量子计算中算子反向传播与可观测量测量的统一框架
A Unified Framework for Operator Backpropagation and Observable Measurement in Quantum Computing
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中文总结 AI 辅助
本文提出量子计算中算子反向传播与可观测量测量的统一框架，结合逐量子比特对易组确定高效测量协议，分析误差源并研究截断策略以优化量子计算流程。
中文摘要 AI 辅助
退相干对量子电路深度施加了严格限制，催生了降低电路深度的方法。算子反向传播是近期提出的一种通过经典方式将可观测量反向传播穿过子电路以降低电路深度的技术。不过，该方法虽能降低电路深度，却会大幅增加需测量的反向传播可观测量的数量，因此需要一种针对这些反向传播可观测量的高效测量协议。此外，误差会在反向传播过程和测量过程中同时产生，并在最终计算中累积。目前尚无前人研究将算子反向传播与高级测量协议相结合，以及如何联合优化这一组合过程。本文中，我们引入了一种综合框架，该框架基于算子反向传播形成的逐量子比特对易（QWC）组的数量，确定能以最少测量次数达到期望精度水平的合适测量协议。我们分析并分类了工作流程中产生的主要误差源，包括反向传播算法产生的误差、截断误差以及 shots 噪声变化。我们还研究了通过表征反向传播可观测量集合的结构来减少反向传播可观测量数量的截断策略。
英文摘要
Decoherence imposes severe limits on quantum circuit depth, motivating methods to reduce circuit depth. Operator backpropagation has recently been proposed as a way to lower circuit depth by classically backpropagating observables through subcircuits. While it lowers the circuit depth, it also significantly increases the number of backpropagated observables that must be measured. This calls for an efficient measurement protocol tailored to these backpropagated observables. Moreover, errors arise both during the backpropagation procedure and during measurement, and they accumulate in the final computation. No prior work has examined how to integrate operator backpropagation with advanced measurement protocols, and how to jointly optimize the combined process. In this paper, we introduce a comprehensive framework to determine the appropriate measurement protocol to achieve a desired level of accuracy with the fewest number of measurements based on the number of qubit-wise commuting (QWC) groups formed from operator backpropagation. We analyze and categorize the primary sources of error that arise through our workflow, including error incurred from the backpropagation algorithm, truncation error, and shot noise variation. We also examine truncation strategies to reduce the number of backpropagated observables by characterizing the structure of the set of backpropagated observables.
