• Open Access

A Taxonomy of Small Markovian Errors

Robin Blume-Kohout, Marcus P. da Silva, Erik Nielsen, Timothy Proctor, Kenneth Rudinger, Mohan Sarovar, and Kevin Young
PRX Quantum 3, 020335 – Published 13 May 2022

Abstract

Errors in quantum logic gates are usually modeled by quantum process matrices (CPTP maps). But process matrices can be opaque and unwieldy. We show how to transform the process matrix of a gate into an error generator that represents the same information more usefully. We construct a basis of simple and physically intuitive elementary error generators, classify them, and show how to represent the error generator of any gate as a mixture of elementary error generators with various rates. Finally, we show how to build a large variety of reduced models for gate errors by combining elementary error generators and/or entire subsectors of generator space. We conclude with a few examples of reduced models, including one with just 9N2 parameters that describes almost all commonly predicted errors on an N-qubit processor.

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  • Received 17 March 2021
  • Accepted 29 March 2022

DOI:https://doi.org/10.1103/PRXQuantum.3.020335

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & Technology

Authors & Affiliations

Robin Blume-Kohout1,*, Marcus P. da Silva2, Erik Nielsen1, Timothy Proctor3, Kenneth Rudinger1, Mohan Sarovar4, and Kevin Young3

  • 1Quantum Performance Laboratory, Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
  • 2Microsoft Quantum, One Microsoft Way, Redmond, Washington 98052, USA
  • 3Quantum Performance Laboratory, Sandia National Laboratories, Livermore, California 94550, USA
  • 4Sandia National Laboratories, California, Livermore, California 94550, USA

  • *rjblume@sandia.gov

Popular Summary

Quantum logic operations (aka quantum gates) on real physical qubits are famously noisy and imperfect. Errors disrupt useful computations. Quantum error correction can protect against errors but only if the errors are (1) pretty rare and (2) of specific well-understood types. Therefore, much effort goes into measuring and characterizing errors in as-built qubits. Quantum process matrices are traditionally used to describe noisy gates—but they are opaque and hard to analyze. Here, we show how to transform the process matrix of a noisy gate into a beautiful useful representation in terms of “error generators,” which makes it easy to identify the errors affecting a gate and their impact.

Error generators contain the same information as process matrices but they isolate errors and present them as a vector of rates—for various physical processes—that can be subdivided. Every possible error on a multiqubit system is classified into one of four categories—Hamiltonian, stochastic, correlation, or active—that describe fundamentally different error processes. We subclassify them by the qubit(s) they affect. Now, it is easy to disentangle different kinds of errors, measure their magnitude, and reason about them.

A really exciting application is the construction of new parsimonious error models focused on likely errors. We give a few examples. One captures all common errors, with exponentially less complexity than N-qubit process matrices. We are convinced that this construction will open up new frontiers of error modeling and characterization.

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Vol. 3, Iss. 2 — May - July 2022

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It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

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