Effect of isotropic errors on the complexity of Grover's algorithm

Abstract

Isotropic errors have been shown to be immune to conventional error correction techniques. While general theoretical frameworks have been proposed to model such errors, there have been no studies so far analysing their concrete impact on practical use-cases. Here we explore the effect of isotropic errors on the complexity of Grover's search algorithm through numerical simulations, with an analysis of the impact on the algorithm's performance and success probability. The results provide insights into the robustness of Grover's algorithm against isotropic errors, highlighting potential challenges for implementations on noisy quantum hardware. All results presented here are obtained through numerical simulations using the open-source python library \texttt{isotropic} developed as part of this work. The source code, numerical simulations and documentation for the library are available online at https://www.github.com/lazyoracle/isotropic-error-analysis .