标题： 一种用于局部哈密顿问题的量子近似优化算法 显示英文标题

标题： A Quantum Approximate Optimization Algorithm for Local Hamiltonian Problems

摘要： 局部哈密顿量问题（LHPs）是计算上属于QMA完备的重要问题，对于多体量子系统具有物理相关性。 量子最大切割（QMC）等价于寻找量子海森堡模型的基态，是各种算法已被提出的典型LHP，包括半定规划和变分量子算法。 我们提出并分析了一种称为哈密顿量子近似优化算法（HamQAOA）的量子近似算法，该算法建立在组合优化的著名方案之上，并适用于近期硬件的实现。 我们建立了HamQAOA在高环长正则图上的QMC的严格性能保证，我们的结果提供了在无限尺寸极限下量子海森堡自旋玻璃的基态能量密度的界限，且随着深度增加而改进。 此外，我们开发了启发式策略以高效获得良好的HamQAOA参数。 通过数值模拟，我们表明HamQAOA在各种QMC实例上经验上优于先前的算法。 特别是，我们的结果表明，线性深度的HamQAOA可以确定性地制备由贝茨假设描述的一维反铁磁海森堡自旋链的精确基态，这与之前协议准备贝茨态所需的指数深度形成对比。 显示英文摘要

摘要： Local Hamiltonian Problems (LHPs) are important problems that are computationally QMA-complete and physically relevant for many-body quantum systems. Quantum MaxCut (QMC), which equates to finding ground states of the quantum Heisenberg model, is the canonical LHP for which various algorithms have been proposed, including semidefinite programs and variational quantum algorithms. We propose and analyze a quantum approximation algorithm which we call the Hamiltonian Quantum Approximate Optimization Algorithm (HamQAOA), which builds on the well-known scheme for combinatorial optimization and is suitable for implementations on near-term hardware. We establish rigorous performance guarantees of the HamQAOA for QMC on high-girth regular graphs, and our result provides bounds on the ground energy density for quantum Heisenberg spin glasses in the infinite size limit that improve with depth. Furthermore, we develop heuristic strategies with which to efficiently obtain good HamQAOA parameters. Through numerical simulations, we show that the HamQAOA empirically outperforms prior algorithms on a wide variety of QMC instances. In particular, our results indicate that the linear-depth HamQAOA can deterministically prepare exact ground states of 1-dimensional antiferromagnetic Heisenberg spin chains described by the Bethe ansatz, in contrast to the exponential depths required in previous protocols for preparing Bethe states.