General Framework for Randomized Benchmarking

Research output: Contribution to journalJournal articlepeer-review

Standard

General Framework for Randomized Benchmarking. / Helsen, J.; Roth, K; Onorati, E.; Werner, A. H.; Eisert, J.

In: PRX Quantum, Vol. 3, No. 2, 020357, 16.06.2022.

Research output: Contribution to journalJournal articlepeer-review

Harvard

Helsen, J, Roth, K, Onorati, E, Werner, AH & Eisert, J 2022, 'General Framework for Randomized Benchmarking', PRX Quantum, vol. 3, no. 2, 020357. https://doi.org/10.1103/PRXQuantum.3.020357

APA

Helsen, J., Roth, K., Onorati, E., Werner, A. H., & Eisert, J. (2022). General Framework for Randomized Benchmarking. PRX Quantum, 3(2), [020357]. https://doi.org/10.1103/PRXQuantum.3.020357

Vancouver

Helsen J, Roth K, Onorati E, Werner AH, Eisert J. General Framework for Randomized Benchmarking. PRX Quantum. 2022 Jun 16;3(2). 020357. https://doi.org/10.1103/PRXQuantum.3.020357

Author

Helsen, J. ; Roth, K ; Onorati, E. ; Werner, A. H. ; Eisert, J. / General Framework for Randomized Benchmarking. In: PRX Quantum. 2022 ; Vol. 3, No. 2.

Bibtex

@article{a56f4732e3ff45358d98e3529294d10b,
title = "General Framework for Randomized Benchmarking",
abstract = "Randomized benchmarking refers to a collection of protocols that in the past decade have become central methods for characterizing quantum gates. These protocols aim at efficiently estimating the quality of a set of quantum gates in a way that is resistant to state preparation and measurement errors. Over the years many versions have been developed, however a comprehensive theoretical treatment of randomized benchmarking has been missing. In this work, we develop a rigorous framework of randomized benchmarking general enough to encompass virtually all known protocols as well as novel, more flexible extensions. Overcoming previous limitations on error models and gate sets, this framework allows us, for the first time, to formulate realistic conditions under which we can rigorously guarantee that the output of any randomized benchmarking experiment is well described by a linear combination of matrix exponential decays. We complement this with a detailed analysis of the fitting problem associated with randomized benchmarking data. We introduce modern signal processing techniques to randomized benchmarking, prove analytical sample complexity bounds, and numerically evaluate performance and limitations. In order to reduce the resource demands of this fitting problem, we introduce novel, scalable postprocessing techniques to isolate exponential decays, significantly improving the practical feasibility of a large set of randomized benchmarking protocols. These postprocessing techniques overcome shortcomings in efficiency of several previously proposed methods such as character benchmarking and linear-cross entropy benchmarking. Finally, we discuss, in full generality, how and when randomized benchmarking decay rates can be used to infer quality measures like the average fidelity. On the technical side, our work substantially extends the recently developed Fourier-theoretic perspective on randomized benchmarking by making use of the perturbation theory of invariant subspaces, as well as ideas from signal processing.",
keywords = "QUANTUM, MIXTURES",
author = "J. Helsen and K Roth and E. Onorati and Werner, {A. H.} and J. Eisert",
year = "2022",
month = jun,
day = "16",
doi = "10.1103/PRXQuantum.3.020357",
language = "English",
volume = "3",
journal = "PRX Quantum",
issn = "2691-3399",
publisher = "American Physical Society",
number = "2",

}

RIS

TY - JOUR

T1 - General Framework for Randomized Benchmarking

AU - Helsen, J.

AU - Roth, K

AU - Onorati, E.

AU - Werner, A. H.

AU - Eisert, J.

PY - 2022/6/16

Y1 - 2022/6/16

N2 - Randomized benchmarking refers to a collection of protocols that in the past decade have become central methods for characterizing quantum gates. These protocols aim at efficiently estimating the quality of a set of quantum gates in a way that is resistant to state preparation and measurement errors. Over the years many versions have been developed, however a comprehensive theoretical treatment of randomized benchmarking has been missing. In this work, we develop a rigorous framework of randomized benchmarking general enough to encompass virtually all known protocols as well as novel, more flexible extensions. Overcoming previous limitations on error models and gate sets, this framework allows us, for the first time, to formulate realistic conditions under which we can rigorously guarantee that the output of any randomized benchmarking experiment is well described by a linear combination of matrix exponential decays. We complement this with a detailed analysis of the fitting problem associated with randomized benchmarking data. We introduce modern signal processing techniques to randomized benchmarking, prove analytical sample complexity bounds, and numerically evaluate performance and limitations. In order to reduce the resource demands of this fitting problem, we introduce novel, scalable postprocessing techniques to isolate exponential decays, significantly improving the practical feasibility of a large set of randomized benchmarking protocols. These postprocessing techniques overcome shortcomings in efficiency of several previously proposed methods such as character benchmarking and linear-cross entropy benchmarking. Finally, we discuss, in full generality, how and when randomized benchmarking decay rates can be used to infer quality measures like the average fidelity. On the technical side, our work substantially extends the recently developed Fourier-theoretic perspective on randomized benchmarking by making use of the perturbation theory of invariant subspaces, as well as ideas from signal processing.

AB - Randomized benchmarking refers to a collection of protocols that in the past decade have become central methods for characterizing quantum gates. These protocols aim at efficiently estimating the quality of a set of quantum gates in a way that is resistant to state preparation and measurement errors. Over the years many versions have been developed, however a comprehensive theoretical treatment of randomized benchmarking has been missing. In this work, we develop a rigorous framework of randomized benchmarking general enough to encompass virtually all known protocols as well as novel, more flexible extensions. Overcoming previous limitations on error models and gate sets, this framework allows us, for the first time, to formulate realistic conditions under which we can rigorously guarantee that the output of any randomized benchmarking experiment is well described by a linear combination of matrix exponential decays. We complement this with a detailed analysis of the fitting problem associated with randomized benchmarking data. We introduce modern signal processing techniques to randomized benchmarking, prove analytical sample complexity bounds, and numerically evaluate performance and limitations. In order to reduce the resource demands of this fitting problem, we introduce novel, scalable postprocessing techniques to isolate exponential decays, significantly improving the practical feasibility of a large set of randomized benchmarking protocols. These postprocessing techniques overcome shortcomings in efficiency of several previously proposed methods such as character benchmarking and linear-cross entropy benchmarking. Finally, we discuss, in full generality, how and when randomized benchmarking decay rates can be used to infer quality measures like the average fidelity. On the technical side, our work substantially extends the recently developed Fourier-theoretic perspective on randomized benchmarking by making use of the perturbation theory of invariant subspaces, as well as ideas from signal processing.

KW - QUANTUM

KW - MIXTURES

U2 - 10.1103/PRXQuantum.3.020357

DO - 10.1103/PRXQuantum.3.020357

M3 - Journal article

VL - 3

JO - PRX Quantum

JF - PRX Quantum

SN - 2691-3399

IS - 2

M1 - 020357

ER -

ID: 312370074