Fidelity of the sum of independent quantum computing errors

Abstract 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 in an $$n-$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>-</mml:mo> </mml:mrow> </mml:math> qubit and obtain a formula for the fidelity of the sum of these errors. We prove this result for isotropic quantum computing errors and conjecture that it also holds true for general quantum computing errors.