Broad applications of quantum computers will require error correction (EC). However, quantum hardware roadmaps indicate that physical qubit numbers will remain limited in the foreseeable future, leading to residual logical errors that limit the size and accuracy of achievable computations. Recent work suggested logical error mitigation (LEM), which applies known error mitigation (EM) methods to logical errors, eliminating their effect at the cost of a runtime overhead. Improving the efficiency of LEM is crucial for increasing the logical circuit volumes it enables to execute. We introduce syndrome-aware logical error mitigation (SALEM), which makes use of the syndrome data measured during error correction, when mitigating the logical errors. The runtime overhead of SALEM is exponentially lower than that of previously proposed LEM schemes, resulting in significantly increased circuit volumes that can be executed accurately. Notably, relative to the routinely used combination of error correction and syndrome rejection (post-selection), SALEM increases the size of reliably executable computations by orders of magnitude. In this practical setting in which space and time are both resources that need to be optimized, our work reveals a surprising phenomenon: SALEM, which tightly combines EC with EM, can outperform physical EM even above the standard fault-tolerance threshold. Thus, SALEM can make use of EC in regimes of physical error rates at which EC is commonly deemed useless.

翻译：量子计算机的广泛应用将需要纠错技术。然而，量子硬件发展路线图表明，物理量子比特的数量在可预见的未来仍将受限，导致残留的逻辑错误限制了可执行计算的规模和精度。近期研究提出了逻辑错误缓解方法，该方法将已知的错误缓解技术应用于逻辑错误，以运行时开销为代价消除其影响。提高逻辑错误缓解的效率对于增加其可执行的逻辑电路规模至关重要。我们提出了症候群感知的逻辑错误缓解方法，该方法在缓解逻辑错误时利用了纠错过程中测量的症候群数据。SALEM的运行时开销相较于先前提出的逻辑错误缓解方案呈指数级降低，从而显著增加了可精确执行的电路规模。值得注意的是，相较于常规使用的纠错与症候群拒绝（后选择）组合方案，SALEM将可靠可执行计算的规模提高了数个数量级。在此需要同时优化空间与时间资源的实际场景中，我们的工作揭示了一个令人惊讶的现象：SALEM将纠错与错误缓解紧密结合，其性能甚至能在标准容错阈值之上超越物理错误缓解。因此，SALEM能够在通常认为纠错无效的物理错误率区间内有效利用纠错技术。