dynamics: Revisiting Carleman Linearization with no Dissipative Conditions

Authors: Hsuan-Cheng Wu (Department of Mathematics, Penn State), Jingyao Wang (Institute for Interdisciplinary Information Science, Tsinghua University) and Xiantao Li (Department of Mathematics, Penn State)

Abstract: We explore the embedding of nonlinear dynamical systems into linear ordinary differential equations (ODEs) via the Carleman linearization method. Under dissipative conditions, numerous previous works have established rigorous error bounds and linear convergence for Carleman linearization, which have facilitated the identification of quantum advantages in simulating large-scale dynamical systems. Our analysis extends these findings by exploring error bounds beyond the traditional dissipative condition, thereby broadening the scope of quantum computational benefits to a new class of dynamical regimes. This novel regime is defined by a resonance condition, and we prove how this resonance condition leads to a linear convergence with respect to the truncation level N in Carleman linearization. We support our theoretical advancements with numerical experiments on a variety of models, including the Burgers’ equation, Fermi-Pasta-Ulam (FPU) chains, and the Korteweg-de Vries (KdV) equations, to validate our analysis and demonstrate the practical implications.

Keywords: Quantum Computing, Non Linear Dynamical System, Carleman Linearization, ODE

[22] Probabilistically Preparing Bethe Ansatz on a Quantum Computer in Constant-Depth Circuits Assisted by Measurements and Feedforward Operations

Authors: Hyeonjun Yeo (Department of Physics and Astronomy, Seoul National University), Ha Eum Kim (Department of Physics, Korea University) and Kabgyun Jeong (Research Institute of Mathematics, Seoul National University)

Abstract: Given the time required for the propagation of correlations, various useful quantum states (such as GHZ states, Toric code states, etc.) cannot be prepared in a constant-depth unitary circuit starting from a product state. However, measurements and feedforward operations enable the preparation of such states in constant depth due to their non-local nature. In this paper, we focus on the Bethe ansatz, which plays a significant role in quantum many-body physics due to its explicit form. We present a measurement-feedforward assisted method for preparing certain (anti)symmetrized states in constant depth, and the Bethe ansatz in constant depth, albeit in a probabilistic manner. Our approach is suitable for specific quantum hardware that has good scalability but poor coherence time.

Keywords: Quantum state preparation, measurements and feedforward operations, bethe ansatz

[23] A Magic-state-free Architecture for Early Fault-tolerant Quantum Computers

Authors: Jacob Nelson (University of New Mexico), Andrew Landahl (Sandia National Laboratories/University of New Mexico) and Andrew Baczewski (Sandia National Laboratories/University of New Mexico)

Abstract: The costs of quantum simulation tasks tend to be dominated by non-Clifford gates. On a surface code architecture these gates must be performed via magic-state distillation and gate teleportation, requiring additional space on a quantum device dedicated to distillation. This additional space may be prohibitive to near-term devices where physical qubits are limited. We present an architecture for early fault-tolerant quantum computers that avoids the need for qubit-costly magic-state distillation during runtime. It uses only transversal gates, boot-time preparations of the +1 eigenstate of the single-qubit Hadamard operator, and state teleportation between [[4,2,2]] (2D) and [[8,3,2]] (3D) error-detecting color codes. Our architecture realizes the universal logical gate basis consisting of measurement and preparation of qubits in the Z-basis, single-qubit Hadamard gates, and controlled-controlled-Z gates. We provide explicit transpilations from the widely used Clifford + T gate basis to this one, allowing for optimal gate synthesis up to a constant prefactor. We characterize our architecture with two performance metrics and propose empirical tests based off mirror circuit fidelity estimation to estimate these performance metrics at various computational volumes.

Keywords: Quantum error correction in quantum simulation, Early fault-tolerance, Compilation into universal gatesets

[24] Exploring Connections Between Molecular Hamiltonians and the Completely Delocalized Model

Authors: Jason Necaise (Dartmouth College), Weishi Wang (Dartmouth College) and James Whitfield (Dartmouth College)

Abstract: The electronic structure problem is known to be a challenging computational task for classical computers. Hartree–Fock (HF) methods provide a compact ground-state approximation of fermionic systems at the level of the mean-field approximation. In the NISQ era, HF often serves as the initial guess for downstream classical or quantum simulation procedures by providing a free-fermion reference state with respect to the discretized electronic Hamiltonian. We introduce a family of permutationally invariant model Hamiltonians, for which mean-field methods become exact, and investigate the applicability of this model to molecular systems. In particular, we define the manifold of completely delocalized (CDL) Hamiltonians up to orbital rotations and quantify the distance between this manifold and discretized molecular Hamiltonians with respect to finite basis sets. We investigate the correlation between such distance and the performance of Hartree–Fock approximation. In this way, we hope to identify the inherent capability of mean-field solvers in the context of fermionic quantum simulation. This research also holds the potential to help develop better state preparation.

Keywords: electronic, structure, electronic structure, chemistry, condensed matter, model, hamiltonian, model hamiltonian, state preparation, initialization, simulation

[25] Instability of Steady-state Mixed Symmetry-protected Topological Order to Strong-to-weak Spontaneous Symmetry Breaking

Authors: Jeet Shah (University of Maryland, College Park), Cheng-Ju Lin (University of Maryland, College Park), Yu-Xin Wang (University of Maryland, College Park), Christopher Fechisin (University of Maryland, College Park), Joseph T. Iosue (University of Maryland, College Park), Brayden Ware (Google Quantum AI), James D. Watson (University of Maryland, College Park), Yan-Qi Wang (University of Maryland, College Park) and Alexey V. Gorshkov (University of Maryland, College Park)

Abstract: We address the question of whether open quantum system dynamics which host mixed symmetry-protected topological (SPT) states as steady states continue to do so after introducing symmetric perturbations. In particular, we discuss the characteristics of the \textit{decohered cluster state} — a mixed SPT protected by a combined strong and weak symmetry — and construct a parent Lindbladian which hosts it as a steady state. The parent Lindbladian can be mapped onto reaction-diffusion dynamics, which is exactly solvable, even in the presence of certain perturbations. This allows us to study the steady states of the parent Lindbladian in detail, including states which, to the best of our knowledge, have not been previously discussed. Through a combination of analytical and numerical methods, we find that the perturbed Lindbladians exhibit strong-to-weak spontaneous symmetry breaking at arbitrarily small perturbation strength for typical symmetric perturbations, leading to instability of the mixed steady-state SPT order. However, for perturbations which only introduce defects of the weak symmetry, we find that the mixed steady-state SPT order survives. Additionally, we construct a quantum channel which replicates the essential physics of the Lindbladian and can be efficiently simulated using only Clifford gates, Pauli measurements, and feedback.

Keywords: Mixed state phases, Symmetry protected topological phases, Strong-Weak symmetry breaking, Condensed matter theory, Quantum information theory, Markovian dynamics, DMRG, Exactly solvable

[26] Topological Physics with Programmable Cavity-Mediated Interactions

Authors: Jonathan Jeffrey (Stanford University), Avikar Periwal (Stanford University), Merrick Ho (Stanford University), Philipp Kunkel (Stanford University), Eric Cooper (Stanford University), Ocean Zhou (Stanford University) and Monika Schleier-Smith (Stanford University)

Abstract: Interactions within a quantum system dictate the structure of entanglement between its constituents. Control of this structure is necessary for analog quantum simulation and novel quantum sensing protocols. Most platforms for quantum science are limited to spatially local interactions, but the photon-mediated interactions inherent to cavity QED systems naturally generate distance agnostic all-to-all interactions. This provides new prospects for engineering interaction graphs that do not simply depend on physical geometries, allowing us to access effective arrangements of the system for which the dimensionality and topology is distinct from its physical ordering. We present work on a cavity-based implementation of the Su-Schrieffer-Heeger (SSH) model, a quasi-1D model with a symmetry protected topological phase. We probe the bulk-boundary correspondence by tuning between open and closed boundary conditions, and make a direct measurement of the topological invariant (Zak phase). We implement a non-local interferometric protocol to measure the edge state dynamics, which are compared to a transverse field Ising model. We demonstrate extensions such as introducing complex coupling terms and engineering flat bands.

Keywords: topology, cavity QED, SSH model

[27] Moving Beyond Single Donor Placement for Silicon Quantum Devices

Authors: Jonathan Wyrick (NIST), Pradeep Namboodiri (NIST), Fan Fei (NIST), Mark-Yves Gaunin (NIST), Brian Courts (NIST), Vijith Kamalon Pulikodan (NIST), Utsav Utsav (NIST) and Richard Silver (NIST)

Abstract: At NIST we have fabricated quantum devices designed to function as quantum simulators using the technique of hydrogen depassivation lithography (HDL) to create small clusters of P atoms in Si, positioned with nanometer precision.  We have found that HDL analog quantum simulators depend critically on the number of atoms incorporated at each site.  When the number of atoms is not precisely controlled, disorder in the fabricated device results in behavior that can only be qualitatively understood, ultimately limiting the usefulness of the device for quantum simulation.  We present our efforts in building fully functioning devices with single perfectly placed P atoms as the key elements, as well as expansion of this method to include placement of B (acceptor) atoms.

Keywords: atom-by-atom fabrication, STM, analog quantum simulation

[28] Brick Wall Quantum Circuits with Global Fermionic Symmetry

Authors: Kareljan Schoutens (University of Amsterdam), Pietro Richelli (Delft University of Technology) and Alberto Zorzato (University of Amsterdam). 

Abstract: We study brick wall quantum circuits enjoying a global fermionic symmetry. The constituent 2-qubit gate, and its fermionic symmetry, derive from a 2-particle scattering matrix in integrable, supersymmetric quantum field theory in 1+1 dimensions. Our 2-qubit gate, as a function of three free parameters, is of so-called free fermionic or matchgate form, allowing us to derive the spectral structure of both the brick wall unitary U_F and its, non-trivial, hamiltonian limit H_γ in closed form. We find that the fermionic symmetry pins H_γ to a surface of critical points, whereas breaking that symmetry leads to non-trivial topological phases. We briefly explore quench dynamics and entanglement build up for this class of circuits.

Keywords: brick wall quantum circuit, fermionic symmetry, integrability, Kitaev chain, quench dynamics

[29] Magic and Entanglement Transitions in Quantum Circuits with Long-Range Interactions

Authors: Kemal Aziz (Rutgers University), Haining Pan (Rutgers University), Michael Gullans (University of Maryland) and Jed Pixley (Rutgers University)

Abstract: Magic is a resource that characterizes the amount of non-Clifford operations needed to prepare quantum states. We study monitored quantum circuits with non-local unitary dynamics, local projective measurements, and a controlled injection of non-Clifford resources. We introduce new algorithms for simulating these circuits and computing the entanglement entropy, allowing us to go up to L = 64 qubits. We also develop a new algorithm for generating bell samples from the quantum circuit. Using these methods, we identify three distinct phase transitions in the magic and entanglement.

Keywords: Measurement Induced Phase Transition, Quantum Circuit Simulation, Open Quantum System

[30] Journey to Quantum Advantage for Configurational Analysis of Materials: A Cross-platform Study

Authors: Kieran McDowall (National Quantum Computing Centre), Theodoros Kapourniotis (National Quantum Computing Centre), Christopher Oliver (National Quantum Computing Centre), Konstantinos Georgopoulos (National Quantum Computing Centre) and Phalgun Lolur (National Quantum Computing Centre)

Abstract: Quantum computers show potential for achieving computational advantage over classical computers, with candidate applications in the domains of computational chemistry and materials science. We address the well-studied problem of configurational analysis of materials, specifically finding the relative energy of defective graphene structures, a task which is generally classically intractable. To solve this problem, we implement two algorithms, the Variational Quantum Eigensolver (VQE) and  Quantum Annealing (QA), on state-of-the-art digital and analog QCaaS devices, correspondingly. We propose a framework for fine-tuning and benchmarking the performance of these solutions, using a toolbox of relevant metrics and compare performances against three classical algorithms. The applicability of this framework goes beyond this configurational analysis problem. Finally, we present our conclusions on the benefits and detriments of the different quantum approaches, digital and analog, and on the practical limitations and possibilities for achieving advantage by scaling the problem to larger sizes.

Keywords: quantum benchmarking, computational advantage, cross-platform

[31] Simulating the Wave Equation on Current Quantum Devices

Authors: Lewis Wright (Quantinuum) and Jeremy First (bp)

Abstract: We design and implement quantum circuits for the simulation of the one-dimensional wave equation on the Quantinuum H1-1 quantum computer. The circuit depth of our approach scales as O(n^2) for n qubits representing the solution on 2^n grid points, and leads to infidelities of O(2^(-4n) t^2) assuming smooth initial conditions. By varying the qubit count we study the interplay between the algorithmic and physical gate errors to identify the optimal working point of minimum total error. Our approach to simulating the wave equation can be adapted to other quantum processors and serve as an application-oriented benchmark.

Keywords: Quantum Computing, Partial differential equations, NISQ, Quantum algorithms, Wave equation, Experimental, Theoretical, Industry, Applications

[32] Quantum Order-by-disorder Induced Phase Transition and Signatures of Novel Many-body Quantum Scars in Rydberg Ladders

Authors: Madhumita Sarkar (University of Exeter), Mainak Pal (Indian Association for the Cultivation of Science), Arnab Sen (Indian Association for the Cultivation of Science) and Krishnendu Sengupta (Indian Association for the Cultivation of Science). 

Abstract: Rydberg atoms are known to have long-lived Rydberg excited states with controllable excitation amplitude (detuning) and strong repulsive van der Waals interaction  between excited atoms.

I shall present the study of such atoms in a two-leg ladder geometry in the presence of both staggered and uniform detuning. My focus will be on the magnetization plateau of quarter filled states where the ground states is selected by a quantum order-by-disorder mechanism from a macroscopically degenerate manifold of Fock states with fixed Rydberg excitation density . This unravels the presence of an emergent Ising transition stabilized via the order-by-disorder mechanism inside the plateau. In addition to this I shall show some theoretical analysis on how to employ Schrieffer-Wolff perturbation technique to identify the competing terms responsible for the transition and estimate a critical detuning  which agrees well with exact-diagonalization based numerical studies. Interestingly, this transition survives for a realistic interaction potential, and the critical point can be estimated analytically as well. [1]

Subsequently, my study of many-body quantum scars in this model shows the presence of novel non-ergodic quantum states at non-zero staggering, exhibiting different entanglement dynamics compared to its Rydberg chain counterpart. Moreover, the time evolution of Sz operator beginning from a Neel state shows site dependent dynamics with the up and down spins having different long time values. [2]

[1] SciPost Physics 14, 004 (2023).

[2] Work in progress.

Keywords: Rydberg atoms, Order-by-disorder induced quantum phase transition, Ising transition in the magnetization plateau, Many body quantum scars, Ergodicity breaking

[33] Observation of Spin Excitation Dynamics in a Quantum Dot Ladder

Authors: Pablo Cova Fariña (QuTech), Daniel Jirovec (QuTech), Xin Zhang (QuTech), Elizaveta Morozova (QuTech), Stefan Oosterhout (TNO), Tzu-Kan Hsiao (National Tsing Hua University), Amir Sammak (TNO), Giordano Scappucci (QuTech), Menno Veldhorst (QuTech) and Lieven Vandersypen (QuTech). 

Abstract: Analog quantum simulators promise to shed light on current problems in natural sciences before digital, fault tolerant quantum computers reach quantum practicality. In recent years, semiconductor gate-defined quantum dot arrays have emerged as a promising platform for both digital and analog efforts. In the past, these systems have been used to simulate a plethora of physical phenomena [1-5], thanks to the in-situ tunability of tunnel couplings and onsite energies, as well as the direct mapping of their Hamiltonian to an extended Fermi-Hubbard or Heisenberg model, depending on the parameter regime.

In this work, we use an array of quantum dots in a Ge/SiGe quantum well to simulate the dynamics of spin excitations, or magnons, based on our previous efforts characterizing charge and two-spin states in similar devices [5,6]. For this purpose, we control exchange interactions between neighbouring sites throughout the array, individually tunable over several orders of magnitude. Using transitions with a controlled degree of adiabaticity and exchange-based gates, we demonstrate initialization and readout of different spin states. This ultimately allows us to initialize single magnons in desired locations in the array and pinpoint their position as they propagate over time. We observe their evolution for different exchange coupling configurations and topologies and compare the results to simulations based on the Heisenberg model.

Furthermore, we exploit the rich physics of holes in germanium to explore the impact of disorder to the spin dynamics. Owing to their strong intrinsic spin-orbit interaction, spins in germanium exhibit site-dependent g-tensors, which act as a source of single-site disorder. We observe how moderately high ratios of disorder to interactions disrupt the ideal dynamics of single magnons and ultimately lead to localization. The obtained results are promising in the context of simulating many-body localization and other disorder-based solid-state phenomena.

[1] Hensgens et al., Nature 548, 70–73 (2017)

[2] Dehollain, Mukhopadhyay et al., Nature 579, 528–533 (2020)

[3] van Diepen, Hsiao et al., Phys. Rev. X 11, 041025 (2021)

[4] Wang et al., npj Q info 9, 58 (2023)

[5] Hsiao, Cova Fariña et al., Phys. Rev. X 14, 011048 (2024)

[6] Zhang, Morozova et al., arXiv:2312.16101 (2023)

Keywords: Quantum dots, Spin qubits, Solid-state platform, Quantum magnetism, Quantum walk

[34] Quantum Zeno Monte Carlo for eigenstate properties

Authors: Mancheon Han (School of Computational Sciences, Korea Institute For Advanced Study (KIAS)), Hyowon Park (Department of Physics, University of Illinois at Chicago) and Sangkook Choi (School of Computational Sciences, Korea Institute For Advanced Study (KIAS)) 

Abstract: In this work, we develop the quantum Zeno Monte Carlo (QZMC), which is an ansatz-free and noise resilient approach to find Hamiltonian eigenstate properties. By implementing the Quantum Zeno effect as a Monte Carlo summation of consecutive time evolutions, we progressively approach to the unknown eigenstate from the easily solvable Hamiltonian’s eigenstate. Our approach can compute eigenstate properties within a polynomial quantum time if the state is energetically gapped. And QZMC is resilient to device noise and the trotter error. We demonstrate applicability of QZMC by computing various properties of one, two and many qubits systems. By applying the method with a NISQ device, we explicitly validate the device noise resilience of our method. The polynomial complexity and resilience to trotter error is shown by computing energy eigenvalues and spectral functions of the Hubbard model for various sizes. Because our algorithm is noise-resilient and can show polynomial computational complexity, we expect our algorithm can achieve quantum advantage with an early fault-tolerant quantum computer.

Keywords: Eigenstate, Quantum Zeno effect, Energy eigenvalues, Monte Carlo

[A] Emergent Strong Zero Mode through Local Floquet Engineering

Authors: Bhaskar Mukherjee (Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom), Ronald Melendrez (Department of Physics, Florida State University, Tallahassee, Florida 32306, USA), Marcin Szyniszewski (Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom), Hitesh J. Changlani (Department of Physics, Florida State University, Tallahassee, Florida 32306, USA) and Arijeet Pal (Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom)

Abstract: Decoherence is the main obstacle for quantum information processing and fault-tolerant quantum computing. That’s why it is extremely important to explore ways to suppress the decoherence of a quantum system.

The constituents of a generic interacting many-body system usually decohere under their own dynamics but some sophisticated (integrable) interaction can lead to long-lived emergent quasiparticles, for example, edge Majorana zeromode of a Kitaev chain. The notion of strong zeromode (SZM) was extended to systems with genuine (yet integrable) interaction but their existence in non-integrable systems has always been an open question. In this talk, I will show how local Floquet driving can be utilized to engineer the emergence of an SZM in a non-integrable system. Individual sites can not be dynamically frozen even by the most optimal choice of drive parameters. Interestingly, a special choice of optimally driven sites can stabilize an SZM, enhancing the decoherence time of the edge qubit exponentially in system size.

Keywords: Strong zero mode, Non-integrable system, Floquet engineering, Entanglement entropy

[B] The Fate of the False Vacuum: Creating Quantized Bubbles on a 5564 Qubit Quantum Annealer

Authors: Jaka Vodeb (Juelich Research Institute), Jean-Yves Desaules (School of Physics and Astronomy, University of Leeds), Andrea Rava (Juelich Research Institute), Gregor Humar (Jožef Stefan Institute), Dennis Willsch (Juelich Research Institute), Fengping Jin (Juelich Research Institute), Madita Willsch (Juelich Research Institute), Kristel Michielsen (Juelich Research Institute) and Zlatko Papić (School of Physics and Astronomy, University of Leeds)

Abstract: For nearly half a century, first-order quantum phase transitions (FOQPT) have been studied intensely in various contexts. False vacuum decay is a potential mechanism for the Universe’s evolution post-Big Bang, the Kibble-Zurek mechanism can be generalized to FOQPTs, quantum metastability has implications for reaction rate theory, and the mechanisms behind FOQPTs can help answer fundamental questions regarding non-equilibrium quantum dynamics. Despite theoretical advancements, direct observation and study of these dynamics have remained elusive due to their non-perturbative nature. However, recent breakthroughs in quantum technology have enabled unprecedented experimental investigation into this fundamental phenomenon. Here, we utilize a quantum annealer with 5564 superconducting flux qubits subjected to transverse and longitudinal fields arranged in a ring to directly observe FOQPT dynamics, revealing quantized bubble formation. Moreover, we identify a parameter regime on the quantum annealer where we observe coherent scaling laws in driven many-body dynamics of 5564 qubits for over 1 μs, which is more than 1000 qubit time units. This study opens avenues for investigating previously inaccessible time scales, system sizes, dimensionality, and topology of many-body dynamics, marking a significant milestone in the study of complex quantum systems and paving the way for future breakthroughs in quantum simulation.

Keywords: Applications of quantum simulation, Many-body physics in quantum simulators, Non-equilibrium quantum dynamics, False vacuum decay, Quantum annealing

[C] Efficient Implementation of Multi-Controlled Quantum Gates

Authors: Ben Zindorf (UCL) and Sougato Bose (University College London)

Abstract: We present an implementation of multi-controlled quantum gates which provides significant reductions of cost compared to state-of-the-art methods. The operator applied on the target qubit is a unitary, special unitary, or the Pauli X operator (Multi-Controlled Toffoli). The required number of ancilla qubits is no larger than one, similarly to known linear cost decompositions. We extend our methods for any number of target qubits, and provide further cost reductions if additional ancilla qubits are available. For each type of multi-controlled gate, we provide implementations for unrestricted (all-to-all) connectivity and for linear-nearest-neighbor. All of the methods use a linear cost of gates from the Clifford+T (fault-tolerant) set. In the context of linear-nearest-neighbor architecture, the cost and depth of our circuits scale linearly irrespective of the position of the qubits on which the gate is applied. Our methods directly improve the compilation process of many quantum algorithms, providing optimized circuits, which will result in a large reduction of errors.

Keywords: Quantum computing, Multi-controlled gates, Multi-controlled Toffoli, MCT, Quantum circuits, Fault-tolerant, Quantum circuit compilation, Quantum circuits optimization

[D] High-order Dynamical Decoupling under Bandwidth Constraints

Authors: Leeseok Kim (University of New Mexico) and Milad Marvian (University of New Mexico)

Abstract: We aim to design a high-order dynamical decoupling (DD) sequence using finite-width pulses that is robust against both free-evolution time and finite pulse width, using two different methods: (1) Symmetrization and Concatenation, and (2) Trotter-Suzuki (TS) formula. When the number of pulses required in the first-order protocol is large (e.g. decoupling all-to-all interactions), the TS-based higher-order sequence uses fewer pulses. This decoupling sequence has valuable applications, including the implementation of quantum gates and robust quantum simulations under physical constraints.

Keywords: quantum control, quantum simulation, dynamical decoupling

[E] Quantum Algorithms to Simulate Open Quantum Systems

Authors: Evan Borras (University of New Mexico) and Milad Marvian (University of New Mexico)

Abstract: We present a quantum algorithm for simulating the dynamics governed by the Lindblad master equation. Our approach incorporates classical randomness into the design of the algorithm and leverages Hamiltonian simulation as a subroutine. The algorithm we present has a gate complexity and ancilla cost independent of the number of jump operators. This leads to improvements for simulating Lindbladians with large amounts of jump operators as well as improved ancilla costs when compared to other Lindblad simulation algorithms. Our approach also generalizes easily to incorporated time-dependent correlations into the simulation.

Keywords:   quantum simulation, quantum algorithms, open quantum systems

[F] Detecting High-dimensional Time-bin Entanglement in Fiber-loop Architectures

Authors: Niklas Euler (University of Jena) and Martin Gärttner (University of Jena)

Abstract: Many quantum communication protocols require the distribution of entanglement between the different participating parties. One example of such a protocol is quantum key distribution (QKD), an application which has matured to the brink of commercial use in recent years. However, difficulties remain, especially with noise resilience and channel capacity in long-distance communication. One way to overcome these problems is to use high-dimensional entanglement, which has been shown to be more robust to noise and facilitates higher secret-key rates. It is therefore important to have access to certifiable high-dimensional entanglement sources to confidently implement these advanced QKD protocols. Here, we investigate a fiber-loop setup that allows the scalable creation of time-bin entanglement and its certification on the same device. Our certification method builds on previous proposals for the certification of angular-momentum entanglement in photon pairs. In particular, measurements in only two experimentally accessible bases are sufficient to obtain a lower bound on the entanglement dimension for both two- and multiphoton quantum states. Numerical simulations show that the method is robust against typical experimental noise effects and works well even with limited measurement statistics, thus establishing time-bin encoded photons as a viable candidate for high-dimensional quantum-communication protocols.

Keywords: entanglement detection, quantum simulation, time-bin entanglement, high-dimensional entanglement

[G] Time-Dependent Variational Principle with Quantum Trajectories for Open Quantum Systems

Authors: Liam J. Bond (University of Amsterdam), Bas Gerritsen (University of Amsterdam), Jiri Minář (University of Amsterdam), Jeremy T. Young (University of Amsterdam), Johannes Schachenmayer (University of Strasbourg), Arghavan Safavi-Naini (University of Amsterdam)

Abstract: We present a new framework to simulate the open dynamics of many-boson quantum systems. We use a superposition of squeezed-displaced states as a non-Gaussian state (NGS) ansatz. It is not restricted to a low excitation subspace, and can describe a variety of interesting quantum states (eg. squeezed cat states). We simulate open dynamics using the time-dependent variational principle and quantum trajectories, avoiding the need to propagate a density matrix. We study the Holstein-Tavis-Cummings model and compare to dTWA, showing that NGS is a complementary method that provides some additional benefits at similar computational cost.

Keywords: open quantum systems, non-Gaussian states, variational ansatz, time-dependent variational principle, truncated Wigner approximation

[H] Quantum Liang Information Flow Probe of Causality Across Critical Points

Authors: Roopayan Ghosh (University College London, London, United Kingdom), Yi Bin (University of Electronic Science and Technology of China Chengdu, China) and Sougato Bose (University College London, London, United Kingdom)

Abstract: Investigating causation in the quantum domain is crucial. Despite numerous studies of correlations in quantum many-body systems, causation, which is very distinct from correlations, has hardly been studied. We address this by demonstrating the efficacy of the newly proposed causation measure, quantum Liang information flow, in quantifying causality across phase diagrams of quantum many-body systems. We focus on quantum criticality, which are highly non-classical points. We extract causation behavior across a spectrum-wide critical point and a ground state second-order phase transition in both integrable and non-integrable systems. We discern a marked shift in causation behavior across criticality, with each case exhibiting distinct hallmarks, different from correlation measures. Notably in the latter case, we observe maximum causation in nearby sites in the ordered phase just preceding the critical point.

Keywords: Quantum Causality, Quantum Criticality, Quantum Liang information, Many-body Quantum chains, Aubry Andre Harper model, Single site quantum tomography

Session 2: Thursday, August 15, 2024

[35] Operator Space Fragmentation in Perturbed Floquet-Clifford Circuits

Authors: Marcell D Kovacs (University College London), Christopher J Turner (University College London), Lluis Masanes (University College London) and Arijeet Pal (University College London)

Abstract: Floquet quantum circuits are able to realise a wide range of non-equilibrium quantum states, exhibiting quantum chaos, topological order and localisation. The circuit based perspective has led to new regimes of many-body quantum dynamics with potential applications to quantum technologies.  In this work, we investigate the stability of operator localisation and emergence of chaos  in random Floquet-Clifford circuits subjected to unitary perturbations which drive them away from the Clifford limit. We construct a nearest-neighbour Clifford circuit with a brickwork pattern and study the effect of including disordered non-Clifford gates. The perturbations are uniformly sampled from single-qubit unitaries with probability $p$ on each qubit. We show that the interacting model exhibits strong localisation of operators for $0 \leq p < 1$ that is characterised by the fragmentation of operator space into disjoint sectors due to the appearance of wall configurations. Such walls give rise to emergent local integrals of motion for the circuit that we construct exactly. We analytically establish the stability of localisation against generic perturbations and calculate the average length of operator spreading tunable by $p$. Although our circuit is not separable across any bi-partition, we further show that  the operator localisation leads to an entanglement bottleneck, where initially unentangled states remain weakly entangled across typical fragment boundaries. Finally, we study the spectral form factor (SFF) to characterise the chaotic properties of the operator fragments and spectral fluctuations as a probe of non-ergodicity. In the $p=1$ model, the emergence of a fragmentation time scale is found before random matrix theory sets in after which the SFF can be approximated by that of the circular unitary ensemble. Our work provides an explicit description of quantum phases in operator dynamics and circuit ergodicity which can be realised on current NISQ devices.

Keywords: random quantum circuits, localisation, ergodicity, quantum chaos, quantum dynamics, many-body theory

[36] Block Encoding of Matrix Product Operators

Authors: Martina Nibbi (Technical University of Munich) and Christian Mendl (Technical University of Munich)

Abstract: Quantum signal processing combined with quantum eigenvalue transformation has recently emerged as a unifying framework for several quantum algorithms.

In its standard form, it consists of two separate routines: block encoding, which encodes a Hamiltonian in a larger unitary, and signal processing, which achieves an almost arbitrary polynomial transformation of such a Hamiltonian using rotation gates.

The bottleneck of the entire operation is typically constituted by block encoding and, in recent years, several problem-specific techniques have been introduced to overcome this problem.

Within this framework, we present a procedure to block-encode a Hamiltonian based on its matrix product operator (MPO) representation.

More specifically, we encode every MPO tensor in a larger unitary of dimension $D+2$, where $D = \lceil\log(\chi)\rceil$ is the number of subsequently contracted qubits that scales logarithmically with the virtual bond dimension $\chi$. 

Given any system of size $L$, our method requires $L+D$ ancillary qubits in total, while the number of one- and two-qubit gates decomposing the block encoding circuit scales as $\mathcal{O}(L\cdot\chi^2)$.

Keywords: block encoding, matrix product operators, tensor networks, unitary dilation, quantum eigenvalue transformation, linear combination of unitaries, qubitization

[37] Exponential Improvements in the Simulation of Lattice Gauge Theories Using Near-optimal Techniques

Authors: Mason Rhodes (Sandia National Laboratories), Michael Kreshchuk (Lawrence Berkeley National Laboratory) and Shivesh Pathak (Sandia National Laboratories). 

Abstract: Simulation of quantum systems of a large number of strongly interacting particles persists as one of the most challenging, and computationally demanding, tasks in classical simulation, involving both non-relativistic applications like condensed matter physics and quantum chemistry, as well as relativistic applications like lattice gauge theory simulation. One of the major motivations for building a fault-tolerant quantum computer is the efficient simulation of many-body systems on such a device. While significant developments have been made in the quantum simulation of non-relativistic systems, the simulation of lattice gauge theories has lagged behind, with state-of-the-art Trotterized simulations requiring many orders of magnitude more resources than non-relativistic simulation, in stark contrast to the similar difficulty of these tasks in classical simulation. In this work, we conduct an in-depth analysis of the cost of simulating Abelian and non-Abelian lattice gauge theories in the Kogut-Susskind formulation using simulation methods with near-optimal scaling in system size, evolution time, and error. We provide explicit circuit constructions, as well as T-gate counts and qubit counts for the entire simulation algorithm. This investigation, the first of its kind, leads to up to 25 orders of magnitude improvement over Trotterization in spacetime volume for non-Abelian simulations. Such a dramatic improvement results largely from our algorithm having polynomial scaling with the number of colors, as opposed to exponential scaling in existing approaches. Our work demonstrates that the use of advanced algorithmic techniques leads to dramatic reductions in the cost of ab initio simulations of fundamental interactions, bringing it in step with resources required for first principles quantum simulation of chemistry and condensed matter physics.

Keywords: lattice gauge theory, qubitization, interaction picture evolution, block encoding, fault-tolerant simulation

[38] Squared Overlap Calculations with Linear Combination of Unitaries

Authors: Michelle Sze (Quantinuum), Nathan Fitzpatrick (Quantinuum) and David Muñoz Ramo (Quantinuum)

Abstract: Linear combination of unitaries (LCU) method has proven to scale better than existing product formulas in simulating long time Hamiltonian dynamics. However, given the number of multi-control gate operations in the standard prepare-select-unprepare architecture of LCU, it is still resource-demanding to implement it on the current hardware machines. For a special purpose of calculating  squared overlaps of two wave functions, we propose an optimized LCU method, based on pre-selecting relevant unitaries, that leads to a significant reduction in the circuit depths and two-qubit counts. We test this approach in simulating Rabi-Hubbard Hamiltonian.

Keywords: Hamiltonian dynamics, LCU, Fault-tolerant quantum simulation algorithms

[39] Disentangling to a Reduction for Estimating Quantum Information Fundamental Properties

Authors: Myeongjin Shin (School of Computing, Korea Advanced Institute of Science and Technology (KAIST).), Seungwoo Lee (School of Computing, Korea Advanced Institute of Science and Technology (KAIST).), Mingyu Lee (Department of Computer Science and Engineering, Seoul National University.), Donghwa Ji (Collage of Liberal Studies, Seoul National University.), Hyeonjun Yeo (Department of physics and astronomy, Seoul National University.), Junseo Lee (School of Electrical and Electronic Engineering, Yonsei University.) and Kabgyun Jeong (Research Institute of Mathematics, Seoul National University.)

Abstract: In the field of Quantum Information, fundamental properties such as quantum entropy and quantum distance measures are of significant importance. In this paper, we develop a unified approach called Disentangling Quantum Neural Networks (DEQNN), which can be applied to all estimations. For the unified estimation, we employed a disentanglement method that reduces the dimension of a state with a small error rate by applying a specific unitary operation. We demonstrated that if the disentanglement error rate is small, the trace distance is preserved, and the values of the respective properties are maintained according to the continuity bound. Subsequently, to find unitary operations to minimize the disentanglement error, we used a layer-wise quantum neural network.

Keywords: Disentanglement, quantum information, quantum entropy, quantum distance measure, quantum neural network

[40] Dressed OTOC and Decoherence

Authors: Nadie LiTenn (Brandeis University) and Brian Swingle (Brandeis University)

Abstract: In recent quantum physics research, quantum chaos has emerged as a pivotal

area of interest, particularly in its potential to provide insights into complex quantum many-body systems such as black holes. While a consensus on a precise definition of quantum chaos remains a debate among scholars, the Out-of-Time-Order Correlator (OTOC) stands out as a probe into quantum chaos and information scrambling. We propose a modified version of OTOC, dubbed the ”dressed OTOC”, where the two branches of time evolutions differ by a perturbation. We show that, in a Brownian cluster model, with small perturbation, the maximum value of the average operator weight will quickly saturate at a lower value than without perturbation, and we show that this happens similarly with decoherence in the form of single qubit dephasing.

Keywords: OTOC, Decoherence, Chaos

[41] Non-linear Bosonic Interactions in a Spin-oscillator System 

Authors: Oana Bazavan (University of Oxford), Sebastian Saner (University of Oxford), Donovan J. Webb (University of Oxford), Ellis M. Ainley (University of Oxford), Peter Drmota (University of Oxford), David Nadlinger (University of Oxford), Gabriel Araneda (University of Oxford), David Lucas (University of Oxford), Chris J. Ballance (University of Oxford) and Raghavendra Srinivas (University of Oxford)

Abstract: Higher-order nonlinear interactions on a quantum harmonic oscillator lead to increasingly nonclassical and resourceful quantum states. Some of these interactions go beyond the Gaussian formalism and, hence, serve as a resource for real-time quantum simulation of many-body models, with the potential to surpass the capabilities of classical hardware. However, studying these interactions has been challenging as they typically become exponentially weaker with increasing order. Using the motion of a trapped ion coupled to its spin, we present the experimental implementation of a new protocol relying solely on linear spin-dependent interactions to generate up to fourth-order interactions [1]. Focusing on generalised squeezing, we demonstrate and characterise squeezing, trisqueezing, and quadsqueezing interactions; the fourth-order quadsqueezing interaction is over 100 times stronger than possible with conventional methods. Our approach imposes no fundamental limit on interaction order and applies universally to platforms supporting spin-dependent linear interactions. Strong higher-order nonlinear interactions unlock the study of fundamental quantum optics, quantum simulation, and computation in a hitherto unexplored regime.

[1] O. Bazavan et al., arXiv:2305.08700 (2023)

Keywords: non-linear bosonic interactions, continuous variables, many-body quantum simulations

[42] Anti-Symmetry of Entanglement: Probing Entanglement through Violation of Fermionic Symmetry Rules

Authors: Peyman Azodi (Princeton University), Benjamin Lienhard (Princeton University) and Herschel Rabitz (Princeton University)

Abstract: Despite advances in experimental quantum sciences, measuring entanglement entropy in many-body quantum systems remains challenging. In this work, we reveal a geometric aspect of entanglement that can be harnessed to measure entanglement. Entanglement in many-body systems can be represented through exterior products, equivalent to volumes, within Hilbert space. We show that various entanglement metrics, including the von Neumann entropy, can be expressed through these volumes, which can be indirectly quantified in the lab by observing probabilities of certain fermionic symmetries. This novel link between entanglement and geometry can lead to highly efficient entanglement measurement protocols.

Keywords: Entanglement, Many-Body quantum systems, quantum geometry, experimental probe

[43] Quantum Chemistry Without the Born-Oppenheimer Approximation: Analog and Digital Approaches

Authors: Ryan MacDonell (Dalhousie University), Jongkwon Ha (Dalhousie University) and Edith Leal-Sánchez (Dalhousie University)

Abstract: The Born-Oppenheimer approximation separates terms in the molecular Hamiltonian into electronic and nuclear parts such that they can be solved separately. This approximation greatly decreases classical simulation costs, and it underpins nearly all quantum chemistry methods. However, high-energy processes in chemistry—such as the absorption of light—lead to a breakdown in the Born-Oppenheimer approximation. We present encodings for a vibronic (vibrational + electronic) pre-Born-Oppenheimer wavefunction ansatz on analog and digital quantum computers. Both approaches show linear resource scaling and polynomial scaling in Hamiltonian implementation with system size. Our approaches allow for a compact basis representation without a reliance on pre-calculation of electronic states on classical computers, making it a promising candidate for a practical quantum advantage in the near term.

Keywords: Quantum chemistry, Photochemistry, Born-Oppenheimer, Analog quantum computing, Digital quantum computing

[44] Simulation of a Rohksar-Kivelson Ladder on a NISQ Device

Authors: Sabhyata Gupta (Institut für Theoretische Physik, Leibniz Universität Hannover), Younes Javanmard (PASQAL), Tobias J. Osborne (Institut für Theoretische Physik, Leibniz Universität Hannover) and Luis Santos (Institut für Theoretische Physik, Leibniz Universität Hannover)

Abstract: We present a quantum-classical algorithm to study the dynamics of the Rohksar-Kivelson plaquette ladder- simplest lattice gauge model with plaquette interactions, on NISQ devices. We show that complexity is largely reduced using gauge invariance, additional symmetries, and a crucial property associated to how plaquettes are blocked against ring-exchange in the ladder geometry. This allows for an efficient simulation of sizable plaquette ladders with a small number of qubits, well suited for the capabilities of present NISQ devices. We illustrate the procedure for ladders with simulation of up to 8 plaquettes in an IBM-Q machine, employing scaled quantum gates.

Keywords: Quantum Simulation, Lattice Gauge Theories, NISQ devices, Quantum gates

[45] Application of Hybrid – Quantum Annealing Solvers for Simulations and Optimization for the Capacitated Vehicle Routing Problem (CVRP)

Authors: Salvatore Sinno (Unisys), Bhavika Bhalgamiya (Unisys), Thomas Groß (Newcastle university), Alan Mott (Unisys), Arati Sahoo (Unisys), Deepak Honnalli (Unisys) and Shruthi Thuravakkath (Unisys)

Abstract: We provide an efficient analysis of the quality of the solutions returned by adiabatic quantum annealers for the Capacitated Vehicle Routing Problem (CVRP). Theoretical studies and simulations on classic hardware often assume that the computation in adiabatically closed systems occurs without environmental interference. However, this is not a realistic assumption for real systems. Therefore, these theory-based simulations on classical hardware or limited tests do not accurately assess the capability of current commercial quantum annealers. Therefore, it becomes essential to analyze the accuracy of solutions returned by commercial quantum annealers. To address this, we first developed the mathematical model using Constrained Quadratic Model to implement the CVRP problem on AQC. Later, we provide the comparative analysis on the accuracy of solutions returned by quantum annealer vs 1. benchmark datasets, 2. data size, 3. constraint density, and 4. problem complexity.

Keywords: Quantum Annealing, Quantum simulation, Quantum Optimization, Capacitated Vehicle Routing Problem (CVRP), D-Wave hybrid Solvers, Constrained Quadratic Model, Quadratic Unconstrained Binary Optimization (QUBO)

[46] Spin squeezing and multi-headed cat generation for quantum-enhanced sensing

Authors: Sean Muleady (University of Maryland, College Park, and NIST)

Abstract: Control over quantum states in atomic systems has enabled the development of the most precise atomic clocks to date. Despite these advancements, demonstrating a quantum advantage in such systems remains challenging. One obstacle is that while current quantum platforms host a variety of finite-range entangling interactions, such as dipolar, van der Waals, and far-detuned phonon-mediated interactions, generating entangled resources for quantum sensing typically requires infinite-range interactions. Here, using chains of trapped ions, we experimentally demonstrate how finite-range interactions can nevertheless be harnessed to generate collective dynamical behavior, enabling production of metrologically useful entanglement. Leveraging interactions that decay as a power law function of the ion separation, we achieve spin squeezing at -3.9 dB below the standard quantum limit, and also observe collective non-Gaussian states in the form of multi-headed cats. These outcomes have immediate applications across various quantum sensing platforms with finite-range interactions, such as arrays of ultracold atoms and molecules or solid-state spin defects.
Keywords: quantum metrology, trapped ions, quantum entanglement

[47] Generating Arbitrary Superpositions of a Quantum Harmonic Oscillator

Authors: Sebastian Saner (University of Oxford), Oana Bazavan (University of Oxford), Donovan Webb (University of Oxford), Gabriel Araneda (University of Oxford), David Lucas (University of Oxford), Chris Ballance (University of Oxford) and Raghavendra Srinivas (University of Oxford)

Abstract: Quantum computing using continuous variables (CVQC) [1] offers a promising alternative to qubit-based approaches. By encoding quantum information in a quantum harmonic oscillator with infinite levels it enables applications like error correction or simulation with significantly fewer physical resources. One important aspect to this is the creation of quantum superposition states. Despite notable progress in the manipulation of harmonic oscillator superpositions, existing demonstrations have been limited to specific configurations such as coherent (displaced) states leading to cat states [2], displaced-squeezed states leading to GKP states [3], or superpositions of two distinct Fock states. However, many degrees of freedom have been impossible to control and have consequently not been explored. Employing the spin conditioning of our recently developed technique [4] to create nonlinear interactions allows us to synthesise a wide range of superpositions but also to gain control over all degrees of freedom that were previously inaccessible. In particular, we create superpositions between squeezed, trisqueezed, and quadsqueezed states with independent control over the complex-valued squeezing parameter and the probability amplitude of each constituent. Such states were theoretically conjectured for decades but not observed [5]. These states exhibit large Wigner negativity and rotational symmetry in phase-space, suggesting their resourcefulness for quantum computing and potential for logical qubit encodings. Additionally, we discuss plans to extend our control techniques to multiple modes for applications such as analogue quantum simulation of gauge fields [6].

[1]: Lloyd, S., & Braunstein, S. L. (1999). Quantum computation over continuous variables. Physical Review Letters, 82(8), 1784.

[2]: Cochrane, P. T., Milburn, G. J., & Munro, W. J. (1999). Macroscopically distinct quantum-superposition states as a bosonic code for amplitude damping. Physical Review A, 59(4), 2631.

[3]: Gottesman, D., Kitaev, A., & Preskill, J. (2001). Encoding a qubit in an oscillator. Physical Review A, 64(1), 012310.

[4]: Băzăvan, O., Saner, S., Webb, D. J., Ainley, E. M., Drmota, P., Nadlinger, D. P., … & Srinivas, R. (2024). Squeezing, trisqueezing, and quadsqueezing in a spin-oscillator system. arXiv preprint arXiv:2403.05471.

[5]: Sanders, B. C. (1989). Superposition of two squeezed vacuum states and interference effects. Physical Review A, 39(8), 4284.

[6]: Băzăvan, O., Saner, S., Tirrito, E., Araneda, G., Srinivas, R., & Bermudez, A. (2023). Synthetic Z2 gauge theories based on parametric excitations of trapped ions. arXiv preprint arXiv:2305.08700.

Keywords: superpositions, continuous variable quantum computing (CVQC), wigner negativity, rotationally symmetric, analogue simulation

[48] Reducing the Cost of Energy Estimation in the Variational Quantum Eigensolver Algorithm with Robust Amplitude Estimation

Authors: Shangjie Guo (bp) and Alex Kunitsa (Zapata AI)

Abstract: Quantum chemistry and materials is one of the most promising applications of quantum computing. Yet much work is still to be done in matching industry-relevant problems in these areas with quantum algorithms that can solve them. Most previous efforts have carried out resource estimations for quantum algorithms run on large-scale fault-tolerant architectures, which include the quantum phase estimation algorithm. In contrast, few have assessed the performance of near-term quantum algorithms, which include the variational quantum eigensolver (VQE) algorithm. Recently, a large-scale

benchmark study found evidence that the performance of the variational quantum eigensolver for a set of industry-relevant molecules may be too inefficient to be of practical use. This motivates the need for developing and assessing methods that improve the efficiency of VQE. In this work, we predict the runtime of the energy estimation subroutine of VQE when using robust amplitude estimation (RAE) to estimate Pauli expectation values. Under conservative assumptions, our resource estimation predicts that RAE can reduce the runtime over the standard estimation method in VQE by one to two orders of magnitude.

Keywords: robust amplitude estimation, resource estimation, ground state estimation

[49] Quantum-classical Hybrid GANs: Their Use in Chemistry Simulation and Beyond

Authors: Shangjie Guo (bp) and Claudia Perry (bp)

Abstract: Quantum-classical hybrid generative adversarial networks (GANs) demonstrate tangible model performance improvements over their classical counterparts, and experimentation by bp’s digital science team is allowing the application of these benefits to chemistry simulation and other key business challenges of relevance to the energy industry. Leveraging the power of quantum computers early requires us to take advantage of the incremental benefits being shown along the journey to fault tolerance, and we aim to be ready to exploit new technology advancements as they become available.

Keywords: Quantum-classical hybrid method, generative adversarial networks, chemistry simulation

[50] The Weak Generalized Bunching Conjecture

Authors: Shawn Geller (National Insitute of Standards and Technology), Manny Knill (National Institute of Standards and Technology) and Scott Glancy (National Institute of Standards and Technology)

Abstract: There has been interest in the dynamics of noninteracting bosons because of the boson sampling problem. These dynamics can be difficult to predict because of the complicated interference patterns that arise due to their indistinguishability. However, if there are unobserved, hidden degrees of freedom, the indistinguishability can be disrupted in the observations. The generalized bunching probability is defined to be the probability that $n$ noninteracting bosons all arrive in a subset of sites $S$. The strong generalized bunching conjecture states that among models where the hidden state of the bosons is separable, the generalized bunching probability is maximized when the bosons are perfectly indistinguishable. This conjecture was shown to be false [Seron et. al. Nat. Phot. 17, 702-709 (2023)]. We show that among models where the hidden state is permutation invariant, the generalized bunching probability is maximized by perfectly indistinguishable bosons if and only if Lieb’s permanental dominance conjecture for immanants is true. We discuss applications of this conjecture to measuring the temperature of bosons trapped in an optical lattice.

Keywords: Quantum Characterization, Boson Sampling, Photonics

[51] Fabricating Novel Surface Ion Trap Architectures

Authors: Simon Gorbaty (Duke Quantum Center), Thomas Kessler (Duke Quantum Center), Joseph Ryan (Duke Quantum Center), Mitch Peaks (Duke Quantum Center) and Crystal Noel (Duke Quantum Center)

Abstract: Engineering more advanced surface ion traps is critical to the success of trapped ion quantum systems. More intricate surface traps can enable scaling to many more individually addressed ions, whether by shuttling ions across zones of electrode arrays or by integrating on-chip laser delivery. Additionally, iterating on new materials and surface treatment techniques during the trap fabrication process may elucidate the mechanisms behind the anomalous heating of ions that limits the scale of trapped-ion processors. In this poster, I present two thrusts to advance ion traps. The first is degenerately-doped silicon traps, whose surface properties are more controllable than that of conventional metal traps, permitting precise manipulation to investigate and reduce anomalous heating. The second thrust is integrating ion traps with waveguides fabricated from thin-film lithium niobate (LN). An electro-optic material, integrated photonics with LN can facilitate on-chip modulation of laser light, eliminating the need for bulky optical modulators and thereby promoting the scalability of trapped ion systems.

Keywords: trapped ions, surface traps, electric field noise, integrated photonics, lithium niobate

[52] Quantum Coarsening and Collective Dynamics on a Programmable Quantum Simulator

Authors: Sophie H. Li (Harvard University), Tom Manovitz (Harvard University), Sepehr Ebadi (Harvard University and Massachusetts Institute  of Technology), Rhine Samajdar (Princeton University), Alexandra A. Geim (Harvard University), Simon J. Evered (Harvard University), Dolev Bluvstein (Harvard University), Hengyun Zhou (Harvard University and QuEra), Nazli Ugur Koyluoglu (Harvard University), Johannes Feldmeier (Harvard University), Pavel E. Dolgirev (Harvard University), Nishad Maskara (Harvard University), Marcin Kalinowski (Harvard University), Subir Sachdev (Harvard University), David A. Huse (Princeton University), Markus Greiner (Harvard University), Vladan Vuletic (Massachusetts Institute of Technology) and Mikhail D. Lukin (Harvard University)

Abstract: Understanding the collective quantum dynamics of nonequilibrium many-body systems is an outstanding challenge in quantum science. In particular, dynamics driven by quantum fluctuations are important for the formation of exotic quantum phases of matter, fundamental high-energy processes, quantum metrology, and quantum algorithms. Here, we use a programmable quantum simulator based on Rydberg atom arrays to experimentally study collective dynamics across a (2+1)D Ising quantum phase transition. After crossing the quantum critical point, we observe a gradual growth of correlations through coarsening of antiferromagnetically ordered domains. By deterministically preparing and following the evolution of ordered domains, we show that the coarsening is driven by the curvature of domain boundaries, and find that the dynamics accelerate with proximity to the quantum critical point. We quantitatively explore these phenomena and further observe long-lived oscillations of the order parameter, corresponding to an amplitude (Higgs) mode. These observations offer a unique viewpoint into emergent collective dynamics in strongly correlated quantum systems and nonequilibrium quantum processes.

Keywords: quantum coarsening, neutral atoms, collective dynamics, amplitude mode, quantum phase transitions

[53] Error Mitigation for Analog Quantum Simulators

Authors: Thomas Steckmann (University of Maryland, College Park), Alexander Schuckert (University of Maryland, College Park), Sean Muleady (University of Maryland, College Park), Yuxin Wang (University of Maryland, College Park), De Luo (Duke University), Or Katz (University of Cornell), Alireza Seif (IBM Quantum), Michael Gullans (NIST and University of Maryland) and Alexey Gorshkov (NIST and University of Maryland)

Abstract: Analog quantum simulators offer a promising pathway to probe quantum phenomena using intermediate-scale quantum systems. However, like their digital counterparts, these platforms suffer from noisy operations that limit their accuracy and scalability. While error mitigation techniques have been developed primarily for digital quantum computers, their application to certain analog systems remains under-explored due to limited control over noise characteristics. Here, we adapt the Zero Noise Extrapolation (ZNE) technique to address shot-to-shot perturbations of the control Hamiltonian, a characteristic noise source in various quantum simulator platforms. We demonstrate this method on trapped ion-based quantum simulations of transverse-field Ising model dynamics, showcasing its effectiveness in extending the lifetime of the dynamics without direct hardware-level improvements beyond current hardware-limited regimes. This work paves the way for more accurate and scalable quantum simulations across diverse platforms, including trapped ion and neutral atom-based systems, potentially accelerating the exploration of quantum phenomena beyond classical computational limits.

Keywords: Error Mitigation, Analog Quantum Simulators, Trapped Ion, Noisy Quantum Computing, Zero Noise Extrapolation

[54] Quantum Computing for Turbulence

Authors: Xiangyu Li (Pacific Northwest National Laboratory), Xiaolong Yin (Colorado School of Mines), Nathan Wiebe (University of Toronto; Pacific Northwest National Laboratory), Jaehun Chun (Pacific Northwest National Laboratory; CUNY City College of New York), Gregory K. Schenter (Pacific Northwest National Laboratory), Margaret S. Cheung (Pacific Northwest National Laboratory; University of Washington) and Johannes Mülmenstädt (Pacific Northwest National Laboratory)

Abstract: Complex systems exhibiting multiscale nonlinear fluid dynamics are responsible for many scientific and engineering challenges, i.e., climate projection. The dynamics of these systems admits no analytic solution and are challenging to simulate due to large number of degrees of freedom N on classical computers. Quantum computers promise an exponential speedup (log N in complexity) for linear systems but shy from strongly nonlinear systems. Here we explore the potential quantum advantage for simulating strongly nonlinear turbulence governed by the notorious Navier-Stokes equations (NSE). We first trade the strong nonlinearity of NSE with additional number of degrees of freedom by approximating NSE to its Lattice-Boltzmann form (LBE) that only exhibits weak local nonlinearity, which is then Carleman-linearized (CLBE) for quantum linear system algorithms (QLSA). We show that the gate complexity of the QLSA in solving CLBE scales logorithmicly with arbitrary system size, i.e., arbitrary nonlinearity, for decaying turbulence with periodic boundary conditions. For forced turbulence, an optimal query complexity can be obtained when applying the Linear Combination of Hamiltonian Simulations to CLBE.

Keywords: Navier-Stokes equation, Lattice-Boltzmann form, nonlinearity, Carleman linearization, LCHS

[55] An Open Source Quantum Computer Based on Trapped-ions

Authors: Yi Hong Teoh (University of Waterloo and Institute for Quantum Computing), Roger Melko (University of Waterloo and Perimeter Institute), Rajibul Islam (University of Waterloo and Institute for Quantum Computing), Crystal Senko (University of Waterloo and Institute for Quantum Computing), Benjamin Maclellan (University of Waterloo, Institute for Quantum Computing and Perimeter Institute), Collin Epstein (University of Waterloo and Institute for Quantum Computing), Anastasiia Bershanka (University of Waterloo and Institute for Quantum Computing), Sainath Motlakunta (University of Waterloo and Institute for Quantum Computing) and Sehmimul Hoque (University of Waterloo and Institute for Quantum Computing)

Abstract: We present our work at Open Quantum Design (OQD) towards building an open source full-stack trapped-ion quantum computer. The control infrastructure in development aims to provide a multilevel interface, where users will be capable of expressing their quantum information experiments

in the abstraction of their choice: digital, analog or atomic. Compilers are built to perform the lowering of these representations down to the real-time control software, based on ARTIQ and DAX. We further extend ARTIQ and DAX with a modular framework that enables the transfer of common components between trapped-ion apparatuses. Here, we describe the real-time control framework, compiler infrastructure and prototype expressions for the analog and atomic abstraction layers. Our entire control infrastructure will be fully open source for all OQD members to contribute to, and will be released under an Apache 2.0 license for use by the whole community.

Keywords: Trapped-ions, Quantum Computing, Real-time Control, Open-source, Full-stack

[56] Quantum Rational Transformation Using Linear Combinations of Hamiltonian Simulations

Authors: Yizhi Shen (Lawrence Berkeley National Laboratory), Niel Van Buggenhout (Universidad Carlos III de Madrid), Daan Camps (Lawrence Berkeley National Laboratory), Katherine Klymko (Lawrence Berkeley National Laboratory) and Roel Van Beeumen (Lawrence Berkeley National Laboratory)

Abstract: Rational functions are powerful for key tasks in scientific computing. However, their abilities to advance quantum algorithms remain largely untapped. In this work, we explore effective implementations of a rational transformation of a target operator through real-time evolution on quantum hardware. Adopting suitable integral representations of the operator resolvent, we show that rational transformations can be performed efficiently with Hamiltonian simulations using the linear-combination-of-unitaries (LCU) routine. We formulate two complementary LCU schemes, the discrete-time and continuous-time schemes, decomposing the exact integral representations of a resolvent via different strategies. We consider rational transformations for the ubiquitous task of approximating functions of a Hermitian operator on a quantum computer, ranging from elementary functions, such as the signum function, to general ones. For illustration, we discuss the use of quantum rational transformation (QRT) as a preprocessing step to accelerate convergence of quantum algorithms for the ground and excited state problems. By combining rational transformations with observable dynamic mode decomposition (ODMD), our recently developed noise-resilient quantum eigensolver, we design a fully real-time approach for resolving a many-body spectrum. Our numerical demonstration on spin systems indicates that our real-time framework is compact and achieves accurate estimation of the low-lying energies. Our proposed quantum algorithms for resolvent computation open new possibilities in the development of quantum algorithms based on rational functions.

Keywords: Quantum linear algebra, Hamiltonian simulation, Hybrid quantum-classical algorithms

[57] Hamiltonian Algebra of Jordan-Wigner Transformed Fermion Models

Authors: Yuichiro Hidaka (QunaSys Inc.), Shoichiro Tsutsui (QunaSys Inc.), Shota Kanasugi (Quantum Laboratory, Fujitsu Research, Fujitsu Limited.), Norifumi Matsumoto (Quantum Laboratory, Fujitsu Research, Fujitsu Limited.), Kazunori Maruyama (Quantum Laboratory, Fujitsu Research, Fujitsu Limited.) and Hirotaka Oshima (Quantum Laboratory, Fujitsu Research, Fujitsu Limited.)

Abstract: The algebraic fast-forwarding method is one of the most powerful methods of implementing the time evolution operator. The depth of the circuit for implementing the algebraic fast-forwarding method depends on the dimension of the Hamiltonian algebra of a given Hamiltonian. However, the algebraic structures of interacting fermion models are still unclear. In this presentation, we prove that the dimension of the Hamiltonian algebra of Jordan-Wigner transformed free-fermion models is in quadratic order of the number of qubits, and that of the interacting fermion models between up and down spins is in exponential order about the qubit number.

Keywords: Hamiltonian algebra, fast-forwarding method, fermionic many-body system

[58] Uncovering Measurement-induced Entanglement via Directional Adaptive Dynamics and Incomplete Information

Authors: Yuxin Wang (University of Maryland, College Park), Alireza Seif (University of Chicago) and Aashish A. Clerk (University of Chicago)

Abstract: The rich entanglement dynamics and transitions exhibited by monitored quantum systems typically only exist in the conditional state, making observation extremely difficult. In this work we construct a general recipe for mimicking the conditional entanglement dynamics of a monitored system in a corresponding measurement-free dissipative system involving directional interactions between the original system and a set of auxiliary register modes. This mirror setup autonomously implements a measurement-feedforward dynamics that effectively retains a small fraction of the information content in a typical measurement record. We illustrate our ideas in a bosonic system featuring a competition between entangling measurements and local unitary dynamics, and also discuss extensions to qubit systems and truly many-body systems.

Keywords: Measurement-induced entanglement transition, Quantum reservoir engineering, Adaptive quantum dynamics, Quantum nonreciprocity

[59] Modulated Time Evolution for Efficient Variational Ground-state Preparation

Authors: Zekun He (Georgetown university), Alexander Kemper (North Carolina State University) and James Freericks (Georgetown university)

Abstract: Adiabatic state preparation seeks to prepare the ground state of a target Hamiltonian from an easily prepared ground state of the initial Hamiltonian. It is guaranteed to work for time-dependent Hamiltonians that always have an energy gap to the first excited state throughout the entire evolution, but it can be excruciatingly slow. To speed up the process, we introduce a scaling factor that modulates the Hamiltonian during the time evolution, controlled by a variational principle on the final energy of the unscaled Hamiltonian. We find the optimized time evolution resembles a local adiabatic time evolution with an additional rapid modulation of the scale, which both reduces diabatic excitation from the ground state, and returns excited states back to the ground state. This approach is particularly simple to implement; it does not require constructing complicated counter-diabatic Hamiltonians nor does it need any a priori knowledge of the energy gap of the system. When the time evolution is discretized into problem and mixer components it closely resembles the quantum approximate optimization algorithm, featuring a local adiabatic field with oscillations arising from the ratio of angles at each layer and from a layer-dependent modulation of the overall scale.

Keywords: state-preparation, optimization, non-adiabatic

[60] Improving Adaptive Variational Quantum Algorithms

Authors: Mafalda Ramôa (Virginia Tech Center for Quantum Information Science and Engineering, Dep. of Physics – Virginia Tech, INL, INESC TEC), Luís Paulo Santos (INL, INESC TEC, Universidade do Minho), Edwin Barnes (Department of Physics – Virginia Tech, Virginia Tech Center for Quantum Information Science and Engineering), Nicholas Mayhall (Department of Chemistry – Virginia Tech, Virginia Tech Center for Quantum Information Science and Engineering) and Sophia Economou (Department of Physics – Virginia Tech, Virginia Tech Center for Quantum Information Science and Engineering)

Abstract: The simulation of molecules with ADAPT-VQE, an adaptive variant of the variational quantum eigensolver, is a leading contender in the quest for practical quantum advantage with near-term quantum computers. ADAPT-VQE grows the ansatz iteratively by appending unitaries whose generators are selected from a pre-defined operator pool. While ADAPT-VQE produces shallower circuits as compared to protocols with static ans\”atze such as UCCSD-VQE, the resulting circuit depth is still beyond current quantum computers, and the adaptive ansatz construction incurs a sizeable measurement overhead. In this work, we propose two improvements to ADAPT-VQE: a Hessian recycling strategy, which decreases the measurement costs of growing the ansatz adaptively; and a new circuit-efficient pool, consisting of a class of operators which we term coupled exchange operators (CEOs). We combine these strategies with others proposed in the literature to create CEO-ADAPT-VQE*, a new variant of the algorithm. We apply CEO-ADAPT-VQE* to the H6 molecule and observe decreases by 88\%, 96\% and 98\% in CNOT count, CNOT depth and measurement costs, respectively, as compared to the original GSD-ADAPT-VQE. We believe our work to be a step forward in the direction of experimental demonstrations of quantum algorithms for the simulation of classically intractable systems.

Keywords: quantum simulation, VQE, adaptive ansatz, quantum chemistry, ADAPT-VQE

[61] Approximating maximum independent set on Rydberg atom arrays using local detunings

Authors: Hyeonjun Yeo (Department of Physics and Astronomy, Seoul National University), Ha Eum Kim (Department of Physics, Korea University) and Kabgyun Jeong (Research Institute of Mathematics, Seoul National University)

Abstract: Rydberg atom arrays operated by a quantum adiabatic principle are among the most promising quantum simulating platforms due to their scalability and long coherence time. From the perspective of combinatorial optimization, they offer an efficient solution for a maximum independent set problem because of the intrinsic resemblance between the Rydberg Hamiltonian and the cost function of the maximum independent set problem. In this paper, we suggest a strategy to approximate maximum independent sets by adjusting local detunings on the Rydberg Hamiltonian according to each vertex’s vertex support, which is a quantity that represents connectivity between vertices. By doing so, we explicitly reflect on the Rydberg Hamiltonian the potential probability that each vertex will be included in maximum independent sets. Our strategy successfully reduces the error rate three times for the checkerboard graphs with defects when the adiabaticity is sufficient. Our strategy decreases the error rate for random graphs of density 3.0 even when the adiabaticity is relatively insufficient. Moreover, we show that our strategy helps to prepare a quantum many-body ground state by raising the fidelity between the evolved quantum state and a 2D cat state on a square lattice.

Keywords:   Quantum combinatorial optimization, Rydberg atom arrays, Quantum adiabatic evolution

[62] Entanglement Spectra Statistics of Free Fermionic Circuits

Authors: Andrew Projansky (Dartmouth College), Joshuah Heath (Dartmouth College) and James Whitfield (Dartmouth College)

Abstract: We study the entanglement spectrum generated by matchgate circuits with various additional resources. We show that, for matchgate circuits acting on product states, Wigner-Dyson entanglement statistics emerges in the thermodynamic limit by virtue of a single SWAP gate. This is analogous to the Clifford case, in which only a single T-gate is needed to achieve universal entanglement spectrum statistics under similar system size scaling. However, this does not require average entropy saturating to entropy of Haar random states, unlike in the Clifford case. We then show that Clifford conjugated matchgate circuits have Wigner-Dyson distributed spectra, despite being simulable. Thus, we provide the first evidence that entanglement spectra cannot be used always as  a proxy for complexity. We also discuss the connection between entanglement spectra and fermionic systems, and discuss the consequences of having different entanglement spectra depending on what Clifford matchgates are conjugated by.

Keywords: Matchgates, Entanglement Spectra, Free Fermions

[63] Tailoring Fault-Tolerance to Quantum Algorithms

Authors: Zhuangzhuang Chen (University of Arizona) and Narayanan Rengaswamy (University of Arizona)

Abstract: The standard approach to universal fault-tolerant quantum computing is to develop a general purpose quantum error correction mechanism that can implement a universal set of logical gates fault-tolerantly. Given such a scheme, any quantum algorithm can be realized fault-tolerantly by composing the relevant logical gates from this set. However, we know that quantum computers provide a significant quantum advantage only for specific quantum algorithms. Hence, a universal quantum computer can likely gain from compiling such specific algorithms using tailored quantum error correction schemes. In this work, we take the first steps towards such algorithm-tailored quantum fault-tolerance. We consider Trotter circuits in quantum simulation, which is an important application of quantum computing. We develop a solve-and-stitch algorithm to systematically synthesize physical realizations of Clifford Trotter circuits on the well-known  [[n,n-2,2]] error-detecting code family. Our analysis shows that this family implements Trotter circuits with optimal depth, thereby serving as an illuminating example of tailored quantum error correction. We achieve fault-tolerance for these circuits using flag gadgets, which add minimal overhead. The solve-and-stitch algorithm has the potential to scale beyond this specific example and hence provide a principled approach to tailored fault-tolerance in quantum computing.

Keywords: quantum error correction, fault-tolerance, Trotter circuits, quantum simulation, error-detecting

[64] Wave Matrix Lindbladization: Sample-Based Simulation of Markovian Dynamics

Authors: Dhrumil Patel (Cornell University) and Mark M. Wilde (Cornell University)

Abstract: Density Matrix Exponentiation is a technique for simulating Hamiltonian dynamics when the Hamiltonian to be simulated is available as a quantum state. We present a natural analogue to this technique, called wave matrix Lindbladization, for simulating Markovian dynamics governed by the well known Lindblad master equation. In order to do so, we introduce an input model in which Lindblad operators are encoded into pure quantum states, called program states, and our technique simulates Lindbladian evolution by means of interacting the system of interest with these program states. We begin by focusing on a simple case in which the Lindbladian consists of only one Lindblad operator and a Hamiltonian. Thereafter, we extend the method to simulating general Lindbladians and other cases in which a Lindblad operator is expressed as a linear combination or a polynomial of the operators encoded into the program states. We propose quantum algorithms for all these cases and also investigate their sample complexities, i.e., the number of program states needed to simulate a given Lindbladian evolution approximately. Finally, we demonstrate that our quantum algorithms provide an efficient route for simulating Lindbladian evolution relative to the full tomography of encoded operators.

Keywords: Quantum Simulation, Quantum Algorithms, Sample Complexity

[65] Tiling excitations for scalable adaptive quantum simulations of condensed matter systems with linear operator pools

Authors: Karunya Shailesh Shirali (Postdoctoral Associate, Department of Physics, Virginia Tech), John S. Van Dyke (Johns Hopkins University Applied Physics Laboratory), Samantha Barron (IBM Quantum, IBM T.J. Watson Research Center), Nicholas J. Mayhall (Virginia Tech), Edwin Barnes (Virginia Tech) and Sophia Economou (Virginia Tech)

Abstract: Quantum computers represent a natural platform for studying many-body interacting electronic systems due to their ability to access an exponential space of states compared to classical computers. Adaptive variational quantum simulation algorithms iteratively construct wavefunction ansätze from a predefined pool of operators tailored to the problem Hamiltonian. A systematic approach to running adaptive variational quantum simulations on strongly correlated lattice Hamiltonians, termed `operator pool tiling’, was proposed in [1], in which the algorithm learns the operators most important to the problem by running several trials on a small problem instance. A tiled operator pool motivated by translation symmetry is then constructed from these operators, which restricts the ansatz to explore a symmetry subspace relevant to the problem, and enables construction of efficient and accurate ansätze for arbitrarily large problem instances. The operator pool for the small problem instance must be highly expressive in order for the algorithm to accurately acquire knowledge of the relevant operators. Here, we show that using operator pools based on fermionic excitations such as the qubit-excitation-based (QEB) pool is advantageous for ADAPT-VQE calculations on fermionic lattice Hamiltonians such as the Fermi-Hubbard model, resulting in significant reductions in the measurement overhead and circuit depth, while simultaneously maintaining the energy accuracy. This method is expected to efficiently scale to larger systems.

[1] J. S. Van Dyke, K. Shirali, G. S. Barron, N. J. Mayhall, E. Barnes, and S. E. Economou, Scaling adaptive quantum simulation algorithms via operator pool tiling, Phys. Rev. Res. 6, L012030 (2024).

Keywords: Adaptive variational quantum simulation, Strongly-correlated, Condensed matter physics, Fermi-Hubbard model

[66] Universal Spreading of Conditional Mutual Information in Noisy Random Circuits

Authors: Su-un Lee (University of Chicago), Changhun Oh (Korea Advanced Institute of Science and Technology), Yat Wong (University of Chicago), Senrui Chen (University of Chicago) and Liang Jiang (University of Chicago)

Abstract: We study the evolution of conditional mutual information (CMI) in generic open quantum systems, focusing on one-dimensional random circuits with interspersed local noise. Unlike in noiseless circuits, where CMI spreads linearly while being bounded by the lightcone, we find that noisy random circuits exhibit superlinear propagation of CMI, which diverges far beyond the lightcone at a critical circuit depth. We demonstrate that the underlying mechanism for such rapid spreading is the combined effect of local noise and a scrambling unitary, which selectively removes short-range correlations while preserving long-range correlations. To analytically capture the dynamics of CMI in noisy random circuits, we introduce a coarse-graining method, and we validate our theoretical results through numerical simulations. Furthermore, we identify a universal scaling law governing the spreading of CMI.

Keywords: Quantum correlation, Random quantum circuit, Quantum many-body physics, Open quantum

[67] Hamiltonian simulation in Zeno subspaces

Authors: Christian Arenz (Arizona State University), Alicia Magann (Sandia National Laboratories), Kasra Rajabzadeh Dizaji (Arizona State University) and Ariq Haqq (Arizona State University)

Abstract: We investigate the quantum Zeno effect as a framework for designing and analyzing quantum algorithms for Hamiltonian simulation. We show that frequent projective measurements of an ancilla qubit register can be used to simulate quantum dynamics on a target qubit register with a circuit complexity similar to randomized approaches. The classical sampling overhead in the latter approaches is traded for ancilla qubit overhead in Zeno-based approaches. A second-order Zeno sequence is developed to improve scaling and implementations through unitary kicks are discussed. We show that the circuits over the combined register can be identified as a subroutine commonly used in postTrotter Hamiltonian simulation methods. We build on this observation to reveal connections between different Hamiltonian simulation algorithms.

Keywords: Hamiltonian simulation algorithm, Quantum Zeno effect, Linear combination of unitaries, Block encodings

[68] Magic boundaries of 3D color codes

Authors: Zijian Song (University of California, Davis), Guanyu Zhu (IBM Quantum)

Abstract: We investigate boundaries of 3D color codes and provide a systematic classification into 101 distinct boundary types, including two novel classes. The first class consists of 1 boundary and is generated by sweeping the codimension-1 (2D) T-domain wall across the system and attaching it to the X-boundary that condenses only magnetic fluxes. Since the T-domain wall cannot condense on the X-boundary, a new magic boundary is produced, where the boundary stabilizers contain XS-stabilizers going beyond the conventional Pauli stabilizer formalism, and hence contains ‘magic’. Neither electric nor magnetic excitations can condense on such a magic boundary, and only the composite of the magnetic flux and codimension-2 (1D) S-domain wall can condense on it, which makes the magic boundary going beyond the classification of the Lagrangian subgroup. The second class consists of 70 boundaries and is generated by sweeping the S-domain wall across a codimension-1 submanifold and attaching it to the boundary. This generates a codimension-2 (1D) nested boundary at the intersection. We also connect these novel boundaries to their previously discovered counterpart in the Z32 gauge theory, equivalent to three copies of 3D toric codes, where the S and T domain walls correspond to gauged symmetry-protected topological (SPT) defects. New boundaries are produced whenever the corresponding symmetry of the SPT defect remains unbroken on the boundary. Applications of the magic boundaries include implementing fault-tolerant non-Clifford logical gates, e.g., in the context of fractal topological codes.

Keywords: SPT defects, strongly correlated electrons, quantum error correction

[69] Equivalence of cost concentration and gradient vanishing for quantum circuits: An elementary proof in the Riemannian formulation

Authors: Qiang Miao (Duke University) and Thomas Barthel (Duke University)

Abstract: The optimization of quantum circuits can be hampered by a decay of average gradient amplitudes with increasing system size. When the decay is exponential, this is called the barren plateau problem. Considering explicit circuit parametrizations (in terms of rotation angles), it has been shown in Arrasmith et al., Quantum Sci. Technol. 7, 045015 (2022) that barren plateaus are equivalent to an exponential decay of the variance of cost-function differences. We show that the issue is particularly simple in the (parametrization-free) Riemannian formulation of such optimization problems and obtain a tighter bound for the cost-function variance. An elementary derivation shows that the single-gate variance of the cost function is strictly equal to half the variance of the Riemannian single-gate gradient, where we sample variable gates according to the uniform Haar measure. The total variances of the cost function and its gradient are then both bounded from above by the sum of single-gate variances and, conversely, bound single-gate variances from above. So, decays of gradients and cost-function variations go hand in hand, and barren plateau problems cannot be resolved by avoiding gradient-based in favor of gradient-free optimization methods.
Keywords: Barren Plateau, Riemannian Gradient, Variational Quantum Algorithms

[K] Fault-tolerant hyperbolic Floquet quantum error correcting codes

Authors: Ali Fahimniya, Hossein Dehghani, Kishor Bharti, Sheryl Mathew, Alicia J. Kollár, Alexey V. Gorshkov, Michael J. Gullans

Abstract: A central goal in quantum error correction is to reduce the overhead of fault-tolerant quantum computing by increasing noise thresholds and reducing the number of physical qubits required to sustain a logical qubit. We introduce a potential path towards this goal based on a family of dynamically generated quantum error correcting codes that we call “hyperbolic Floquet codes.” These codes are defined by a specific sequence of non-commuting two-body measurements arranged periodically in time that stabilize a topological code on a hyperbolic manifold with negative curvature. We focus on a family of lattices for n qubits that, according to our prescription that defines the code, probably achieve a finite encoding rate (1/8+2/n) and have a depth-3 syndrome extraction circuit. Similar to hyperbolic surface codes, the distance of the code at each time-step scales at most logarithmically in n. The family of lattices we choose indicates that this scaling is achievable in practice. We develop and benchmark an efficient matching-based decoder that provides evidence of a threshold near 0.1% in a phenomenological noise model and 0.25% in an entangling measurements noise model. Utilizing weight-two check operators and a qubit connectivity of 3, one of our hyperbolic Floquet codes uses 400 physical qubits to encode 52 logical qubits with a code distance of 8, i.e., it is a [[400,52,8]] code. At small error rates, comparable logical error suppression to this code requires 5x as many physical qubits (1924) when using the honeycomb Floquet code with the same noise model and decoder.

Keywords: error correction

[L] More Quantum Chemistry with Fewer Qubits

Authors: Jakob Günther (University of Copenhagen), Alberto Baiardi (ETH Zurich), Markus Reiher (ETH Zurich) and Matthias Christandl (University of Copenhagen)
Abstract: Quantum computation is one of the most promising new paradigms for the simulation of physical systems composed of electrons and atomic nuclei, with applications
in chemistry, solid-state physics, materials science, or molecular biology.
This requires a truncated representation of the electronic structure Hamiltonian using a finite number of orbitals.
While it is, in principle, obvious how to improve on the representation by including more orbitals, this is usually unfeasible in practice (e.g., because of the limited number of qubits available on a quantum computer) and severely compromises the accuracy of the obtained results.
Here, we propose a quantum algorithm that improves on the representation of the physical problem by virtue of second-order perturbation theory.
In particular, our quantum algorithm evaluates the second-order energy correction through a series of time-evolution steps under the unperturbed Hamiltonian.
An important application is to go beyond the active-space approximation, allowing to include corrections of virtual orbitals, which is known as multireference perturbation theory.
Here, we exploit that the unperturbed Hamiltonian is diagonal for virtual orbitals and show that the number of qubits is independent of the number of virtual orbitals.
This gives rise to more accurate energy estimates without increasing the number of qubits.
Moreover, we demonstrate numerically for realistic chemical systems that the overall runtime of our method has highly favourable scaling in the number of virtual orbitals compared to previous work.
Numerical calculations also confirm the necessity of the multireference perturbation theory energy corrections to reach accurate ground state energy estimates.
Our perturbation theory quantum algorithm can also be applied to Symmetry-Adapted Perturbation Theory.
As such, we reduce the quantum hardware requirements for quantum chemistry by leveraging perturbation theory.

Keywords: Fault-tolerant quantum simulation algorithms, Quantum Chemistry, Perturbation Theory

[M] Efficient Quantum Simulation Algorithms in the Path Integral Formulation

Authors: Serene Shum (University of Toronto) and Nathan Wiebe (University of Toronto)

Abstract: The Feynman path integral formulation is an alternative, but equivalent, way of expressing the time evolution of a quantum state to the Schrodinger formulation.  Despite this, existing quantum algorithms for simulating quantum dynamics require the elements of the Hamiltonian matrix to be computable.  In contrast, Feynman path integrals require the classical Lagrangian (or action integral) function to be computed to simulate the quantum dynamics and is widely used in quantum field theory which limits the utility of Hamiltonian simulation methods in the field.

We address this problem here by presenting three new algorithms for quantum simulation that are based on the path integral formulation. The first two algorithms are for Hamiltonian-based path integral simulations wherein the  Hamiltonians are written as a sum of several Hamiltonian terms and utilizes higher-order Trotter-Suzuki formulas and linear combination of unitaries to implement the evolution as sums over paths.  The first algorithm requires a number of queries to oracles that give the eigenvalues and overlaps between the eigenvectors of the Hamiltonian terms that scales as $t^{o(1)}/\epsilon^{o(1)}$, the second approach uses long-time path integrals for near-adiabatic systems and has query complexity that scales as $O(1/\sqrt{\epsilon})$ if the energy eigenvalue gaps and simulation time is sufficiently long.

These approaches are not equivalent to existing simulation methods because they use different oracles than traditional simulation approaches.  In the last part of the paper, we derive a Lagrangian formulation of quantum time evolution within the discrete, finite framework of quantum computing that preserves the unitarity of the process and thus is straightforward to implement on a quantum computer.

Keywords: quantum computing, quantum algorithms, Hamiltonian simulation, quantum simulation, linear combination of unitaries, quantum Fourier transform, path integrals, Lagrangian

[N] Evaluating Ground State Energy with Low-Depth Quantum Circuit and High Accuracy

Authors: Shuo Sun (Technical University of Munich), Chandan Kumar (BMW Group), Elvira Shishenina (BMW Group), Edwin Knobbe (BMW Group), Christian B Mendl (Technical University of Munich)

Abstract: Solving electronic structure problems is widely recognized as one of the most promising applications of quantum computing. However, due to limitations imposed by the coherence time of qubits in the NISQ (Noisy Intermediate Scale Quantum) era, it’s vital to design algorithms with shallow circuits.

In this project, we develop a novel Variational Quantum Eigensolver (VQE) ansatz based on the QCC (Qubit Coupled Cluster) [1, 2] approach, which demands optimization over only n parameters rather than the usual n+2m parameters, where n represents the number of Pauli word time evolution gates e-itP, and m is the number of qubits involved.

We evaluate the ground state energy of O3, Li4, Cr2, and C4H8, using CASCI(4,4) method in conjunction with the enhanced QCC ansatz, UCCSD (Unitary Coupled Cluster Single-Double) ansatz, or FCI (Full Configuration Interaction) method as the active space solver. Furthermore, we assess our enhanced QCC ansatz on two distinct quantum hardware platforms, one superconducting-based and one trapped-ion-based. In the end, we conclude with a gate count analysis on both setups.

References:

(1) Ryabinkin, I. G.; Yen, T.-C.; Genin, S. N.; Izmaylov, A. F. Journal of Chemical Theory and Computation 2018, 14, 6317–6326.

(2) Ryabinkin, I. G.; Lang, R. A.; Genin, S. N.; Izmaylov, A. F. Journal of Chemical Theory and Computation 2020, 16, 1055–1063

Keywords: NISQ, VQE, QCC