arXiv 2408.148282024-08quant-ph

在量子错误检测码中实现弱故障容忍计算

Weakly Fault-Tolerant Computation in a Quantum Error-Detecting Code

Ming Hsieh Department of Electrical and Computer Engineering, University of Southern California（南加州大学明海电气与计算机工程学院）

Christopher Gerhard, Todd A. Brun

备注：: 24 pages, 16 figures; added a citation to the Introduction and clarified the Resource state symmetrization section
发表信息：: Phys. Rev. A 114, 012429 (2026)
DOI：: 10.1103/7pv5-46nd

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AI总结：

本文提出了一种在量子错误检测码中实现弱故障容忍计算的方法，通过测量码的稳定子生成器和附加辅助量子比特，能够检测单个故障门引起的错误，从而在低物理错误概率下提高小规模计算的效率，同时减少传统全故障容忍码的开销。

摘要：

许多当前实现全故障容忍的量子纠错码由于逻辑量子比特与物理量子比特的比例低以及显著的开销，难以在现有的噪声中等标量子计算机上实现，导致无法在近期量子处理器上执行有用规模的量子算法。因此，通常不进行编码进行计算。我们提出了一种介于这两种方法之间的方法：在$[[n,n-2,2]]$量子错误检测码中，通过在计算结束时测量码的稳定子生成器和附加辅助量子比特，能够检测由单个故障门引起的任何错误，从而实现弱故障容忍。我们证明，这在小规模计算中，当物理错误概率足够低时，比无纠错显著优越，并且比实现全故障容忍的码所需的开销要小得多。我们还给出了实现通用量子计算的一组门的构造，这些门在物理旋转门的类比不精确度范围内满足弱故障容忍。

英文摘要：

Many current quantum error-correcting codes that achieve full fault tolerance suffer from having low ratios of logical to physical qubits and significant overhead. This makes them difficult to implement on current noisy intermediate-scale quantum (NISQ) computers and results in the inability to perform quantum algorithms at useful scales with near-term quantum processors. As a result, calculations are generally done without encoding. We propose a middle ground between these two approaches: constructions in the $[[n,n-2,2]]$ quantum error-detecting code that can detect any error from a single faulty gate by measuring the stabilizer generators of the code and additional ancillas at the end of the computation. This achieves weak fault tolerance. As we show, this yields a significant improvement over no error correction for small computations with low enough physical error probabilities and requires much less overhead than codes that achieve full fault tolerance. We give constructions for a set of gates that achieve universal quantum computation in this error-detecting code, while satisfying weak fault tolerance up to analog imprecision on the physical rotation gate.

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