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arXiv · 2209.15523

Convergence condition of simulated quantum annealing for closed and open systems

Yusuke Kimura·Hidetoshi Nishimori
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Abstract

Simulated quantum annealing is a generic classical protocol to simulate some aspects of quantum annealing and is sometimes regarded as a classical alternative to quantum annealing in finding the ground state of a classical Ising model. We derive a generic condition for simulated quantum annealing to converge to thermal equilibrium at a given, typically low, temperature. Both closed and open systems are treated. We rewrite the classical master equation for simulated quantum annealing into an imaginary-time Schrödinger equation, to which we apply the imaginary-time variant of asymptotic adiabatic condition to deduce the convergence condition. The result agrees qualitatively with a rigorous convergence condition of simulated quantum annealing for closed systems, which was derived from the theory of inhomogeneous Markov process. Also observed is qualitative agreement with a rigorous convergence condition of quantum annealing for closed systems under the real-time Schrödinger dynamics. This coincidence of convergence conditions for classical stochastic processes for simulated quantum annealing and the real-time quantum dynamics for quantum annealing is highly non-trivial and calls for further scrutiny.

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BibTeXRIS

Yusuke Kimura, Hidetoshi Nishimori. 2022-12-20. Convergence condition of simulated quantum annealing for closed and open systems. https://doi.org/10.1103/physreva.106.062614

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