Landscape approximation of low energy solutions to binary optimization problems
Abstract
We show how the localization landscape, originally introduced to bound low energy eigenstates of disordered wave media and many-body quantum systems, can form the basis for hardware-efficient quantum algorithms for solving binary optimization problems. Many binary optimization problems can be cast as finding low-energy eigenstates of Ising Hamiltonians. First, we apply specific perturbations to the Ising Hamiltonian such that the low energy modes are bounded by the localization landscape. Next, we demonstrate how a variational method can be used to prepare and sample from the peaks of the localization landscape. Numerical simulations of problems of up to binary variables show that the localization landscape-based sampling can outperform QAOA circuits of similar depth, as measured in terms of the probability of sampling the exact ground state.
Cite
@article{arxiv.2307.02461,
title = {Landscape approximation of low energy solutions to binary optimization problems},
author = {Benjamin Y. L. Tan and Beng Yee Gan and Daniel Leykam and Dimitris G. Angelakis},
journal= {arXiv preprint arXiv:2307.02461},
year = {2023}
}
Comments
11 pages, 7 figures