The sum of quantum computing errors is the key element both for the estimation and control of errors in quantum computing and for its statistical study. In this article we analyze the sum of two independent quantum computing errors, $X_1$ and $X_2$, and we obtain the formula of the variance of the sum of these errors: $$ V(X_1+X_2)=V(X_1)+V(X_2)-\frac{V(X_1)V(X_2)}{2}. $$ We conjecture that this result holds true for general quantum computing errors and we prove the formula for independent isotropic quantum computing errors.

翻译：量子计算误差之和是量子计算误差估计与控制以及其统计研究的关键要素。本文分析了两个独立量子计算误差$X_1$与$X_2$之和，并推导出这些误差之和的方差公式：$$ V(X_1+X_2)=V(X_1)+V(X_2)-\frac{V(X_1)V(X_2)}{2}. $$ 我们推测该结果对一般量子计算误差均成立，并针对独立各向同性量子计算误差证明了该公式。