Monte Carlo sampling from a projected entangled-pair state in simulations of quantum annealing in the three dimensional random Ising model

TL;DR

This paper employs tensor network methods and Monte Carlo sampling to simulate quantum annealing in a 3D random Ising model, analyzing residual energy behavior and validating the Kibble-Zurek law.

Contribution

It introduces a Monte Carlo sampling approach for PEPS in 3D quantum annealing simulations, enabling efficient analysis of residual energy scaling.

Findings

Residual energy follows the Kibble-Zurek power law with increasing annealing time.

Monte Carlo sampling improves efficiency for finite lattice simulations.

Deterministic methods accurately evaluate final energy for infinite lattices.

Abstract

Quantum annealing with the D-Wave Advantage system in the random Ising model on a cubic lattice is simulated using a three-dimensional (3D) tensor network. The Hamiltonian is driven across a quantum phase transition from a paramagnetic phase to a spin-glass phase. The network is represented as a tensor product state, also known-particularly in two dimensions-as a projected entangled-pair state (PEPS). The annealing procedure is repeated for a range of annealing times in order to test the Kibble-Zurek (KZ) power law governing the residual energy at the end of the annealing ramp. For an infinite lattice with periodic nearest-neighbor random Ising couplings, the final energy is evaluated using a deterministic method. For a finite lattice with open boundaries, we introduce a more efficient Monte Carlo sampling approach. In both cases, the residual energy as a function of annealing time approaches the KZ power law as the annealing time increases.