Universality of universal single-qubit-gate decomposition with coherent errors

TL;DR

This paper investigates how coherent errors impact the universality of single-qubit gate decompositions in quantum computing, providing analytical insights and methods to mitigate these errors to preserve operation accuracy.

Contribution

It analytically characterizes the effects of coherent errors on the universality of single-qubit gate decompositions and proposes strategies to restore accuracy in quantum operations.

Findings

Some coherent errors do not affect universality.

Certain coherent errors can destroy universality.

Analytical solutions and fidelity metrics are provided for error assessment.

Abstract

To generate arbitrary one- and two-qubit gates, the universal decompositions are usually used in quantum computing, and the universality of these decompositions has been demonstrated. However, in realistic experiments, gate errors may affect the universality of the universal decompositions. Here, we focus on the single-qubit-gate decomposition scheme and study the coherent-error effects on universality. We prove that, in the parameter space which we studied, some kinds of coherent errors will not affect the original universality, but some others will destroy it. We provide the definition and analytical solutions for universality with coherent errors and propose methods to resume the accuracy of the operations with coherent errors based on our analysis. We also give the analytical results for three kinds of fidelities, which provide another metric for universality and comprehensively depict the resilience of the decomposition scheme with various kinds of coherent errors. Our work introduces a different way of thinking for quantum compilation than existing methods.