Robustness of quantum algorithms against coherent control errors

Daniel Fink, Julian Berberich

Coherent control errors, for which ideal Hamiltonians are perturbed by unknown multiplicative noise terms, are a major obstacle for reliable quantum computing. In this talk, we propose a framework for analyzing robustness of quantum algorithms against coherent control errors using Lipschitz bounds. We present worst-case fidelity bounds which show that the resilience against coherent control errors is mainly influenced by the norms of the Hamiltonians. These bounds are explicitly computable even for large circuits, and they can be used to guarantee fault-tolerance via threshold theorems. Moreover, our theoretical framework can be applied to derive a novel guideline for robust quantum algorithm design and transpilation. This guideline amounts to reducing the norms of the Hamiltonians, which quantify robustness more accurately than existing metrics based on circuit depth or gate count. Further, we discuss the effect of parameter regularization in variational quantum algorithms. We show how our theoretical results can be used to analyze the robustness of the Quantum Fourier Transform for different elementary gate set transpilations. Finally, we present implementation results in simulation and on a quantum computer in order to validate our theoretical findings.

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