skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Operational, gauge-free quantum tomography

Abstract

As increasingly impressive quantum information processors are realized in laboratories around the world, robust and reliable characterization of these devices is now more urgent than ever. These diagnostics can take many forms, but one of the most popular categories is tomography, where an underlying parameterized model is proposed for a device and inferred by experiments. Here, we introduce and implement efficient operational tomography, which uses experimental observables as these model parameters. This addresses a problem of ambiguity in representation that arises in current tomographic approaches (the gauge problem). Solving the gauge problem enables us to efficiently implement operational tomography in a Bayesian framework computationally, and hence gives us a natural way to include prior information and discuss uncertainty in fit parameters. We demonstrate this new tomography in a variety of different experimentally-relevant scenarios, including standard process tomography, Ramsey interferometry, randomized benchmarking, and gate set tomography.

Authors:
 [1];  [2];  [2];  [3];  [4]
  1. TRIUMF, Vancouver, BC (Canada); Univ. of Waterloo, ON (Canada)
  2. Microsoft Research, Redmond, WA (United States). Quantum Architectures and Computation Group
  3. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
  4. Microsoft Research, Redmond, WA (United States). Quantum Architectures and Computation Group; Univ. of Washington, Seattle, WA (United States); Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
Publication Date:
Research Org.:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1725845
Report Number(s):
SAND-2020-12530J
Journal ID: ISSN 2521-327X; 692239
Grant/Contract Number:  
AC04-94AL85000; NA0003525
Resource Type:
Accepted Manuscript
Journal Name:
Quantum
Additional Journal Information:
Journal Volume: 4; Journal ID: ISSN 2521-327X
Publisher:
Quantum Science Open Community
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

Citation Formats

Di Matteo, Olivia, Gamble, John, Granade, Chris, Rudinger, Kenneth, and Wiebe, Nathan. Operational, gauge-free quantum tomography. United States: N. p., 2020. Web. https://doi.org/10.22331/q-2020-11-17-364.
Di Matteo, Olivia, Gamble, John, Granade, Chris, Rudinger, Kenneth, & Wiebe, Nathan. Operational, gauge-free quantum tomography. United States. https://doi.org/10.22331/q-2020-11-17-364
Di Matteo, Olivia, Gamble, John, Granade, Chris, Rudinger, Kenneth, and Wiebe, Nathan. Tue . "Operational, gauge-free quantum tomography". United States. https://doi.org/10.22331/q-2020-11-17-364. https://www.osti.gov/servlets/purl/1725845.
@article{osti_1725845,
title = {Operational, gauge-free quantum tomography},
author = {Di Matteo, Olivia and Gamble, John and Granade, Chris and Rudinger, Kenneth and Wiebe, Nathan},
abstractNote = {As increasingly impressive quantum information processors are realized in laboratories around the world, robust and reliable characterization of these devices is now more urgent than ever. These diagnostics can take many forms, but one of the most popular categories is tomography, where an underlying parameterized model is proposed for a device and inferred by experiments. Here, we introduce and implement efficient operational tomography, which uses experimental observables as these model parameters. This addresses a problem of ambiguity in representation that arises in current tomographic approaches (the gauge problem). Solving the gauge problem enables us to efficiently implement operational tomography in a Bayesian framework computationally, and hence gives us a natural way to include prior information and discuss uncertainty in fit parameters. We demonstrate this new tomography in a variety of different experimentally-relevant scenarios, including standard process tomography, Ramsey interferometry, randomized benchmarking, and gate set tomography.},
doi = {10.22331/q-2020-11-17-364},
journal = {Quantum},
number = ,
volume = 4,
place = {United States},
year = {2020},
month = {11}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Save / Share:

Works referenced in this record:

Multiqubit randomized benchmarking using few samples
journal, September 2019


Multiple Comparisons among Means
journal, March 1961


Robust online Hamiltonian learning
journal, October 2012


On Wald's Complete Class Theorems
journal, March 1953


Self-consistent quantum process tomography
journal, June 2013


Bayesian estimation and the Kalman filter
journal, November 1995


Detector tomography on IBM quantum computers and mitigation of an imperfect measurement
journal, November 2019


Self-Guided Quantum Tomography
journal, November 2014


What Randomized Benchmarking Actually Measures
journal, September 2017


Randomized benchmarking of quantum gates
journal, January 2008


A practical and efficient approach for Bayesian quantum state estimation
journal, June 2020

  • Lukens, Joseph M.; Law, Kody J. H.; Jasra, Ajay
  • New Journal of Physics, Vol. 22, Issue 6
  • DOI: 10.1088/1367-2630/ab8efa

Superconducting quantum circuits at the surface code threshold for fault tolerance
journal, April 2014


Scalable and Robust Randomized Benchmarking of Quantum Processes
journal, May 2011


Bayesian Confirmation Theory and The Likelihood Principle
journal, February 2007


Randomized benchmarking with gate-dependent noise
journal, January 2018


Minimax quantum state estimation under Bregman divergence
journal, March 2019


Gauge invariant information concerning quantum channels
journal, April 2018


Investigating the limits of randomized benchmarking protocols
journal, June 2014


Experimental quantum verification in the presence of temporally correlated noise
journal, February 2018


Demonstration of a parametrically activated entangling gate protected from flux noise
journal, January 2020

  • Hong, Sabrina S.; Papageorge, Alexander T.; Sivarajah, Prasahnt
  • Physical Review A, Vol. 101, Issue 1
  • DOI: 10.1103/PhysRevA.101.012302

Demonstration of qubit operations below a rigorous fault tolerance threshold with gate set tomography
journal, February 2017

  • Blume-Kohout, Robin; Gamble, John King; Nielsen, Erik
  • Nature Communications, Vol. 8, Issue 1
  • DOI: 10.1038/ncomms14485

Benchmarking a High-Fidelity Mixed-Species Entangling Gate
journal, August 2020


Ancilla-Assisted Quantum Process Tomography
journal, May 2003


Symmetrized Characterization of Noisy Quantum Processes
journal, September 2007


Characterizing universal gate sets via dihedral benchmarking
journal, December 2015


Near-optimal quantum tomography: estimators and bounds
journal, December 2015


Monte Carlo sampling methods using Markov chains and their applications
journal, April 1970


Three-Qubit Randomized Benchmarking
journal, May 2019


Probing Context-Dependent Errors in Quantum Processors
journal, June 2019


Random quantum operations
journal, January 2009


Practical Bayesian tomography
journal, March 2016


On the Optimality of Conditional Expectation as a Bregman Predictor
journal, July 2005

  • Banerjee, A.; Guo, X.; Wang, H.
  • IEEE Transactions on Information Theory, Vol. 51, Issue 7
  • DOI: 10.1109/TIT.2005.850145

Scalable noise estimation with random unitary operators
journal, September 2005

  • Emerson, Joseph; Alicki, Robert; Życzkowski, Karol
  • Journal of Optics B: Quantum and Semiclassical Optics, Vol. 7, Issue 10
  • DOI: 10.1088/1464-4266/7/10/021

Self-Consistent Calibration of Quantum-Gate Sets
journal, April 2020


Experimental Demonstration of a Cheap and Accurate Phase Estimation
journal, May 2017


Restless Tuneup of High-Fidelity Qubit Gates
journal, April 2017


Adaptive Bayesian quantum tomography
journal, May 2012


Optimal, reliable estimation of quantum states
journal, April 2010


Probing quantum processor performance with pyGSTi
journal, July 2020

  • Nielsen, Erik; Rudinger, Kenneth; Proctor, Timothy
  • Quantum Science and Technology, Vol. 5, Issue 4
  • DOI: 10.1088/2058-9565/ab8aa4

Accelerated randomized benchmarking
journal, January 2015


Randomized benchmarking with restricted gate sets
journal, June 2018


Elucidating reaction mechanisms on quantum computers
journal, July 2017

  • Reiher, Markus; Wiebe, Nathan; Svore, Krysta M.
  • Proceedings of the National Academy of Sciences, Vol. 114, Issue 29
  • DOI: 10.1073/pnas.1619152114

Bootstrapping quantum process tomography via a perturbative ansatz
journal, February 2020


Scalable randomised benchmarking of non-Clifford gates
journal, April 2016

  • Cross, Andrew W.; Magesan, Easwar; Bishop, Lev S.
  • npj Quantum Information, Vol. 2, Issue 1
  • DOI: 10.1038/npjqi.2016.12

Random Bures mixed states and the distribution of their purity
journal, January 2010

  • Al Osipov, V.; Sommers, H-J; Życzkowski, K.
  • Journal of Physics A: Mathematical and Theoretical, Vol. 43, Issue 5
  • DOI: 10.1088/1751-8113/43/5/055302

Real Randomized Benchmarking
journal, August 2018


Characterizing quantum gates via randomized benchmarking
journal, April 2012


Rigorous measurement error correction
journal, June 2020


Implementing a universal gate set on a logical qubit encoded in an oscillator
journal, July 2017


QInfer: Statistical inference software for quantum applications
journal, April 2017


Quantum Information Scrambling in a Trapped-Ion Quantum Simulator with Tunable Range Interactions
journal, June 2020