Contemporary quantum computers have relatively high levels of noise, making it difficult to use them to perform useful calculations, even with a large number of qubits. Quantum error correction is expected to eventually enable fault-tolerant quantum computation at large scales, but until then, it will be necessary to use alternative strategies to mitigate the impact of errors. We propose a near-term friendly strategy to mitigate errors by entangling and measuring $M$ copies of a noisy state $\rho$. This enables us to estimate expectation values with respect to a state with dramatically reduced error ${\rho }^M/\mathrm{Tr}({\rho }^M)$ without explicitly preparing it, hence the name “virtual distillation.” As $M$ increases, this state approaches the closest pure state to $\rho$ exponentially quickly. We analyze the effectiveness of virtual distillation and find that it is governed in many regimes by the behavior of this pure state (corresponding to the dominant eigenvector of $\rho$). We numerically demonstrate that virtual distillation is capable of suppressing errors by multiple orders of magnitude and explain how this effect is enhanced as the system size grows. Finally, we show that this technique can improve the convergence of randomized quantum algorithms, even in the absence of device noise.

中文翻译：

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用于减轻量子误差的虚拟蒸馏

当代量子计算机具有相对较高的噪声水平，因此即使有大量量子位，也很难使用它们来执行有用的计算。量子纠错有望最终实现大规模的容错量子计算，但在此之前，有必要使用替代策略来减轻错误的影响。我们提出了一种近期友好的策略，通过纠缠和测量来减少错误$米$ 嘈杂状态的副本 $\rho$. 这使我们能够估计相对于错误显着减少的状态的期望值${\rho }^{米}/\mathrm{时间}({\rho }^{米})$没有明确准备它，因此得名“虚拟蒸馏”。作为$米$ 增加，该状态接近最接近的纯状态 $\rho$以指数方式快速。我们分析了虚拟蒸馏的有效性，发现它在许多情况下都受这种纯状态的行为控制（对应于 $\rho$）。我们在数值上证明了虚拟蒸馏能够将错误抑制多个数量级，并解释了这种效果如何随着系统规模的增长而增强。最后，我们表明即使在没有设备噪声的情况下，该技术也可以提高随机量子算法的收敛性。