Convergence condition of simulated quantum annealing for closed and open systems

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.

10 pages. Added references

References in corpus (14)

• Mathematical Foundation of Quantum Annealing
• Coherent quantum annealing in a programmable 2000-qubit Ising chain
• Prospects for Quantum Enhancement with Diabatic Quantum Annealing
• Phase diagram and critical exponents of a dissipative Ising spin chain in a transverse magnetic field
• A Quantum Approach to Classical Statistical Mechanics
• Convergence theorems for quantum annealing
• Quantum Computing for Quantum Tunnelling
• Convergence of Quantum Annealing with Real-Time Schrodinger Dynamics
• Comparative Study of the Performance of Quantum Annealing and Simulated Annealing
• Simulated quantum annealing as a simulator of non-equilibrium quantum dynamics
• Griffiths-McCoy singularity on the diluted Chimera graph: Monte Carlo simulations and experiments on the quantum hardware
• Quantum Optimisation of Complex Systems with a Quantum Annealer
• Quantum and classical annealing in a continuous space with multiple local minima
• Rigorous convergence condition for quantum annealing

Cited by in corpus (3)

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• Adiabatic theorem for classical stochastic processes