Classical simulation of short-time quantum dynamics

Abstract

Recent progress in the development of quantum technologies has enabled the direct investigation of dynamics of increasingly complex quantum many-body systems. This motivates the study of the complexity of classical algorithms for this problem in order to benchmark quantum simulators and to delineate the regime of quantum advantage. Here we present classical algorithms for approximating the dynamics of local observables and nonlocal quantities such as the Loschmidt echo, where the evolution is governed by a local Hamiltonian. For short times, their computational cost scales polynomially with the system size and the inverse of the approximation error. In the case of local observables, the proposed algorithm has a better dependence on the approximation error than algorithms based on the Lieb-Robinson bound. Our results use cluster expansion techniques adapted to the dynamical setting, for which we give a novel proof of their convergence. This has important physical consequences besides our efficient algorithms. In particular, we establish a novel quantum speed limit, a bound on dynamical phase transitions, and a concentration bound for product states evolved for short times.

23 pages, 5 figures, comments welcome

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• Group-theoretic error mitigation enabled by classical shadows and symmetries
• Fault-tolerant quantum algorithms for quantum molecular systems: A survey
• Phase-Sensitive Quantum Measurement without Controlled Operations
• Algorithmic Cluster Expansions for Quantum Problems
• Wireless energy transfer in non-Hermitian quantum battery
• Matrix product state approximations to quantum states of low energy variance
• Heisenberg-limited metrology with perturbing interactions
• Subspace-Based Local Compilation of Variational Quantum Circuits for Large-Scale Quantum Many-Body Simulation
• Hardware-efficient quantum phase estimation via local control
• Provably Efficient Simulation of 1D Long-Range Interacting Systems at Any Temperature
• Quantum concentration inequalities and equivalence of the thermodynamical ensembles: an optimal mass transport approach
• Strong decay of correlations for Gibbs states in any dimension
• Short-time simulation of quantum dynamics by Pauli measurements
• Lieb-Robinson bounds with exponential-in-volume tails
• Gibbs state sampling via cluster expansions
• High-temperature partition functions and classical simulatability of long-range quantum systems
• Short-time dynamics in phase-ordering kinetics
• Sampling (noisy) quantum circuits through randomized rounding
• Learning and simulating bosonic systems via finite-energy locality
• Direct Gradient Computation for Barren Plateaus in Parameterized Quantum Circuits