Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:quant-ph/0608246 · Physical Review A

Efficient error characterization in quantum information processing

Benjamin Lévi, Cecilia C. López, Joseph Emerson, David G. Cory

Published Feb 16, 2007• 65 citations
arXivHTMLPDF

Abstract

We describe how to use the fidelity decay as a tool to characterize the errors affecting a quantum information processor through a noise generator ${G}_{\ensuremath{\tau}}$. For weak noise, the initial decay rate of the fidelity proves to be a simple way to measure the magnitude of the different terms in ${G}_{\ensuremath{\tau}}$. When the generator has only terms associated with few-body couplings, our proposal is scalable. We present the explicit protocol for estimating the magnitude of the noise generators when the noise consists of only one- and two-body terms, and describe a method for measuring the parameters of more general noise models. The protocol focuses on obtaining the magnitude with which these terms affect the system during a time step of length $\ensuremath{\tau}$; measurement of this information has critical implications for assessing the scalability of fault-tolerant quantum computation in any physical setup.

DOI
10.1103/physreva.75.022314

Related papers

Characterizing Errors in Quantum Information Processors

Yuval R. Sanders

Error-free computation is an unattainable ideal, yet our world now contains many computers that appear error-free to their users. That such things are possible is explained by sophisticated theorems that demonstrate the possibility of efficiently reducing computational errors introduced by reasonably well-behaved noise. My thesis is about the problem of determining whether noise in prototype quantum information processors is sufficiently well-behaved for fault-tolerant quantum computing to be possible. My work is divided into two themes. The first theme is the interpretation of average gate fidelity, a quantity that has become the standard performance metric for assessing progress towards fault tolerance. I have elucidated the connection between average gate fidelity and the requirements of fault-tolerant quantum computing by demonstrating the limits of fidelity as a proxy for error rate, the usual metric in fault-tolerance literature. I thereby conclude that information additional to fidelity is required to assess progress towards fault-tolerance. The second theme is the characterization of two-level defect systems, a particularly deleterious kind of noise that can affect superconducting-integrated-circuit-based quantum computing prototypes. I have designed statistical experimental design algorithms that can rigorously assess the influence of these defect systems, and I helped develop a proposal to mitigate their influence. I thereby demonstrate that existing experimental techniques can become much more powerful by employing advanced data collection procedures. My work has immediate implications for current research efforts towards the first working quantum computer. Theoretical work should be directed at assessing noise sources using metrics other than average gate fidelity, and future experimental characterization techniques should become more modular in order to incorporate advanced statistical inference techniques like the ones I develop herein.

•May 12, 2016•2 citations

Extensions of Randomized Benchmarking

Marie Barnhill

The characterization of noisy quantum circuits is an important step in the development of large-scale quantum computers. As experimental quantum architectures approach the threshold for fault-tolerant quantum computing, obtaining a benchmark of process fidelities is needed to verify the integrity of the system and ensure functionality. Additionally, the ability to successfully implement a quantum code of choice may depend on the type of noise that is present in the system. It is therefore necessary to characterize not only the fidelity of the process, but also the structure of the noise. \n \nRandomized benchmarking is a characterization protocol which extracts partial information from a noisy quantum process. This thesis gives a detailed review of the randomized benchmarking protocol, and presents the results of three collaborative projects which use techniques similar to randomized benchmarking to obtain previously hidden information. The first protocol is designed to obtain a benchmark on loss errors. This protocol also provides information on the detector efficiency and an additional constraint on estimated parameters from randomized benchmarking. The second protocol is an extension of the first, under the special case of coherent leakage errors, for which we obtain an estimate of the leakage rate. The third protocol provides a method of testing for spatial correlations in noisy processes. This test may be used to determine the correlation structure of errors, and the error correcting codes needed for successful experiments in a particular architecture. All protocols presented in this thesis are scalable, platform-independent and insensitive to state preparation and measurement errors. We also provide results of numerical tests of these protocols for simulated noise, which show their accuracy and robustness.

•Aug 18, 2015•1 citation

Scalable and Robust Randomized Benchmarking of Quantum Processes

Easwar Magesan, Jay Gambetta, Joseph Emerson

In this Letter we propose a fully scalable randomized benchmarking protocol for quantum information processors. We prove that the protocol provides an efficient and reliable estimate of the average error-rate for a set operations (gates) under a very general noise model that allows for both time and gate-dependent errors. In particular we obtain a sequence of fitting models for the observable fidelity decay as a function of a (convergent) perturbative expansion of the gate errors about the mean error. We illustrate the protocol through numerical examples.

arXiv:1009.3639•Physical Review Letters•May 6, 2011•726 citations

Characterizing Noise in Quantum Systems

Easwar Magesan

In practice, quantum systems are not completely isolated from their environment and the resulting system-environment interaction can lead to information leakage from the system. As a result, if a quantum system is to be used for storing or manipulating information, one would like to characterize these environmental noise effects. Such a characterization affords one the ability to design robust methods for preserving the information contained in the system. Unfortunately, completely characterizing the noise in a realistic amount of time is impossible for even moderately large systems. \n \nIn this thesis we discuss methods and diagnostics for partially characterizing quantum noise processes that are especially useful in quantum information and computation. We present a randomized benchmarking protocol that provides a scalable method for determining important properties of the noise affecting the set of gates used on a quantum information processor. We also prove various properties of the quantum gate fidelity, which is a useful state-dependent measure of the distance between two quantum operations, and an important diagnostic of the noise affecting a quantum process. Some non-intuitive generic features of quantum operations acting on large-dimensional quantum systems are also presented.

•Jul 26, 2012•2 citations

Scalable noise estimation with random unitary operators

Joseph Emerson, Robert Alicki, Karol Życzkowski

We describe a scalable stochastic method for the experimental measurement of generalized fidelities characterizing the accuracy of the implementation of a coherent quantum transformation. The method is based on the motion reversal of random unitary operators. In the simplest case our method enables direct estimation of the average gate fidelity. The more general fidelities are characterized by a universal exponential rate of fidelity loss. In all cases the measurable fidelity decrease is directly related to the strength of the noise affecting the implementation, quantified by the trace of the superoperator describing the non-unitary dynamics. While the scalability of our stochastic protocol makes it most relevant in large Hilbert spaces (when quantum process tomography is infeasible), our method should be immediately useful for evaluating the degree of control that is achievable in any prototype quantum processing device. By varying over different experimental arrangements and error-correction strategies, additional information about the noise can be determined.

arXiv:quant-ph/0503243•Journal of Optics B Quantum and Semiclassical Optics•Sep 21, 2005•503 citations

Characterization of Complex Quantum Dynamics with a Scalable NMR Information Processor

Colm A. Ryan, Joseph Emerson, David Poulin +2 more

We present experimental results on the measurement of fidelity decay under contrasting system dynamics using a nuclear magnetic resonance quantum information processor. The measurements were performed by implementing a scalable circuit in the model of deterministic quantum computation with only one quantum bit. The results show measurable differences between regular and complex behavior and for complex dynamics are faithful to the expected theoretical decay rate. Moreover, we illustrate how the experimental method can be seen as an efficient way for either extracting coarse-grained information about the dynamics of a large system or measuring the decoherence rate from engineered environments.

arXiv:quant-ph/0506085•Physical Review Letters•Dec 15, 2005•39 citations
We describe how to use the fidelity decay as a tool to characterize the errors affecting a quantum information processor through a noise generator G\ensuremathτ{G}_{\ensuremath{\tau}}G\ensuremathτ​. For weak noise, the initial decay rate of the fidelity proves to be a simple way to measure the magnitude of the different terms in G\ensuremathτ{G}_{\ensuremath{\tau}}G\ensuremathτ​. When the generator has only terms associated with few-body couplings, our proposal is scalable. We present the explicit protocol for estimating the magnitude of the noise generators when the noise consists of only one- and two-body terms, and describe a method for measuring the parameters of more general noise models. The protocol focuses on obtaining the magnitude with which these terms affect the system during a time step of length \ensuremathτ\ensuremath{\tau}\ensuremathτ; measurement of this information has critical implications for assessing the scalability of fault-tolerant quantum computation in any physical setup.
Error-free computation is an unattainable ideal, yet our world now contains many computers that appear error-free to their users. That such things are possible is explained by sophisticated theorems that demonstrate the possibility of efficiently reducing computational errors introduced by reasonably well-behaved noise. My thesis is about the problem of determining whether noise in prototype quantum information processors is sufficiently well-behaved for fault-tolerant quantum computing to be possible. My work is divided into two themes. The first theme is the interpretation of average gate fidelity, a quantity that has become the standard performance metric for assessing progress towards fault tolerance. I have elucidated the connection between average gate fidelity and the requirements of fault-tolerant quantum computing by demonstrating the limits of fidelity as a proxy for error rate, the usual metric in fault-tolerance literature. I thereby conclude that information additional to fidelity is required to assess progress towards fault-tolerance. The second theme is the characterization of two-level defect systems, a particularly deleterious kind of noise that can affect superconducting-integrated-circuit-based quantum computing prototypes. I have designed statistical experimental design algorithms that can rigorously assess the influence of these defect systems, and I helped develop a proposal to mitigate their influence. I thereby demonstrate that existing experimental techniques can become much more powerful by employing advanced data collection procedures. My work has immediate implications for current research efforts towards the first working quantum computer. Theoretical work should be directed at assessing noise sources using metrics other than average gate fidelity, and future experimental characterization techniques should become more modular in order to incorporate advanced statistical inference techniques like the ones I develop herein.
The characterization of noisy quantum circuits is an important step in the development of large-scale quantum computers. As experimental quantum architectures approach the threshold for fault-tolerant quantum computing, obtaining a benchmark of process fidelities is needed to verify the integrity of the system and ensure functionality. Additionally, the ability to successfully implement a quantum code of choice may depend on the type of noise that is present in the system. It is therefore necessary to characterize not only the fidelity of the process, but also the structure of the noise. \n \nRandomized benchmarking is a characterization protocol which extracts partial information from a noisy quantum process. This thesis gives a detailed review of the randomized benchmarking protocol, and presents the results of three collaborative projects which use techniques similar to randomized benchmarking to obtain previously hidden information. The first protocol is designed to obtain a benchmark on loss errors. This protocol also provides information on the detector efficiency and an additional constraint on estimated parameters from randomized benchmarking. The second protocol is an extension of the first, under the special case of coherent leakage errors, for which we obtain an estimate of the leakage rate. The third protocol provides a method of testing for spatial correlations in noisy processes. This test may be used to determine the correlation structure of errors, and the error correcting codes needed for successful experiments in a particular architecture. All protocols presented in this thesis are scalable, platform-independent and insensitive to state preparation and measurement errors. We also provide results of numerical tests of these protocols for simulated noise, which show their accuracy and robustness.
In this Letter we propose a fully scalable randomized benchmarking protocol for quantum information processors. We prove that the protocol provides an efficient and reliable estimate of the average error-rate for a set operations (gates) under a very general noise model that allows for both time and gate-dependent errors. In particular we obtain a sequence of fitting models for the observable fidelity decay as a function of a (convergent) perturbative expansion of the gate errors about the mean error. We illustrate the protocol through numerical examples.
In practice, quantum systems are not completely isolated from their environment and the resulting system-environment interaction can lead to information leakage from the system. As a result, if a quantum system is to be used for storing or manipulating information, one would like to characterize these environmental noise effects. Such a characterization affords one the ability to design robust methods for preserving the information contained in the system. Unfortunately, completely characterizing the noise in a realistic amount of time is impossible for even moderately large systems. \n \nIn this thesis we discuss methods and diagnostics for partially characterizing quantum noise processes that are especially useful in quantum information and computation. We present a randomized benchmarking protocol that provides a scalable method for determining important properties of the noise affecting the set of gates used on a quantum information processor. We also prove various properties of the quantum gate fidelity, which is a useful state-dependent measure of the distance between two quantum operations, and an important diagnostic of the noise affecting a quantum process. Some non-intuitive generic features of quantum operations acting on large-dimensional quantum systems are also presented.
We describe a scalable stochastic method for the experimental measurement of generalized fidelities characterizing the accuracy of the implementation of a coherent quantum transformation. The method is based on the motion reversal of random unitary operators. In the simplest case our method enables direct estimation of the average gate fidelity. The more general fidelities are characterized by a universal exponential rate of fidelity loss. In all cases the measurable fidelity decrease is directly related to the strength of the noise affecting the implementation, quantified by the trace of the superoperator describing the non-unitary dynamics. While the scalability of our stochastic protocol makes it most relevant in large Hilbert spaces (when quantum process tomography is infeasible), our method should be immediately useful for evaluating the degree of control that is achievable in any prototype quantum processing device. By varying over different experimental arrangements and error-correction strategies, additional information about the noise can be determined.
We present experimental results on the measurement of fidelity decay under contrasting system dynamics using a nuclear magnetic resonance quantum information processor. The measurements were performed by implementing a scalable circuit in the model of deterministic quantum computation with only one quantum bit. The results show measurable differences between regular and complex behavior and for complex dynamics are faithful to the expected theoretical decay rate. Moreover, we illustrate how the experimental method can be seen as an efficient way for either extracting coarse-grained information about the dynamics of a large system or measuring the decoherence rate from engineered environments.