Classical Simulation of Short-Time Quantum Dynamics

Recent progress in the development of quantum technologies has enabled direct investigation dynamics increasingly complex many-body systems. This motivates study complexity classical algorithms for this problem order to benchmark simulators and delineate regime advantage. Here, we present approximating local observables nonlocal quantities such as Loschmidt echo, where evolution is governed by a Hamiltonian. For short times, their computational cost scales polynomially with system size inverse approximation error. In case observables, proposed algorithm better dependence on error than based Lieb-Robinson bound. Our results use cluster-expansion techniques adapted dynamical setting, which give novel proof convergence. important physical consequences besides our efficient algorithms. particular, establish speed limit, bound phase transitions, concentration product states evolved times.Received 2 November 2022Accepted 25 April 2023DOI:https://doi.org/10.1103/PRXQuantum.4.020340Published American Physical Society under terms Creative Commons Attribution 4.0 International license. Further distribution work must maintain attribution author(s) published article's title, journal citation, DOI.Published SocietyPhysics Subject Headings (PhySH)Research AreasQuantum information theoryQuantum statistical mechanicsPhysical SystemsLattice models physicsQuantum spin modelsTechniquesApproximation methods systemsComputational complexitySeries expansions & exact enumerationQuantum InformationStatistical Physics