Virtual distillation has been proposed as an error mitigation protocol for estimating the expectation values of observables in quantum algorithms. It proceeds by creating a cyclic permutation of $M$ noisy copies of a quantum state using a sequence of controlled-swap gates. If the noise does not shift the dominant eigenvector of the density operator away from the ideal state, then the error in expectation-value estimation can be exponentially reduced with $M$. In practice, subsequent error mitigation techniques are required to suppress the effect of noise in the cyclic permutation circuit itself, leading to increased experimental complexity. Here, we perform a careful analysis of the effect of uncorrelated, identical noise in the cyclic permutation circuit and find that the estimation of expectation value of observables are robust against dephasing noise. We support the analytical result with numerical simulations and find that $67\%$ of errors are reduced for $M=2$, with physical dephasing error probabilities as high as $10\%$. Our results imply that a broad class of quantum algorithms can be implemented with higher accuracy in the near-term with qubit platforms where non-dephasing errors are suppressed, such as superconducting bosonic qubits and Rydberg atoms.

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用于减轻量子误差的虚拟蒸馏电路中的噪声研究


虚拟蒸馏已被提议作为一种误差缓解协议，用于估计量子算法中可观测值的期望值。它通过使用一系列受控交换门来创建量子态的 $M$ 噪声副本的循环排列。如果噪声没有使密度算子的主特征向量偏离理想状态，则期望值估计的误差可以随着 $M$ 呈指数减少。在实践中，需要后续的错误缓解技术来抑制循环置换电路本身中的噪声影响，从而导致实验复杂性增加。在这里，我们对循环置换电路中不相关、相同噪声的影响进行了仔细分析，发现可观测量期望值的估计对于相移噪声具有鲁棒性。我们通过数值模拟支持分析结果，发现 $M=2$ 时误差减少了 $67\%$，而物理相移误差概率高达 $10\%$。我们的结果意味着，在短期内，可以通过抑制非相移误差的量子位平台（例如超导玻色子量子位和里德伯原子）以更高的精度实现一类广泛的量子算法。