发表机构
CWI, Amsterdam（阿姆斯特丹中央数学和计算机科学中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明在标准门集下，中间测量可被消除，使RQL等于RQUL，保持多项式时间、对数空间和零错误接受，并扩展至更广门集及量子验证场景。
AI 中文摘要
中间测量使量子计算能够丢弃信息并重用其工作空间。将所有测量延迟到末尾可能需要存储其整个历史，这不一定能保持对数空间。Fefferman和Remscrim证明了在双侧有界误差下可以消除测量，并询问在单侧误差下是否同样成立[FR21]。我们证明了对于标准门集Γ = {H, T, CNOT}，RQLΓ = RQULΓ成立，同时保持多项式时间、对数空间以及在否定实例上精确为零接受率。我们的证明将Girish、Raz和Zhan [GRZ21]的密度矩阵加倍方法扩展到一般信道，包括重置和经典存储器。我们还证明了对于具有精确逆的更广泛的有限门集（包括具有超越项的门）的测量消除，并建立了对指定代数门集族的门集独立性。一个独立的历史检查构造证明了在显式门假设下QMAL1,G = QUMAL1,G：测量也可以从对数空间量子验证中消除，同时保持完美完备性。
英文摘要
Intermediate measurements let quantum computations discard information and reuse their workspace. Deferring all measurements can require storing their entire history, which need not preserve logarithmic space. Fefferman and Remscrim proved that measurements can nevertheless be eliminated with two-sided bounded error, and asked whether the same holds with one-sided error [FR21]. We prove RQLΓ = RQULΓ for the standard gate set Γ = {H, T, CNOT}, preserving polynomial time, logarithmic space, and exactly zero acceptance on no-instances. Our proof extends the density-matrix doubling method of Girish, Raz and Zhan [ GRZ21 ] to general channels, including resets and classical memory. We also prove measurement elimination for broader finite gate sets with exact inverses, including suitable gates with transcendental entries, and establish gate-set independence for a specified family of algebraic gate sets. A separate history-checking construction proves QMAL1,G = QUMAL1,G under explicit gate assumptions: measurements can also be eliminated from logarithmic-space quantum verification while preserving perfect completeness
Comments50 pages, 9 figures
