预处理阶段的量子误差缓解
Quantum Error Mitigation at the pre-processing stage
AI总结：
本文提出一种预处理量子误差缓解方法，利用张量网络在减少计算复杂性和测量开销方面优于传统后处理技术。
摘要：
实现容错量子计算机的现实化仍是一个具有挑战性的任务，迫使当前最先进的量子硬件严重依赖于噪声缓解技术。标准的量子误差缓解通常基于后处理策略。相比之下，本文探讨了一种预处理方法，在进行输出态测量之前就缓解噪声的影响。主要思想是找到一个可观测量Y，使得其在受噪声影响的量子态E(ρ)上的期望值与目标可观测量X在无噪声量子态ρ上的期望值相匹配。我们的方法需要执行一个受噪声影响的量子电路，然后测量替代可观测量Y。在实际场景中，我们的方法的主要促进因素是张量网络。所提出的方法在平均误差、电路深度和复杂性方面优于张量误差缓解（TEM），在测量开销方面接近理论下限。在经典计算复杂性方面，与TEM的后处理计算成本相比，提升幅度大约是10^6倍。这种提升来自于不再需要执行信息完整正算子值测量（IC-POVM）所要求的集合，以及任何其他测度策略。
英文摘要：
The realization of fault-tolerant quantum computers remains a challenging endeavor, forcing state-of-the-art quantum hardware to rely heavily on noise mitigation techniques. Standard quantum error mitigation is typically based on post-processing strategies. In contrast, the present work explores a pre-processing approach, in which the effects of noise are mitigated before performing a measurement on the output state. The main idea is to find an observable $Y$ such that its expectation value on a noisy quantum state $\mathcal{E(ρ)}$ matches the expectation value of a target observable $X$ on the noiseless quantum state $ρ$. Our method requires the execution of a noisy quantum circuit, followed by the measurement of the surrogate observable $Y$. The main enablers of our method in practical scenarios are Tensor Networks. The proposed method improves over Tensor Error Mitigation (TEM) in terms of average error, circuit depth, and complexity, attaining a measurement overhead that approaches the theoretical lower bound. The improvement in terms of classical computation complexity is in the order of $\sim 10^6$ times when compared to the post-processing computational cost of TEM in practical scenarios. Such gain comes from eliminating the need to perform the set of informationally complete positive operator-valued measurements (IC-POVM) required by TEM, as well as any other tomographic strategy.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
