Quantum annealing of an Ising spin-glass by Green's function Monte Carlo

Abstract

We present an implementation of Quantum Annealing (QA) via lattice Green's function Monte Carlo (GFMC), focusing on its application to the Ising spin-glass in transverse field. In particular, we study whether or not such method is more effective than the Path-Integral Monte Carlo (PIMC) based QA, as well as classical simulated annealing (CA), previously tested on the same optimization problem. We identify the issue of importance sampling, i.e., the necessity of possessing reasonably good (variational) trial wavefunctions, as the key point of the algorithm. We have considered two possible classes of trial wavefunctions, a mean-field single-site one -- whose optimization is however a very difficult task -- and a Boltzmann-like choice. We performed GFMC-QA runs using such a Boltzmann-like trial wavefunction, finding results for the residual energies that are qualitatively similar to those of CA (but at a much larger computational cost), and definitely worse than PIMC-QA. We conclude that, at present, without a serious effort in constructing reliable importance sampling variational wavefunctions for a quantum glass, GFMC-QA is not a true competitor of PIMC-QA.

9 pages, 4 figures, REVTex 4

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• Spin-Glass Theory for Pedestrians
• Wave function optimization in the variational Monte Carlo method
• Quantum annealing of the Traveling Salesman Problem
• Optimization by Quantum Annealing: Lessons from hard 3-SAT cases
• Optimization by Quantum Annealing: Lessons from Simple Cases
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• Understanding Quantum Tunneling using Diffusion Monte Carlo Simulations
• Approaching the Ground State of a Quantum Spin Glass using a Zero-Temperature Quantum Monte Carlo
• Tunneling in projective quantum Monte Carlo simulations with guiding wave functions
• Rapid mixing of path integral Monte Carlo for 1D stoquastic Hamiltonians
• Zero-temperature Monte Carlo simulations of two-dimensional quantum spin glasses guided by neural network states