AI 中文总结
该研究解决了自适应测量量子计算中代数语境性的开放问题，证明自适应$\boldsymbol{\boldsymbol{Z}_2}$线性MBQC协议计算非仿射布尔函数时会出现代数悖论，可通过上同调检测，为量子优势的代数分析提供了关键方法。
AI 中文摘要
基于测量的量子计算（MBQC）是一种通用量子计算模型，其完整能力依赖于适应性。已知语境性为MBQC中的量子优势提供支撑，但在自适应语境下却难以进行代数分析。我们证明：若一个自适应$\boldsymbol{\boldsymbol{Z}_2}$线性基于测量的量子计算协议确定性地计算非仿射布尔函数，则其底层量子资源满足一组不一致的线性方程。这见证了一种代数形式的强语境性，推广了Mermin的全对无论证。这种代数语境性可通过上同调检测，解决了Raussendorf提出的一个开放问题——Raussendorf已为非自适应协议建立了语境性的上同调见证，但未解决自适应情形。我们构造性地证明该结果：将自适应测量协议建模为树状测量更大场景下的普通测量，并归纳式地显式构建不一致方程。
英文摘要
Measurement-based quantum computation (MBQC) is a universal model of quantum computation whose full power requires adaptivity. Contextuality is known to power quantum advantage in MBQC, yet it has resisted algebraic analysis in the adaptive setting. We show that if an adaptive $\mathbb{Z}_2$-linear measurement-based quantum computing protocol deterministically computes a non-affine Boolean function, then the underlying quantum resource satisfies an inconsistent set of linear equations. This witnesses an algebraic form of strong contextuality generalising Mermin's All-versus-Nothing arguments. Such algebraic contextuality can be detected cohomologically, resolving an open question posed by Raussendorf, who had established cohomological witnesses of contextuality for non-adaptive protocols, but left the adaptive case open. We prove this result constructively: we model adaptive measurement protocols as ordinary measurements on a larger scenario of tree-like measurements, and explicitly build the inconsistent equations inductively.
Comments39 pages
