Iterative quantum optimization of spin glass problems with rapidly oscillating transverse fields

TL;DR

This paper introduces IST-SAT, an iterative quantum algorithm that uses high-frequency oscillating transverse fields to efficiently solve spin glass problems, demonstrating polynomial speedups over existing methods.

Contribution

The paper presents a novel iterative quantum algorithm, IST-SAT, which leverages oscillating transverse fields and iterative refinement to improve optimization of spin glass problems.

Findings

Polynomial speedups over TAQC and classical algorithms.

Convergence to exact solutions with good initial approximations.

Identification of a critical Hamming radius for polynomial scaling.

Abstract

In this work, we introduce a new iterative quantum algorithm, called Iterative Symphonic Tunneling for Satisfiability problems (IST-SAT), which solves quantum spin glass optimization problems using high-frequency oscillating transverse fields. IST-SAT operates as a sequence of iterations, in which bitstrings returned from one iteration are used to set spin-dependent phases in oscillating transverse fields in the next iteration. Over several iterations, the novel mechanism of the algorithm steers the system toward the problem ground state. We benchmark IST-SAT on sets of hard MAX-3-XORSAT problem instances with exact state vector simulation, and report polynomial speedups over trotterized adiabatic quantum computation (TAQC) and the best known semi-greedy classical algorithm. When IST-SAT is seeded with a sufficiently good initial approximation, the algorithm converges to exact solution(s) in a polynomial number of iterations. Our numerical results identify a critial Hamming radius(CHR), or quality of initial approximation, where the time-to-solution crosses from exponential to polynomial scaling in problem size. By combining IST-SAT with future classical or quantum approximation algorithms, larger gains may be achieved. The mechanism we present in this work thus presents a new path toward achieving quantum advantage in optimization.