Southwest Quantum Information and Technology

Classical simulation of high temperature quantum Ising models

Presenting Author: Sam Slezak, University of New Mexico CQuIC
Contributing Author(s): Elizabeth Crosson

We consider generalized quantum Ising models, including those which could describe disordered materials or quantum annealing devices, and we rigorously prove that the path integral Monte Carlo method yields an efficient algorithm for approximating the partition function above some system-size independent threshold temperature. This threshold temperature depends on the local interaction energy of each qubit, and in one formulation of the bound it suffices for the temperature to be greater than two + the maximum interaction degree (valence) over all qubits, measured in units of the local coupling constant. For example, this implies that the classical simulation of the thermal state of a superconducting device modeling a quantum Ising model with maximum valence of 6 and coupling strengths of 1 GHz is possible at all temperatures above 400 mK. Our proof is based on a probabilistic method called coupling which allows us to analyze the relaxation time of the worldline update PIMC Markov chain, showing that it equilibrates in the shortest possible time of O(n log n) worldline updates, where n is the number of qubits. In contrast, most previous rigorous simulations of systems without a sign problem only work when all of the couplings in the system are ferromagnetic. While the kind of quantum-to-classical transitions we identify were already known experimentally and from heuristic arguments, this result rigorously justifies the empirical success of PIMC in simulating such syst

(Session 5 : Saturday from 5:00pm - 7:00pm)