Simulated quantum annealing of double-well and multi-well potentials

Abstract

We analyze the performance of quantum annealing as a heuristic optimization method to find the absolute minimum of various continuous models, including landscapes with only two wells and also models with many competing minima and with disorder. The simulations performed using a projective quantum Monte Carlo (QMC) algorithm are compared with those based on the finite-temperature path-integral QMC technique and with classical annealing. We show that the projective QMC algorithm is more efficient than the finite-temperature QMC technique, and that both are inferior to classical annealing if this is performed with appropriate long-range moves. However, as the difficulty of the optimization problem increases, classical annealing looses efficiency, while the projective QMC algorithm keeps stable performance and is finally the most effective optimization tool. We discuss the implications of our results for the outstanding problem of testing the efficiency of adiabatic quantum computers using stochastic simulations performed on classical computers.

11 pages, 7 figures

References in corpus (5)

• Mathematical Foundation of Quantum Annealing
• Reexamining classical and quantum models for the D-Wave One processor
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Cited by in corpus (11)

• Adiabatic Quantum Computing
• Understanding Quantum Tunneling through Quantum Monte Carlo Simulations
• Simulated Quantum Annealing Can Be Exponentially Faster than Classical Simulated Annealing
• Projective quantum Monte Carlo simulations guided by unrestricted neural network states
• Quantum Monte Carlo tunneling from quantum chemistry to quantum annealing
• Self-learning projective quantum Monte Carlo simulations guided by restricted Boltzmann machines
• Quantum annealing speedup over simulated annealing on random Ising chains
• Understanding Quantum Tunneling using Diffusion Monte Carlo Simulations
• Effectiveness of quantum annealing for continuous-variable optimization
• Tunneling in projective quantum Monte Carlo simulations with guiding wave functions
• Quantum Monte Carlo simulation of BEC-impurity tunneling