Randomized Benchmarking as Convolution: Fourier Analysis of Gate Dependent Errors
We show that the Randomized Benchmarking (RB) protocol is a convolution amenable to Fourier space analysis. By adopting the mathematical framework of Fourier transforms of matrix-valued functions on groups established in recent work from Gowers and Hatami \cite{GH15}, we provide an alternative proof...
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| Autores principales: | , , |
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| Formato: | article |
| Lenguaje: | EN |
| Publicado: |
Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
2021
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| Materias: | |
| Acceso en línea: | https://doaj.org/article/111010d3a3a147feb885c0a914a32398 |
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| Sumario: | We show that the Randomized Benchmarking (RB) protocol is a convolution amenable to Fourier space analysis. By adopting the mathematical framework of Fourier transforms of matrix-valued functions on groups established in recent work from Gowers and Hatami \cite{GH15}, we provide an alternative proof of Wallman's \cite{Wallman2018} and Proctor's \cite{Proctor17} bounds on the effect of gate-dependent noise on randomized benchmarking. We show explicitly that as long as our faulty gate-set is close to the targeted representation of the Clifford group, an RB sequence is described by the exponential decay of a process that has exactly two eigenvalues close to one and the rest close to zero. This framework also allows us to construct a gauge in which the average gate-set error is a depolarizing channel parameterized by the RB decay rates, as well as a gauge which maximizes the fidelity with respect to the ideal gate-set. |
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