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.
翻译:量子误差缓解(QEM)是减少变量算法计算错误的有希望的技术类别。一般来说,计算误差减少是以采样管理费用为代价的,因为频道反转操作造成差异加速效应,最终限制了QEM的适用性。QEM的现有采样间接管理分析通常假定是精确的频道反向,在实际情况下是不现实的。在这项分析中,我们认为基于蒙特卡洛取样的实用渠道反向战略,它引入了额外的计算错误,而这种错误反过来又可能以额外抽样管理的费用来消除。特别是,我们表明,如果计算错误小于无误结果的动态范围,则它与门数的平方根成比例。相反,错误显示的线性缩放与QEM没有在相同假设下的门数相比。因此,即使没有额外的抽样间接费用,QEM的错误缩放仍然更可取。我们的分析结果附有数字实例。