约束局部哈密顿量：Vertex Cover 的量子推广
Constrained local Hamiltonians: quantum generalizations of Vertex Cover
AI总结：
本文受经典 Vertex Cover 启发研究约束局部哈密顿量，提出等价于含 Pauli-Z 项 PXP 模型的 TVC，证明其 StoqMA-hard，并用量子局部比率方法给出线性时间经典近似算法。
摘要：
近期在为 Quantum Max Cut 等局部哈密顿量问题构造严格近似算法方面取得的成功，利用了其与无约束经典离散优化问题之间的联系。我们以已被充分研究的经典 Vertex Cover 问题为启发，开启了对约束局部哈密顿量问题近似算法的研究。我们考虑 Vertex Cover 的自然量子推广，其中之一称为 Transverse Vertex Cover（TVC），它等价于带有额外 1-局域 Pauli-Z 项的 PXP 模型。我们证明 TVC 是 StoqMA-hard 的，并基于经典局部比率方法的量子推广为其开发了一种近似算法。这产生了一种简单的线性时间经典近似算法，且不依赖于求解凸松弛。我们还在一个传统的无约束量子局部哈密顿量版本的 Vertex Cover 上展示了我们的量子局部比率方法，该版本等价于反铁磁横场 Ising 模型。
英文摘要：
Recent successes in producing rigorous approximation algorithms for local Hamiltonian problems such as Quantum Max Cut have exploited connections to unconstrained classical discrete optimization problems. We initiate the study of approximation algorithms for constrained local Hamiltonian problems, using the well-studied classical Vertex Cover problem as inspiration. We consider natural quantum generalizations of Vertex Cover, and one of them, called Transverse Vertex Cover (TVC), is equivalent to the PXP model with additional 1-local Pauli-Z terms. We show TVC is StoqMA-hard and develop an approximation algorithm for it based on a quantum generalization of the classical local ratio method. This results in a simple linear-time classical approximation algorithm that does not depend on solving a convex relaxation. We also demonstrate our quantum local ratio method on a traditional unconstrained quantum local Hamiltonian version of Vertex Cover which is equivalent to the anti-ferromagnetic transverse field Ising model.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
