Landscape approximation of low-energy solutions to binary optimization problems

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 ten binary variables show that the localization landscape-based sampling can outperform quantum approximate optimization algorithm (QAOA) circuits of similar depth, as measured in terms of the probability of sampling the exact ground state.