Robustness of quantum algorithms: Worst-case fidelity bounds and implications for design

Abstract: Errors occurring on noisy hardware pose a key challenge to reliable quantum computing. Existing techniques such as error correction, mitigation, or suppression typically separate the error handling from the algorithm analysis and design. In this paper, we develop an alternative, algorithm-centered framework for understanding and improving the robustness against errors. For a given quantum algorithm and error model, we derive worst-case fidelity bounds which can be explicitly computed to certify the robustness. We consider general error models including coherent and (Markovian) incoherent errors and allowing for set-based error descriptions to address uncertainty or time-dependence in the errors. Our results give rise to guidelines for robust algorithm design and compilation by optimizing our theoretical robustness measure. Numerical results on algorithm analysis and robust optimization demonstrate the practicality of the framework.