Classical simulation of short-time quantum dynamics
- URL: http://arxiv.org/abs/2210.11490v2
- Date: Tue, 11 Jul 2023 12:45:31 GMT
- Title: Classical simulation of short-time quantum dynamics
- Authors: Dominik S. Wild, \'Alvaro M. Alhambra
- Abstract summary: We present classical algorithms for approximating the dynamics of local observables and nonlocal quantities.
We establish a novel quantum speed limit, a bound on dynamical phase transitions, and a concentration bound for product states evolved for short times.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- 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.
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