用于经典加速量子错误缓解的光锥着色
Lightcone shading for classically accelerated quantum error mitigation
AI总结：
本文提出“着色光锥”方法，通过经典计算各错误通道对结果偏差的更紧边界来选择性应用PEC，在127量子比特Trotter电路中将运行时间降低约两个数量级。
摘要：
量子错误缓解（QEM）能够通过以偏差换取方差，从含噪量子计算机中恢复准确的期望值，从而使平均结果更加准确，但需要更长时间才能收敛。概率错误抵消（PEC）在QEM方法中脱颖而出，是一种尤为稳健、可控地消除偏差的手段。然而，PEC通常表现出远高于其他方法的方差，在给定错误率下抑制了其在大规模问题中的应用。近期分析表明，通过不缓解位于目标可观测量因果光锥之外的错误，可以降低PEC的方差。本文中，我们通过经典计算电路中每个错误通道对最终结果产生偏差程度的更紧边界，改进了光锥方法。这组边界被我们称为“着色光锥”，能够更有针对性地应用PEC，改善偏差与方差之间的权衡空间，同时阐明电路结构如何决定错误缓解计算的难度。尽管精确计算一个紧的着色光锥具有指数级难度，我们提出了一种算法，即使在适度的经典资源下，也能为某些问题带来实际收益；该算法利用演化错误而非演化状态或可观测量的便利性。在一个127量子比特Trotter电路示例中，与标准光锥PEC相比，该算法将在目标精度下应用PEC所需的运行时间减少约两个数量级，从而扩展了可通过在含噪硬件上直接应用PEC进行计算的问题范围。
英文摘要：
Quantum error mitigation (QEM) can recover accurate expectation values from a noisy quantum computer by trading off bias for variance, such that an averaged result is more accurate but takes longer to converge. Probabilistic error cancellation (PEC) stands out among QEM methods as an especially robust means of controllably eliminating bias. However, PEC often exhibits a much larger variance than other methods, inhibiting application to large problems for a given error rate. Recent analyses have shown that the variance of PEC can be reduced by not mitigating errors lying outside the causal lightcone of the desired observable. Here, we improve the lightcone approach by classically computing tighter bounds on how much each error channel in the circuit can bias the final result. This set of bounds, which we refer to as a "shaded lightcone," enables a more targeted application of PEC, improving the tradespace of bias and variance, while illuminating how the structure of a circuit determines the difficulty of error-mitigated computation. Although a tight shaded lightcone is exponentially hard to compute, we present an algorithm providing a practical benefit for some problems even with modest classical resources, leveraging the ease of evolving an error instead of the state or the observable. The algorithm reduces the runtime that would be needed to apply PEC for a target accuracy in an example 127-qubit Trotter circuit by approximately two orders of magnitude compared to standard lightcone-PEC, expanding the domain of problems that can be computed via direct application of PEC on noisy hardware.
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