发表机构
University of Washington; Harvard & UC Berkeley; MIT（华盛顿大学; 哈佛大学与加州大学伯克利分校; 麻省理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出首个量子保持局部性的间隙放大模板，通过容错计算框架放大局部哈密顿量的组合间隙，为将经典PCP核心成分引入量子设置开辟了新途径。
AI 中文摘要
量子PCP猜想是量子复杂性理论中的重大开放问题之一。该猜想之所以难以攻克，部分原因在于经典PCP定理证明中使用的许多原语（如保持局部性的间隙放大和字母表缩减）由于量子不可克隆定理而没有明显的量子对应物。保持局部性的间隙放大是一种过程，它接收一个局部哈密顿量问题实例，并产生一个具有更大承诺间隙的新实例，同时不增加哈密顿量的局部性，而是适度增加其局部量子比特维度。在间隙放大过程中获得对局部性的这种控制，对于证明经典PCP定理的许多已知策略的成功至关重要。在这项工作中，我们提出了第一个已知的量子保持局部性间隙放大的可行模板，并证明了我们的过程放大了局部哈密顿量的组合间隙。我们的工作引入了一个新的框架，用于以容错计算的方式推理量子间隙放大，并阐明了将经典PCP中的核心成分之一引入量子设置的途径。特别是，我们借鉴了最近基于高维展开图的Bafna--Minzer--Vyas经典PCP的思想，以及Anshu--Breuckmann--Nguyen的电路到哈密顿量构造，此外还利用了量子编码理论中的几项最新进展。
英文摘要
The quantum PCP conjecture is one of the major open problems in quantum complexity theory. It has resisted attack in part because many primitives used in the proof of the classical PCP theorem, such as locality-preserving gap amplification and alphabet reduction, have no obvious quantum analogues due to quantum no-cloning. Locality-preserving gap amplification is a procedure that takes as input a local Hamiltonian problem instance and produces a new instance with a larger promise gap, without increasing the locality of the Hamiltonian, and instead moderately increasing its local qudit dimension. Obtaining this kind of control over the locality during gap amplification is critical to the success of many known strategies for proving the classical PCP theorem. In this work, we put forth the first known viable template for quantum locality-preserving gap amplification, and we prove that our procedure amplifies the combinatorial gap of local Hamiltonians. Our work introduces a new framework for reasoning about quantum gap amplification in terms of fault-tolerant computation, and illuminates a route toward importing one of the central ingredients in classical PCPs into the quantum setting. In particular, we build upon ideas from the recent classical PCP of Bafna--Minzer--Vyas based on high-dimensional expanders, and the circuit-to-Hamiltonian construction of Anshu--Breuckmann--Nguyen, in addition to several recent advances in quantum coding theory.
CommentsAccepted to FOCS 2026
