Talks

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Monday

Randomized Hamiltonian simulation protocols such as qDRIFT are known to be able to outperform their deterministic cousins in some cases, such as when Hamiltonians with many local terms. We will discuss limitations on these protocols and the benefits of running them in an adaptive way that can take advantage of information about the initial state.

Alexander Zlokapa, Rolando Somma

We consider the task of simulating time evolution under a Hamiltonian H within its low-energy subspace. Assuming access to a block-encoding of H′=(H−E)/λ for some E∈R, the goal is to implement an ϵ-approximation to e−itH when the initial state is confined to the subspace corresponding to eigenvalues [−1,−1+Δ/λ] of H′. We present a quantum algorithm that uses O(tλΓ−−−√+λ/Γ−−−√log(1/ϵ)) queries to the block-encoding for any Γ such that Δ≤Γ≤λ. When log(1/ϵ)=o(tλ) and Δ/λ=o(1), this result improves over generic methods with query complexity Ω(tλ). Our quantum algorithm leverages spectral gap amplification and the quantum singular value transform. Using standard access models for H, we show that the ability to efficiently block-encode H′ is equivalent to H being what we refer to as a “gap-amplifiable” Hamiltonian. This includes physically relevant examples such as frustration-free systems, and it encompasses all previously considered settings of low-energy simulation algorithms. We also provide lower bounds for low-energy simulation. In the worst case, we show that the low-energy condition cannot be used to improve the runtime of Hamiltonian simulation. For gap-amplifiable Hamiltonians, we prove that our algorithm is tight in the query model with respect to t, Δ, and λ. In the practically relevant regime where log(1/ϵ)=o(tΔ) and Δ/λ=o(1), we also prove a matching lower bound in gate complexity (up to log factors). To establish the query lower bounds, we consider PARITY∘OR and degree bounds on trigonometric polynomials. To establish the lower bound on gate complexity, we use a circuit-to-Hamiltonian reduction acting on a low-energy state.

Hamiltonian simulation becomes more challenging as the underlying unitary becomes more oscillatory. In such cases, an algorithm with commutator scaling and a weak dependence, such as logarithmic, on the derivatives of the Hamiltonian is desired. We introduce a new time-dependent Hamiltonian simulation algorithm based on the Magnus series expansion that exhibits both features. Importantly, when applied to unbounded Hamiltonian simulation in the interaction picture, we prove that the commutator in the second-order algorithm leads to a surprising fourth-order superconvergence, with an error preconstant independent of the number of spatial grids. The proof of superconvergence is based on microlocal semiclassical analysis that is of independent interest.

Jan Lukas Bosse, Andrew M. Childs, Charles Derby, Filippo Maria Gambetta, Ashley Montanaro and Raul A. Santos

In this work we propose an approach for implementing time-evolution of a quantum system using product formulas. The quantum algorithms we develop have provably better scaling (in terms of gate complexity and circuit depth) than a naive application of well-known Trotter formulas, for systems where the evolution is determined by a Hamiltonian with different energy scales (i.e., one part is “large” and another part is “small”).
Our algorithms generate a decomposition of the evolution operator into a product of simple unitaries that are directly implementable on a quantum computer. Although the theoretical scaling is suboptimal compared with state-of-the-art algorithms (e.g., quantum signal processing), the performance of the algorithms we propose is highly competitive in practice.
We illustrate this via extensive numerical simulations for several models. For instance, in the strong-field regime of the 1D transverse-field Ising model, our algorithms achieve an improvement of one order of magnitude in both the system size and evolution time that can be simulated with a fixed budget of 1000 arbitrary 2-qubit gates, compared with standard Trotter formulas.

Classical Markov Chain Monte Carlo methods have been essentialfor simulating statistical physical systems and have proven well applicable to other systems with complex degrees of freedom. In this talk, I will describe an efficiently implementable discrete-time quantum counterpart to Metropolis sampling that preserves the following desirable features of classical Glauber / Metropolis dynamics: (i) exactly detailed balanced, (ii) efficiently implementable, and (iii) quasi-local for geometrically local systems. This complements the recent results of Chen, Kastoryano, and Gilyén [CKG23] who proposed a smoothed continuous-time variant of the Davies generator featuring the above properties (i)-(iii). Further, I describe a novel highly coherent quantum generalization of detailed balanced dynamics that resembles another physically derived master equation. I will discuss important properties of all constructions, including the uniqueness of the fixed-point and the locality of the resulting operators.

Joint work with Chi-Fang Chen, Joao F. Doriguello, and Michael J.
Kastoryano.

Kunal Sharma and Minh Tran

We propose an algorithm for simulating the dynamics of a geometrically local Hamiltonian~$A$ under a small geometrically local perturbation~$\alpha B$.
In certain regimes, the algorithm achieves the optimal scaling and outperforms the state-of-the-art algorithms. By moving into the interaction frame of $A$ and classically computing the Magnus expansion of the interaction-picture Hamiltonian, our algorithm bypasses the need for ancillary qubits. In analyzing its performance, we develop a framework to capture the quasi-locality of the Magnus operators, leading to a tightened bound for the error of the Magnus truncation. The Lieb-Robinson bound also guarantees the efficiency of computing the Magnus operators and of their subsequent decomposition into elementary quantum gates. These features make our algorithm appealing for near-term and early-fault-tolerant simulations.

We will talk about recent developments in exploiting thermalization in Nature as a quantum algorithmic tool to prepare thermal state and, consequently, the aspects of quantum advantage. First, we discuss how thermodynamic Lindbladians (Davies generators and their variants) inspire efficient quantum Gibbs sampling algorithms (2303.18224, 2311.09207). Next, we discuss two recent theoretical arguments for quantum advantage in this context: low-temperature cooling is universal for quantum computation (2309.16596), and constant-temperature Gibbs sampling is as hard as random circuit sampling (2404.14639).

The Lindblad equation generalizes the Schr\”{o}dinger equation to quantum systems that undergo dissipative dynamics. The quantum simulation of Lindbladian dynamics is therefore non-unitary, preventing a naive application of state-of-the-art quantum algorithms. Here, we make use of an approximate correspondence between Lindbladian dynamics and evolution based on Repeated Interaction (RI) CPTP maps to write down a Hamiltonian formulation of the Lindblad dynamics and derive a rigorous error bound on the master equation. Specifically, we show that the number of interactions needed to simulate the Liouvillian $e^{t\mathcal{L}}$ within error $\epsilon$ scales in a weak coupling limit as $\nu\in O(t^2\|\mathcal{L}\|_{1\rightarrow 1}^2/\epsilon)$. This is significant because the error in the Lindbladian approximation to the dynamics is not explicitly bounded in existing quantum algorithms for open system simulations. We then provide quantum algorithms to simulate RI maps using an iterative Qubitization approach and Trotter-Suzuki formulas and specifically show that for iterative Qubitization the number of operations needed to simulate the dynamics (for a fixed value of $\nu$) scales in a weak coupling limit as $O(\alpha_0 t + \nu \log(1/\epsilon)/\log\log(1/\epsilon))$ where $\alpha_0$ is the coefficient $1$-norm for the system and bath Hamiltonians. This scaling would appear to be optimal if the complexity of $\nu$ is not considered, which underscores the importance of considering the error in the Liouvillian that we reveal in this work.

Warm dense matter (WDM) is a thermodynamic regime typified by quantum degeneracy in the presence of significant thermal excitation. It occurs in certain astrophysical objects, planetary interiors, and inertial confinement fusion targets on their way to ignition. In fact, the properties of materials in these extreme conditions play a critical role in the hydrodynamic instabilities that limit the performance of inertial fusion energy designs. However, creating and studying WDM requires access to expensive and specialized experimental facilities that produce short-lived and non-uniform samples at low repetition rates. Thus computer simulations of WDM are especially valuable and they occupy a significant fraction of the operating cycles on some of the world’s largest supercomputers. However, even the best classical simulations are subject to severe uncertainties due to uncontrolled approximations that are difficult to quantify.

In this talk, I will discuss work aimed at understanding the prospects for using fault-tolerant quantum computers to simulate WDM with accuracy exceeding the classical state of the art. I will focus primarily on a recent result describing a quantum algorithm and constant-factor resource estimates for calculating electronic stopping powers, of relevance to inertial fusion models (https://www.pnas.org/doi/abs/10.1073/pnas.2317772121) . I will also briefly describe some early work on applications in astrophysics and planetary science.

Oriel Kiss, Utkarsh Azad, Alessandro Roggero, Borja Requena, David Wakeham and Juan Miguel Arazola

We explore the practicality of early fault-tolerant quantum algorithms, focusing on ground state problems. Specifically, we address the computation of the cumulative distribution function (CDF) of the spectral measure and the identification of its discontinuities. Scaling to bigger system sizes unveils three challenges: the smoothness of the CDF for large supports, the absence of tight lower bounds on the overlap with the actual ground state, and the complexity of preparing high-quality
initial states. To tackle these challenges, we introduce a signal processing technique for identifying the inflection point of the CDF. Furthermore, we offer quantitative resource estimates for the maximum time evolution needed to approximate the error function and the maximum number of samples required to identify a jump of a given size. Our claims are supported by numerical experiments conducted on a 26-qubit fully connected Heisenberg model using a truncated density-matrix renormalization group (DMRG) initial state of low bond dimension. Results show that the DMRG-converged energy aligns well with the prediction obtained with the CDF. Hence, this algorithm emerges as a viable alternative for quantum phase estimation in resource-limited scenarios.

Tuesday

We present quantum computations of electronic structure that go beyond problem sizes amenable to current state-of-the-art exact diagonalization. Our results are obtained in a quantum-centric supercomputing architecture, using 6400 nodes of the Fugaku supercomputer to assist an IBM Heron quantum processor. We simulate the N2 triple bond breaking in a correlation-consistent cc-pVDZ basis set, and the active-space electronic structure of methyl-capped [2Fe–2S] and [4Fe–4S] clusters, using 58, 45 and 77 qubits respectively, with quantum circuits of up to 10570 (of which 3590 are 2-qubit gates) quantum gates.

Regards,

Sophia Simon, Matthias Degroote, Nikolaj Moll, Raffaele Santagati, Michael Streif and Nathan Wiebe

We provide a method for estimating the expectation value of an operator that can utilize prior knowledge to accelerate the learning process on a quantum computer. Specifically, suppose we have an operator that can be expressed as a concise sum of projectors whose expectation values we know a priori to be $O(\epsilon)$. In that case, we can estimate the expectation value of the entire operator within error $\epsilon$ using a number of quantum operations that scales as $O(1/\sqrt{\epsilon})$. We then show how this can be used to reduce the cost of learning a potential energy surface in quantum chemistry applications by exploiting information gained from the energy at nearby points. Furthermore, we show, using Newton-Cotes methods, how these ideas can be exploited to learn the energy via integration of derivatives that we can estimate using a priori knowledge. This allows us to reduce the cost of energy estimation if the block-encodings of directional derivative operators have a smaller normalization constant than the Hamiltonian of the system.

In this talk, we present improvements to state preparation algorithms for the first-quantized simulation of electronic structure. We show that the cost of preparing physically meaningful initial states, either for ground state energy estimation or for dynamical simulation, can be exponentially reduced when compared with the naive linear scaling in the basis set size. We address the preparation of both Hartree-Fock and post-Hartree-Fock states derived from efficient classical calculations, and provide a general prescription that allows for a variety of work on second-quantized simulations in a typical Gaussian basis set to be used to construct initial states for first-quantized simulations in a plane wave basis. The main improvements come from leveraging tensor network methods, but we also use modern compilation techniques designed to reduce the number of non-Clifford gates required for our state preparation scheme.

Daniel Marti Dafcik, Nicholas Lee, Hugh G.A. Burton and David P. Tew

The performance of quantum algorithms for eigenvalue problems, such as computing Hamiltonian spectra, depends strongly on the overlap of the initial wavefunction and the target eigenvector. This limits the power of quantum computers for solving challenging quantum chemistry problems, as typical initial states with a simple description have an overlap with the target Hamiltonian eigenstate that diminishes exponentially in the number of strongly correlated electrons. In this talk, we present a framework for understanding and approximating the low-energy wave functions in strongly correlated molecular systems in terms of a few spin-coupled states that are highly entangled, but highly structured. We also provide efficient quantum circuits for initial state preparation. Our approach avoids the need for expensive classical or quantum heuristics. Instead, we exploit symmetries to directly encode the dominant entanglement structure of the simulated system on quantum computers. For a range of popular quantum algorithms, including quantum phase estimation and several variational quantum algorithms, we demonstrate that using spin-coupled initial states drastically reduces the quantum resources required to compute strongly correlated ground and excited states.

Large language models, like transformers, have recently demonstrated immense powers in text and image generation. This success is driven by the ability to capture long-range correlations between elements in a sequence. The same feature makes the transformer a powerful wavefunction ansatz that addresses the challenge of describing correlations in simulations of qubit systems. In this talk I consider two-dimensional Rydberg atom arrays to demonstrate that transformers reach higher accuracies than conventional recurrent neural networks for variational ground state searches. I further introduce large, patched transformer models, which consider a sequence of large atom patches, and show that this architecture significantly accelerates the simulations.

Wenhao He, Tongyang Li, Xiantao Li, Zecheng Li, Chunhao Wang and Ke Wang

The optimal control problem for open quantum systems can be formulated as a time-dependent Lindbladian that is parameterized by a number of time-dependent control variables. Given an observable and an initial state, the goal is to tune the control variables so that the expected value of some observable with respect to the final state is maximized. In this paper, we present algorithms for solving this optimal control problem efficiently, i.e., having a poly-logarithmic dependency on the system dimension, which is exponentially faster than best-known classical algorithms. Our algorithms are hybrid, consisting of both quantum and classical components. The quantum procedure simulates time-dependent Lindblad evolution that drives the initial state to the final state, and it also provides access to the gradients of the objective function via quantum gradient estimation. The classical procedure uses the gradient information to update the control variables.
At the technical level, we provide the first (to the best of our knowledge) simulation algorithm for time-dependent Lindbladians with an ℓ1-norm dependence. As an alternative, we also present a simulation algorithm in the interaction picture to improve the algorithm for the cases where the time-independent component of a Lindbladian dominates the time-dependent part. On the classical side, we heavily adapt the state-of-the-art classical optimization analysis to interface with the quantum part of our algorithms. Both the quantum simulation techniques and the classical optimization analyses might be of independent interest

Despite fundamental interests in learning and training quantum circuits, the existence of a computationally efficient algorithm for learning shallow quantum circuits remains an open question. Because shallow quantum circuits can generate distributions that are classically hard to sample from, existing learning algorithms do not apply. In this work, we present a polynomial-time classical algorithm for learning the description of any unknown n-qubit shallow quantum circuit U (with arbitrary unknown architecture) within a small diamond distance using single-qubit measurement data on the output states of U. Our approach uses a quantum circuit representation based on local inversions and a technique to combine these inversions. This circuit representation yields an optimization landscape that can be efficiently navigated and enables efficient learning of quantum circuits that are classically hard to simulate. The talk will discuss applications of the new learning algorithm to quantum simulation.

Zhenning Liu, Dhruv Devulapalli, Dominik Hangleiter, Yi-Kai Liu, Alicia Kollár, Alexey Gorshkov and Andrew Childs

Existing schemes for demonstrating quantum computational advantage are subject to various practical restrictions, including the hardness of verification and challenges in experimental implementation. Meanwhile, analog quantum simulators have been realized in many experiments to study novel physics. In this work, we propose a quantum advantage protocol based on \emph{single-step Feynman-Kitaev} verification of an analog quantum simulation, in which the verifier need only run an $O(\lambda^2)$-time classical computation, and the prover need only prepare $O(1)$ samples of a history state and perform $O(\lambda^2)$ single-qubit measurements, for a security parameter $\lambda$. We also propose a near-term feasible strategy for honest provers and discuss potential experimental realizations.

Measurements and wavefunction collapse provide a fresh perspective on many-body entangled states and quantum phases of matter. At a conceptual level, it is an open question which many-body states of matter can(not) be efficiently created by measurement. In part of this talk, I will discuss recent developments in this direction. I will also discuss a collaboration with IBM studying the stability of such measurement-prepared states in the presence of imperfections. Lastly, I will touch on on-going work with Quantinuum on novel topological states in a trapped-ion processor.

Andreas Bauer

I will introduce an approach for analyzing and constructing explicit topological fault-tolerant circuits, by relating them to imaginary-time path integrals representing topological phases. This approach unifies different microscopic protocols for topological quantum computation such as the stabilizer toric code, measurement-based protocols, or Floquet codes. It also allows us to construct many new examples of such fault-tolerant circuits. Further, it makes it possible to construct explicit topological fault-tolerant circuits beyond the Pauli stabilizer/Clifford framework and beyond the toric-code phase. In particular, we construct such circuits for all abelian topological phases as well as selected non-abelian examples. The approach thus makes it possible to simulate exotic topological phases.

Oles Shtanko, Victor V. Albert, Alexey Gorshkov, Simon Lieu and Yujie Liu

To outperform modern classical methods, quantum devices must operate on large-scale quantum physical systems that maintain coherence through quantum error correction. Recent efforts have been devoted to the development of physical systems that are capable of reversing the effects of errors by themselves. We analyze Markovian autonomous decoders, which can be implemented with a wide range of qubit and bosonic error-correcting codes, and derive several upper and lower bounds on the logical error rate in terms of correction and noise rates. These bounds are useful to determine the criteria for scalable autonomous quantum memories.

Wednesday

Density Functional Theory (DFT) is the workhorse of computational chemistry and materials modelling. In many cases, it successfully solves the many-body electronic structure problem without any need for quantum computers. But in other industrially important cases, DFT produces not just quantitatively but even qualitatively wrong answers. Meanwhile, quantum computation promises to provide accurate solutions to quantum many-body problems. But near-term quantum computers remain too small and noisy to be able to simulate meaningful systems. In this talk, I will present methods invented at Phasecraft along with numerical and early experimental results using data taken on Google’s hardware, which leverage the best of both worlds. We show that using small-scale, noisy quantum computation, we can enhance DFT’s ability to accurately solve large-scale many-body problems that conventional DFT struggles with.

Quantum simulation with neutral atoms has enabled engineering and probing quantum matter in new parameter regimes and with compelling novel probes. Individual snapshots can reveal the position and spin of each atom in the system thereby providing access to complex correlations in materials that are often crucial to understand their behaviour. In my talk, I will discuss recent progress on quantum simulation with ultracold bosonic and fermionic atoms and molecules in optical lattices and tweezers. The physics of strongly correlated electronic materials can e.g. be efficiently realized using ultracold fermionic atoms. Tuneable lattice geometries allow one to introduce programmable geometries and mixed dimensional situations in which doping can continuously tuned. I will show, how pairing of charge carriers and extended stripe-like structures emerge under such conditions due to an interplay of mobile dopant, mixed dimensions, and an antiferromagnetic background. Quantum simulation also offers new possibilites for probing out-of-equilibrium dynamics. I will present recent results on the observation of Hilbert space fragmentation in two-dimensionsl. Preparing localized defects on top of states within such fragments has also enables us to observe fractonic excitations. Their dynamics is shown to play a fundamental role when connecting thermalizing and non-thermalizing states of different fragments connected through a domain wall boundary.

Finally, I will show how polar molecules provide an alternative platform for realizing long-range interacting itinerant systems but have for a long time been plagued by uncontrolled losses. I will delineate how such losses can be overcome using microwave radiation and gives rise to novel field-linked scattering resonances that allow assembling larger ultracold molecular complexes also opening the route to p-wave superfluids.

Thursday

Quantum computers can offer dramatic speed-ups over their classical counterparts for certain problems. However, noise remains the biggest impediment to realizing the full potential of quantum computing. While the theory of quantum error correction offers a solution to this challenge, a large scale realization of fault tolerance is still pending. What can one hope to do then, with existing noisy processors? In this talk, I will present various experiments that produce reliable expectation values from a noisy 127 qubit processor, at a scale that is well beyond brute-force classical computation. We argue that this represents evidence for the utility of quantum computing in a pre-fault-tolerant era. I will also discuss recent classical benchmarking of our experiments beyond exact verification.

The real-time simulation of large many-body quantum systems is a formidable task, that may only be achievable with a genuine quantum computational platform. Currently, quantum hardware with a number of qubits sufficient to make classical emulation challenging is available. This condition is necessary to pursue a so-called quantum advantage, but it also makes verifying the results very difficult. In this talk, I will present a method that utilizes known theoretical results about many-body quantum critical dynamics to benchmark quantum hardware and various error mitigation techniques on up to 133 qubits. In particular, we benchmark against known universal scaling laws in the Hamiltonian simulation of a time-dependent transverse field Ising Hamiltonian. Incorporating only basic error mitigation and suppression methods, our study shows reliable control up to a two-qubit gate depth of 28, featuring a maximum of 1396 two-qubit gates, before noise becomes prevalent. These results are transferable to applications such as Hamiltonian simulation, variational algorithms, optimization, or quantum machine learning. We demonstrate this in the example of digitized quantum annealing for optimization and identify an optimal working point in terms of both circuit depth and time step on a 133-site optimization problem.

Many-body quantum simulation using experimental quantum processors is a highly promising avenue toward practical quantum advantage. Traditionally, such a task is accomplished via unitary dynamics which is limited by gate fidelities and oftentimes Trotter errors. Here we explore the non-unitary dynamics arising from the interplay between unitary evolution applied to a system of qubits and an engineered dissipative environment realized by auxiliary qubits that are frequently reset to their ground states. We find that by appropriate choice of interaction between the system qubits and auxiliaries, the quantum system may be steered to an entangled steady state resembling low-temperature states of 1D and 2D transverse Ising models. Furthermore, by coupling the system to auxiliaries stabilized to different states, we discover a new, subdiffusive form of quantum transport in the Heisenberg XXZ model. These results demonstrate the feasibility of utilizing engineered dissipation toward preparing complex quantum matter, enriching the capability of near-term superconducting processors.

Kostyantyn Kechedzhi

Recently, digital quantum processors surpassed classical supercomputers on Random Circuit Sampling (RCS) tasks despite the presence of a finite level of noise. Noise suppresses quantum correlations and therefore may limit the extent of quantum correlation across the system. It is important to identify the boundary between the weak and strong noise regimes where in the former case all of the Hilbert space of the quantum processor may be leveraged and in the latter quantum correlations are limited by noise. In this presentation we demonstrate that a discontinuous phase transition can be identified in the statistics of the noisy random circuit output which separates weak and strong noise regimes. We describe a statistical model in which the phase transition can be identified and described analytically in the thermodynamic limit. We demonstrate the signatures of the transition in numerics and experiments on a digital quantum processor. The phase transition separates the parameter regimes where XEB is a reliable estimator of fidelity and where it is not. The presence of the discontinuous phase transition also allows us to identify bounds on the best performance of the so-called spoofing algorithms which attempt to reproduce samples with XEB equal to that of the noisy quantum processor using only polynomial resources.

We will discuss recent advances in quantum information processing using dynamically reconfigurable arrays of neutral atoms. With this platform we have realized programmable quantum processing with encoded logical qubits, combining the use of 280 physical qubits, high two-qubit gate fidelities, arbitrary connectivity, and mid-circuit readout. Using this logical processor with various types of error-correcting codes, we demonstrate that we can improve logical two-qubit gates by increasing code size, outperform physical qubit fidelities, create logical GHZ states, and perform computationally complex quantum simulation of information scrambling. We will show new results exploring trotterized digital implementations of quantum simulation, new theoretical advances enabling large speed-up in error correction using transversal gates and correlated decoding, as well as recent experimental advances enabling deep computation. We will highlight nuances and opportunities in near-term error-corrected quantum simulation.

Matthias Bock

We present a two-dimensional trapped-ion quantum simulator to explore the 2D transverse-field Ising model with flexible interaction range. Its heart is a novel linear Paul trap capable of creating stable trapping conditions and sufficient control to routinely operate with ion crystals up to 105 particles. We implement the transverse-field Ising model and demonstrate the build-up of quantum correlations after a global quench and the creation of spin squeezing with Wineland parameters of 11 dB in a 91-ion crystal. On top, we make use of variational optimization to tweak the parameters of multi-layer protocols to further enhance the achievable squeezing.

Alberto Nocera

The overarching goal of noisy intermediate-scale quantum era is the demonstration that Quantum Processing Units (QPU) can solve a problem of practical interest that is impossible for any existing classical computer.
A natural playground for such a demonstration is the simulation of coherent Schrodinger dynamics of a quantum-mechanical system, where the analogue quantum simulator closely mimics the quantum-mechanical system’s physical microscopic degrees of freedom and their interactions.
Focusing on the non-equilibrium dynamics of a magnetic spin-glass system (in two, three, and infinite dimensions) quenched through a quantum phase transition, I show that the latest D-Wave superconducting quantum annealing processor faithfully simulates the quantum spin-glass dynamics in close agreement with solutions of the Schr̈odinger equation solved using the best known classical simulation method for the problem: time-dependent variational principle applied to Matrix Product States (MPS).
After benchmarking the QPU accuracy on the largest classically tractable systems, MPS simulations provide the key demonstration of area-law scaling of quantum entanglement in the model quench, opening a route to establish computational supremacy of the D-Wave device as an analogue quantum simulator: extrapolation of classical computational resources beyond the simulable scale of a few hundred qubits, far below the maximum experimental scale, amount to a hypothetical runtime of millions of years on the ORNL Frontier supercomputer, with infeasible memory and energy requirements. Beyond the classically tractable system sizes, verification of the D-Wave analogue quantum simulator is established measuring critical exponents closely matching estimates from the expected universality class using Kibble-Zurek theory.
Finally, I consider approximate methods based on cluster-MPS techniques, other tensor networks approaches (PEPS), and neural networks concluding that no known classical approach can achieve the same accuracy as the D-Wave analogue quantum simulator within a reasonable time frame.

References
A. D. King, A. Nocera, et al. arXiv:2403.00910 [quant-ph] https://arxiv.org/abs/2403.00910

Lata Joshi, Johannes Franke, Aniket Rath, Filiberto Ares, Sara Murciano, Florian Kranzl, Rainer Blatt, Peter Zoller, Benoıt Vermersch, Pasquale Calabrese, Christian Roos and Manoj Kumar Joshi

The non-equilibrium physics of many-body quantum systems harbor various unconventional phenomena. In recent studies on thermalization following quantum quenches on specific states an interesting and puzzling phenomena has emerged — the quantum Mpemba effect. In this effect, following a quantum quench, an initially tilted ferromagnet restores its symmetry more rapidly when it is farther from a symmetric state compared to when it is closer. In this talk I will present the first experimental evidence of this effect in a trapped-ion quantum simulator. The symmetry breaking and restoration are monitored through entanglement asymmetry, probed via randomized measurements, and postprocessed using the classical shadows technique. Furthermore, a direct comparison between the late time thermal symmetric theoretical state and the experimental state offer direct evidence of subsystem thermalization.

Friday

The connectivity of interactions in a quantum simulator plays a crucial role in dictating which problems can efficiently be mapped onto the hardware. While local interactions are well suited to simulating a wide range of problems in condensed-matter physics, adding nonlocal connectivity opens the door to new applications, from simulating models of quantum gravity to manipulating topologically encoded quantum information. I will report on experiments in which we achieve programmable nonlocal connectivity within an array of atom clouds trapped in an optical resonator, letting photons mediate interactions between distant atoms. We have harnessed this toolbox to simulate a toy model of holographic duality and to interferometrically probe topological edge states. To illustrate the capacity for accessing demonstrably entangled states, we have further demonstrated a versatile protocol for preparing graph states enabling a quantum enhancement in multiparameter sensing.

Trond Andersen, Nikita Astrakhantsev, Xiao Mi and Dmitry Abanin

Understanding how interacting particles approach thermal equilibrium is a major goal of quantum simulation. Analog quantum simulators (AQS) are appealing platforms for achieving this goal since they directly implement Hamiltonian dynamics, which are faster and less constrained by decoherence than in digital Trotter schemes. We here present a hybrid digital-analog quantum simulator comprising 69 superconducting qubits which exhibits very low analog evolution errors and performance beyond the reach of classical simulation in cross-entropy benchmarking experiments. Simulating an XY quantum magnet, we observe clear signatures of the Kosterlitz-Thouless transition – including the emergence of algebraically decaying correlations with an exponent near the expected universal value of ¼ – as well as a consequent breakdown of Kibble-Zurek scaling. We substantiate our interpretations by injecting variable energy density into the initial state, which enables studying the effects of the eigenstate thermalization hypothesis in targeted parts of the spectrum. Finally, we digitally prepare the system in pairwise-entangled dimer states and image the transport of energy and vorticity during thermalization. These results establish the efficacy of superconducting analog-digital quantum processors for preparing states across many-body spectra and unveiling their thermalization dynamics.

Nuclear spins in diamond offer a unique platform to study many-body phenomena, as they are well-isolated from environmental noise and have long coherence times. They are coupled via dipole-dipole interactions and can be accessed through a Nitrogen-Vacancy center in their proximity.
In this talk, we explore our toolbox to read-out and control 40 individual 13C-spins in diamond and engineer their Hamiltonian. We discuss novel phases of matter, such as a discrete time crystal, and investigate thermalization mechanisms in open 3D systems.

Ilan Rosen, Sarah Muschinske, Cora Barrett, Arkya Chatterjee, Max Hays, Jeffrey Grover and William Oliver

Superconducting quantum processors are a compelling platform for analog quantum simulation due to the precision control, fast operation, and site-resolved readout inherent to the hardware. Arrays of coupled superconducting qubits natively emulate the dynamics of interacting particles according to the Bose-Hubbard model. However, many interesting condensed-matter phenomena emerge only in the presence of electromagnetic fields. Here, we emulate the dynamics of charged particles in an electromagnetic field using a superconducting quantum simulator. We realize a broadly adjustable synthetic magnetic vector potential by applying continuous modulation tones to all qubits. We verify that the synthetic vector potential obeys requisite properties of electromagnetism: a spatially-varying vector potential breaks time-reversal symmetry and generates a gauge-invariant synthetic magnetic field, and a temporally-varying vector potential produces a synthetic electric field. We demonstrate that the Hall effect–the transverse deflection of a charged particle propagating in an electromagnetic field–exists in the presence of the synthetic electromagnetic field.

Laser-cooled trapped ions are a versatile platform for studying out-of-equilibrium dynamics of open quantum systems as they provide highly tunable unitary and non-unitary operations on both internal and external degrees of freedom. After an introduction to the trapped-ion platform, I will discuss our recent results [1] on the simulation of electron transfer in a multi-species trapped-ion crystal. We use the hyperfine qubit of a 171Yb+ ion to simulate the electron degree of freedom and the optical qubit of a 172Yb+ ion to perform reservoir engineering on a collective mode encoding a molecular vibration. This setting allows us to realize a paradigmatic model of molecular electron transfer [2] where we can precisely control the donor-acceptor gap, the electronic and the spin-phonon bath couplings, and the bath properties. We study the electron transfer dynamics in the nonperturbative regime where there is no clear hierarchy among the energy scales in the model, as it often occurs in biochemical systems [3,4]. Secondly, I will discuss our ongoing theoretical investigation of the role of entanglement and excitation delocalization in electron transfer in the case of a multi-ion spin chain with engineered dissipation [5]. Finally, I will also show our progress in the construction of a new trapped-ion system based on a monolithic 3D linear trap. Thanks to a combination of laser writing and etching, this trap combines the repeatability and modularity of microfabricated chip traps with the typical advantages of 3D traps, such as eV-deep trapping potentials, robustness to stray fields, larger ion-electrode distance, as well as wider and multi-directional optical access.

[1] V. So, M. D. Suganthi et al., arXiv:2405.10368, (2024)
[2] P. Wolynes, The Journal of Chemical Physics 86, 1957 (1987)
[3] D. J. Gorman et al., PRX 8, 011038 (2018)
[4] F. Schlawin, M. Gessner, et al., PRXQ, 2, 010314 (2021)
[5] D. Fallas-Padilla, et al., in preparation (2024)

Rhine Samajdar, Tom Manovitz, Sophie Li, Sepehr Ebadi, Mikhail Lukin and David Huse

Understanding the out-of-equilibrium dynamics of a closed quantum system driven across a quantum phase transition is an important problem with widespread implications for quantum state preparation and adiabatic algorithms. While the quantum Kibble-Zurek mechanism elucidates part of these dynamics, the subsequent and significant coarsening processes lie beyond its scope. Here, we develop a universal description of such coarsening dynamics—and their interplay with the Kibble-Zurek mechanism—in terms of scaling theories. This comprehensive theoretical framework applies to a diverse set of ramp protocols of analog quantum simulators and encompasses various coarsening scenarios involving both quantum and thermal fluctuations. We present detailed experimental results probing such many-body coarsening dynamics using a locally programmable Rydberg-atom quantum simulator. Our results showcase the power of quantum simulation in addressing a tremendously challenging problem, namely, studying the nonequilibrium dynamics of large quantum systems at late times.

Daniel González-Cuadra, Torsten V. Zache, Boris Braverman, Alexei Bylinskii, Milan Kornjaca, Fangli Liu, Shengtao Wang, Mikhail Lukin and Peter Zoller

Simulating the real-time dynamics of lattice gauge theories remains a formidable computational challenge. Although quantum simulators can tackle this problem more efficiently than classical devices, experiments have so far been restricted to 1D, leaving the more challenging but also richer higher-dimensional cases unexplored. In this talk, I will show how the latter can be readily addressed using Rydberg atom arrays. In particular, I will show how a Kagome lattice of Rydberg atoms in optical tweezers gives rise to an emergent 2D gauge theory, where U(1) gauge fields mediate interactions between scalar matter fields. Moreover, in this setup long-range Rydberg interactions confine matter particles, connected by strings of gauge-field excitations, into mesonic bound states. This mechanism allows us to investigate dynamical string breaking in 2D, where gauge-field fluctuations are driven by effective plaquette interactions. Our quantum simulation protocol is based on adiabatic state preparation followed by global quench dynamics, that we benchmarked using tensor-network methods. Finally, I will show some preliminary experimental results where string states were prepared using QuEra’s Rydberg quantum simulator.

In confining theories, separating two charges results in the generation of new charges that screen the original ones. This process, known as “string breaking”, prevents isolation of individual charges and is one of the fundamental phenomena in gauge theories such as quantum chromodynamics, as well as in simpler models exhibiting confinement. The rapid development of analog and digital quantum simulators represents a promising path toward the ab-initio simulation of real-time evolution in these models. In this talk, I will focus on the dynamics of string breaking in a trapped-ion quantum simulator. I will describe the observation of string breaking in the evolution after a quantum quench and in a non-equilibrium protocol where the string tension is gradually increased over time.

Tsung-Cheng Lu, Zhehao Zhang, Sagar Vijay and Timothy Hsieh

We propose a general framework for using local measurements, local unitaries, and nonlocal classical communication to construct quantum channels, which can efficiently prepare mixed states with long-range quantum order or quantum criticality. As an illustration, symmetry-protected topological phases can be universally converted into mixed states with long-range entanglement, which can undergo phase transitions with quantum critical correlations of local operators and a logarithmic scaling of the entanglement negativity, despite coexisting with volume-law entropy. Within the same framework, we present two applications using fermion occupation-number measurement to convert (i) spinful free fermions in one dimension into a quantum critical mixed state with enhanced algebraic correlations between spins and (ii) Chern insulators into a mixed state with critical quantum correlations in the bulk. The latter is an example where mixed-state quantum criticality can emerge from a gapped state of matter in constant depth using local quantum operations and nonlocal classical communication.

Quantum computers (QC) promise to solve computational challenges in chemistry by requiring only linear resource scaling. However, almost all chemical applications of QC have focused on static molecular properties, usually energies, making them unsuitable for addressing chemical dynamic problems, especially in strong vibronic (vibrational + electronic) coupling regimes where the Born-Oppenheimer approximation breaks down. Here, we show that vibronic Hamiltonians representing ultrafast molecular dynamics can be scalably and efficiently simulated on a mixed qudit-boson (MQB) simulator that provides order-of-magnitude resource savings compared to conventional qubit-only approaches [1]. We will discuss a series of analog quantum simulation experiments performed with a programmable trapped-ion MQB simulator, including simulations of molecular dynamics and predictions of the molecular spectra [2,3].

[1] Analog quantum simulation of chemical dynamics, Chem. Sci. 12, 9794 (2021).

[2] Predicting molecular vibronic spectra using time-domain analog quantum simulation, Chem. Sci. 14, 9439 (2023).

[3] Direct observation of geometric-phase interference in dynamics around a conical intersection, Nat. Chem. 15, 1503 (2023).

Siva Darbha, Milan Kornjača, Fangli Liu, Jan Balewski, Mark R. Hirsbrunner, Pedro L. S. Lopes, Sheng-Tao Wang, Roel Van Beeumen, Katherine Klymko, and Daan Camps

Metastable states of quantum many-body systems with confinement offer a means to simulate false vacuum phenomenology, including non-equilibrium dynamical processes like decay by nucleation, in truncated limits. Recent work has examined false vacuum phenomena in 1D ferromagnetic Ising spins and superfluids. In this talk, we present work on metastability dynamics in 1D antiferromagnetic neutral atom chains with Rydberg interactions, using both numerical simulations and analytic modeling. We use a staggered local detuning field to achieve confinement. Our efforts focus on three dynamical regimes: decay, nucleation, and long-lived oscillations. In the first, we corroborate the phenomenological decay rate scaling and determine the associated parameter range for the decay process; in the second, we uncover and elucidate a procedure to anneal the metastable state from the initial to the final system, with intermediate nucleation events; in the third, we identify novel spectral signatures of quasiparticle oscillations distinct to antiferromagnetic neutral atom systems and interpret them using a classical energy model of short-range meson repulsion. We propose experimental protocols to prepare the required states and perform quenches on near-term neutral atom quantum simulators, examining the experimental feasibility of our proposed setup and parameter regime.

References:
[1] S. Darbha et al., arXiv:2404.12360 , (2024).
[2] S. Darbha et al., arXiv:2404.12371 , (2024).