二元优化问题低能量解的局域化景观近似
Landscape approximation of low energy solutions to binary optimization problems
AI总结：
本文提出利用局域化景观约束伊辛哈密顿量低能量模式，并结合变分方法从景观峰值采样，数值模拟表明该方法在求解二元优化问题时优于相似深度的QAOA电路。
摘要：
我们展示了最初为界定无序波介质和多体量子系统中低能量本征态而引入的局域化景观（localization landscape），如何能够构成求解二元优化问题的硬件高效量子算法的基础。许多二元优化问题可以被转化为寻找伊辛哈密顿量（Ising Hamiltonian）的低能量本征态。首先，我们对伊辛哈密顿量施加特定的微扰，使得低能量模式被局域化景观所约束。接下来，我们演示了如何利用变分方法来制备局域化景观的峰值并从中进行采样。对多达10个二元变量问题的数值模拟表明，基于局域化景观的采样在采样到精确基态的概率方面能够优于相似深度的QAOA电路。
英文摘要：
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.
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