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We show how the localization landscape, originally introduced to bound lowenergy eigenstates of disordered wave media and many-body quantum systems, canform the basis for hardware-efficient quantum algorithms for solving binaryoptimization problems. Many binary optimization problems can be cast as findinglow-energy eigenstates of Ising Hamiltonians. First, we apply specificperturbations to the Ising Hamiltonian such that the low energy modes arebounded by the localization landscape. Next, we demonstrate how a variationalmethod can be used to prepare and sample from the peaks of the localizationlandscape. Numerical simulations of problems of up to $10$ binary variablesshow that the localization landscape-based sampling can outperform QAOAcircuits of similar depth, as measured in terms of the probability of samplingthe exact ground state.

Landscape approximation of low energy solutions to binary optimization problems