发表机构
University of Oxford; Quantum Motion; Imperial College London（牛津大学; 量子运动; 伦敦帝国理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
从量子纠错视角提出测量驱动逆计算（MBU）代数框架，通过零综合征后选择省去逆计算预言机，并利用原始预言机进行相位校正，实现校正成本、工作空间与重复次数的权衡。
AI 中文摘要
相干逆计算（coherent uncomputation）的成本可能与原计算本身相当，从而产生巨大的时空开销，这在早期容错量子计算机上可能是难以承受的。我们通过量子纠错图像为测量驱动逆计算（MBU）建立了一个代数框架：垃圾寄存器的测量会诱发相对相位，这些相位类似于导致非平凡综合征（syndrome）的错误。仅接受零综合征结果可实现后选择式MBU，从而省去逆计算预言机（uncomputation oracle），但代价是成功率由所填充垃圾支撑集的仿射秩（affine rank）决定，该成功率具有概率性。这个秩可能远小于垃圾量子比特的数量，正如HHL算法的示例所示。随后我们推导出一个结构性条件，在该条件下，原始的逆计算预言机可以被复用来对所有测量结果进行相位校正。零综合征无需校正，而非零综合征的校正可以进一步针对单个测量结果进行适配，以简化电路，正如现有的模运算、QROM和QRAM MBU构造所示。相位校正电路可以通过将其实现与测量诱发相位的表示进行协同优化来进一步简化。选择要校正的综合征类别可以在后选择式、部分校正式和确定式MBU之间进行插值，从而在校正成本、工作空间和重复次数之间实现权衡。
英文摘要
Coherent uncomputation can be as costly as the computation itself, creating substantial spacetime overheads that can be prohibitive on early fault-tolerant quantum computers. We develop an algebraic framework for measurement-based uncomputation (MBU) through a quantum error-correction picture: measurements of the garbage register induce relative phases analogous to errors causing non-trivial syndromes. Accepting only zero-syndrome outcomes achieves post-selected MBU, removing the need for an uncomputation oracle at the cost of a probabilistic success rate determined by the affine rank of the populated garbage support. This rank can be much smaller than the number of garbage qubits, as illustrated through an example of the HHL algorithm. We then derive a structural condition under which the original uncomputation oracle can be reused to correct the phase for all measurement outcomes. No correction is required for the zero syndrome, while corrections for non-zero syndromes can be further adapted to individual measurement outcomes for simpler circuits, as illustrated by existing modular-arithmetic, QROM, and QRAM MBU constructions. Phase-correction circuits can be further simplified by co-optimising their implementation with the representation of the measurement-induced phases. Selecting which syndrome classes to correct interpolates between post-selected, partially corrected, and deterministic MBU, enabling trade-offs among correction cost, workspace, and repetitions.
