Relation of classical non-equilibrium dynamics and quantum annealing

Abstract

Non-equilibrium dynamics of the Ising model is a classical stochastic process whereas quantum mechanics has no stochastic elements in the classical sense. Nevertheless, it has been known that there exists a close formal relationship between these two processes. We reformulate this relationship and use it to compare the efficiency of simulated annealing that uses classical stochastic processes and quantum annealing to solve combinatorial optimization problems. It is shown that classical dynamics can be efficiently simulated by quantum-mechanical processes whereas the converse is not necessarily true. This may imply that quantum annealing may be regarded as a more powerful tool than simulated annealing for optimization problems.

Proceedings of STATPHYS-KOLKATA VIII

References in corpus (5)

• Defining and detecting quantum speedup
• Mathematical Foundation of Quantum Annealing
• Glassy Chimeras could be blind to quantum speedup: Designing better benchmarks for quantum annealing machines
• Convergence theorems for quantum annealing
• Convergence of Quantum Annealing with Real-Time Schrodinger Dynamics

Cited by in corpus (1)

• Diabatic quantum and classical annealing of the Sherrington-Kirkpatrick model