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

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.

12 pages, 10 figures; v2 with improved presentation accepted in Phys.Rev.B

Quantum Physics (quant-ph); Disordered Systems and Neural Networks (cond-mat.dis-nn); Strongly Correlated Electrons (cond-mat.str-el)

arXiv:2603.16509 [quant-ph]

(or arXiv:2603.16509v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2603.16509 Focus to learn more arXiv-issued DOI via DataCite

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