Landscape approximation of low energy solutions to binary optimization problems

Benjamin Y.L. Tan, Beng Yee Gan, Daniel Leykam, and Dimitris G. Angelakis.

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 10 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 as BibTex

@misc{tan2023landscape,
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},
year={2023},
eprint={2307.02461},
archivePrefix={arXiv},
primaryClass={quant-ph}
}