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:	Seth T. Merkel, Emily J. Pritchett, Bryan H. Fong
Formato:	article
Lenguaje:	EN
Publicado:	Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften 2021
Materias:	Physics QC1-999
Acceso en línea:	https://doaj.org/article/111010d3a3a147feb885c0a914a32398
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id	oai:doaj.org-article:111010d3a3a147feb885c0a914a32398
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spelling	oai:doaj.org-article:111010d3a3a147feb885c0a914a323982021-11-16T13:31:19ZRandomized Benchmarking as Convolution: Fourier Analysis of Gate Dependent Errors2521-327X10.22331/q-2021-11-16-581https://doaj.org/article/111010d3a3a147feb885c0a914a323982021-11-01T00:00:00Zhttps://quantum-journal.org/papers/q-2021-11-16-581/pdf/https://doaj.org/toc/2521-327XWe 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.Seth T. MerkelEmily J. PritchettBryan H. FongVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenarticlePhysicsQC1-999ENQuantum, Vol 5, p 581 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Physics QC1-999
spellingShingle	Physics QC1-999 Seth T. Merkel Emily J. Pritchett Bryan H. Fong Randomized Benchmarking as Convolution: Fourier Analysis of Gate Dependent Errors
description	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.
format	article
author	Seth T. Merkel Emily J. Pritchett Bryan H. Fong
author_facet	Seth T. Merkel Emily J. Pritchett Bryan H. Fong
author_sort	Seth T. Merkel
title	Randomized Benchmarking as Convolution: Fourier Analysis of Gate Dependent Errors
title_short	Randomized Benchmarking as Convolution: Fourier Analysis of Gate Dependent Errors
title_full	Randomized Benchmarking as Convolution: Fourier Analysis of Gate Dependent Errors
title_fullStr	Randomized Benchmarking as Convolution: Fourier Analysis of Gate Dependent Errors
title_full_unstemmed	Randomized Benchmarking as Convolution: Fourier Analysis of Gate Dependent Errors
title_sort	randomized benchmarking as convolution: fourier analysis of gate dependent errors
publisher	Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
publishDate	2021
url	https://doaj.org/article/111010d3a3a147feb885c0a914a32398
work_keys_str_mv	AT sethtmerkel randomizedbenchmarkingasconvolutionfourieranalysisofgatedependenterrors AT emilyjpritchett randomizedbenchmarkingasconvolutionfourieranalysisofgatedependenterrors AT bryanhfong randomizedbenchmarkingasconvolutionfourieranalysisofgatedependenterrors
_version_	1718426465596342272

Randomized Benchmarking as Convolution: Fourier Analysis of Gate Dependent Errors

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