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