论文标题
使用基于蒙特卡洛的频道反演，准确性与抽样量子折衷的量子折衷
The Accuracy vs. Sampling Overhead Trade-off in Quantum Error Mitigation Using Monte Carlo-Based Channel Inversion
论文作者
论文摘要
量子误差缓解（QEM）是一类有希望的技术，用于减少变异量子算法的计算误差。通常，由于通道反转操作引起的方差增强效果，计算误差降低的成本为开销成本，这最终限制了QEM的适用性。 QEM的现有抽样开销分析通常假定精确的通道反演，这在实际情况下是不现实的。在这篇论文中，我们考虑了基于蒙特卡洛采样的实用渠道反演策略，该策略引入了其他计算错误，而这些误差又可能以额外的采样开销来消除。特别是，我们表明，与无误差结果的动态范围相比，计算误差很小时，它会以门数的平方根缩放。相比之下，在相同假设下没有QEM的情况下，该误差表现出线性缩放，而门的数量则表现出。因此，即使没有额外的抽样开销，QEM的误差缩放仍然是可取的。我们的分析结果伴随着数值示例。
Quantum error mitigation (QEM) is a class of promising techniques for reducing the computational error of variational quantum algorithms. In general, the computational error reduction comes at the cost of a sampling overhead due to the variance-boosting effect caused by the channel inversion operation, which ultimately limits the applicability of QEM. Existing sampling overhead analysis of QEM typically assumes exact channel inversion, which is unrealistic in practical scenarios. In this treatise, we consider a practical channel inversion strategy based on Monte Carlo sampling, which introduces additional computational error that in turn may be eliminated at the cost of an extra sampling overhead. In particular, we show that when the computational error is small compared to the dynamic range of the error-free results, it scales with the square root of the number of gates. By contrast, the error exhibits a linear scaling with the number of gates in the absence of QEM under the same assumptions. Hence, the error scaling of QEM remains to be preferable even without the extra sampling overhead. Our analytical results are accompanied by numerical examples.
