We present a method for estimating the number of shots required to achieve a desired variance in the results of a quantum circuit. First, we establish a baseline for single-qubit characterisation of individual noise sources. We then move on to multi-qubit circuits, focusing on expectation-value circuits. We decompose the variance of the estimator into a sum of a statistical term and a bias floor. These are independently estimated with one additional run of the circuit. We test our method on a Variational Quantum Eigensolver for $H_2$ and show that we can predict the variance to within known error bounds. We go on to show that for IBM Pittsburgh's noise characteristics, at that instant, 7000 shots for the given circuit would have achieved a $σ^2 \approx 0.01$

翻译：本文提出了一种估计量子电路结果达到期望方差所需测量次数的方法。首先，我们为单量子比特的独立噪声源表征建立了基准。随后扩展到多量子比特电路，重点关注期望值电路。我们将估计量的方差分解为统计项与偏差底限之和，并通过电路的额外单次运行独立估计这两项。我们在$H_2$分子的变分量子本征求解器上测试了该方法，结果表明可在已知误差范围内预测方差。进一步分析表明，针对当时IBM Pittsburgh的噪声特性，给定电路进行7000次测量即可实现$σ^2 \approx 0.01$的方差水平。