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

This content will become publicly available on July 19, 2020

Title: Direct Randomized Benchmarking for Multiqubit Devices

Abstract

Benchmarking methods that can be adapted to multiqubit systems are essential for assessing the overall or “holistic” performance of nascent quantum processors. The current industry standard is Clifford randomized benchmarking (RB), which measures a single error rate that quantifies overall performance. But, scaling Clifford RB to many qubits is surprisingly hard. It has only been performed on one, two, and three qubits as of this writing. This reflects a fundamental inefficiency in Clifford RB: the n-qubit Clifford gates at its core have to be compiled into large circuits over the one- and two-qubit gates native to a device. As n grows, the quality of these Clifford gates quickly degrades, making Clifford RB impractical at relatively low n. In this Letter, we propose a direct RB protocol that mostly avoids compiling. Instead, it uses random circuits over the native gates in a device, which are seeded by an initial layer of Clifford-like randomization. We demonstrate this protocol experimentally on two to five qubits using the publicly available ibmqx5. We believe this to be the greatest number of qubits holistically benchmarked, and this was achieved on a freely available device without any special tuning up. Our protocol retains the simplicity and convenientmore » properties of Clifford RB: it estimates an error rate from an exponential decay. But, it can be extended to processors with more qubits—we present simulations on 10+ qubits—and it reports a more directly informative and flexible error rate than the one reported by Clifford RB. Here, we show how to use this flexibility to measure separate error rates for distinct sets of gates, and we use this method to estimate the average error rate of a set of cnot gates.« less

Authors:
 [1];  [2];  [3];  [3];  [3];  [1]
  1. Sandia National Lab. (SNL-CA), Livermore, CA (United States)
  2. Univ. of Waterloo, Waterloo, ON (Canada)
  3. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Publication Date:
Research Org.:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Sandia National Laboratories, Livermore, CA (United States)
Sponsoring Org.:
IARPA; USDOE
OSTI Identifier:
1544805
Alternate Identifier(s):
OSTI ID: 1543176
Report Number(s):
SAND-2019-7860J
Journal ID: ISSN 0031-9007; PRLTAO; 677251
Grant/Contract Number:  
AC04-94AL85000; NA0003525
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review Letters
Additional Journal Information:
Journal Volume: 123; Journal Issue: 3; Journal ID: ISSN 0031-9007
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 97 MATHEMATICS AND COMPUTING

Citation Formats

Proctor, Timothy J., Carignan-Dugas, Arnaud, Rudinger, Kenneth, Nielsen, Erik, Blume-Kohout, Robin, and Young, Kevin. Direct Randomized Benchmarking for Multiqubit Devices. United States: N. p., 2019. Web. doi:10.1103/PhysRevLett.123.030503.
Proctor, Timothy J., Carignan-Dugas, Arnaud, Rudinger, Kenneth, Nielsen, Erik, Blume-Kohout, Robin, & Young, Kevin. Direct Randomized Benchmarking for Multiqubit Devices. United States. doi:10.1103/PhysRevLett.123.030503.
Proctor, Timothy J., Carignan-Dugas, Arnaud, Rudinger, Kenneth, Nielsen, Erik, Blume-Kohout, Robin, and Young, Kevin. Fri . "Direct Randomized Benchmarking for Multiqubit Devices". United States. doi:10.1103/PhysRevLett.123.030503.
@article{osti_1544805,
title = {Direct Randomized Benchmarking for Multiqubit Devices},
author = {Proctor, Timothy J. and Carignan-Dugas, Arnaud and Rudinger, Kenneth and Nielsen, Erik and Blume-Kohout, Robin and Young, Kevin},
abstractNote = {Benchmarking methods that can be adapted to multiqubit systems are essential for assessing the overall or “holistic” performance of nascent quantum processors. The current industry standard is Clifford randomized benchmarking (RB), which measures a single error rate that quantifies overall performance. But, scaling Clifford RB to many qubits is surprisingly hard. It has only been performed on one, two, and three qubits as of this writing. This reflects a fundamental inefficiency in Clifford RB: the n-qubit Clifford gates at its core have to be compiled into large circuits over the one- and two-qubit gates native to a device. As n grows, the quality of these Clifford gates quickly degrades, making Clifford RB impractical at relatively low n. In this Letter, we propose a direct RB protocol that mostly avoids compiling. Instead, it uses random circuits over the native gates in a device, which are seeded by an initial layer of Clifford-like randomization. We demonstrate this protocol experimentally on two to five qubits using the publicly available ibmqx5. We believe this to be the greatest number of qubits holistically benchmarked, and this was achieved on a freely available device without any special tuning up. Our protocol retains the simplicity and convenient properties of Clifford RB: it estimates an error rate from an exponential decay. But, it can be extended to processors with more qubits—we present simulations on 10+ qubits—and it reports a more directly informative and flexible error rate than the one reported by Clifford RB. Here, we show how to use this flexibility to measure separate error rates for distinct sets of gates, and we use this method to estimate the average error rate of a set of cnot gates.},
doi = {10.1103/PhysRevLett.123.030503},
journal = {Physical Review Letters},
number = 3,
volume = 123,
place = {United States},
year = {2019},
month = {7}
}

Journal Article:
Free Publicly Available Full Text
This content will become publicly available on July 19, 2020
Publisher's Version of Record

Save / Share:

Works referenced in this record:

An addressable quantum dot qubit with fault-tolerant control-fidelity
journal, October 2014

  • Veldhorst, M.; Hwang, J. C. C.; Yang, C. H.
  • Nature Nanotechnology, Vol. 9, Issue 12
  • DOI: 10.1038/nnano.2014.216

Experimental comparison of two quantum computing architectures
journal, March 2017

  • Linke, Norbert M.; Maslov, Dmitri; Roetteler, Martin
  • Proceedings of the National Academy of Sciences, Vol. 114, Issue 13
  • DOI: 10.1073/pnas.1618020114

Optimal Quantum Control Using Randomized Benchmarking
journal, June 2014


Robust Characterization of Loss Rates
journal, August 2015


Hybrid benchmarking of arbitrary quantum gates
journal, June 2017


Self-consistent quantum process tomography
journal, June 2013


What Randomized Benchmarking Actually Measures
journal, September 2017


Stabilizer states and Clifford operations for systems of arbitrary dimensions and modular arithmetic
journal, April 2005


Randomized benchmarking of quantum gates
journal, January 2008


Experimental quantum compressed sensing for a seven-qubit system
journal, May 2017

  • Riofrío, C. A.; Gross, D.; Flammia, S. T.
  • Nature Communications, Vol. 8, Issue 1
  • DOI: 10.1038/ncomms15305

Noise tailoring for scalable quantum computation via randomized compiling
journal, November 2016


Quantifying the quantum gate fidelity of single-atom spin qubits in silicon by randomized benchmarking
journal, March 2015


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


Characterizing errors on qubit operations via iterative randomized benchmarking
journal, January 2016


Improved simulation of stabilizer circuits
journal, November 2004


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


Fast scramblers
journal, October 2008


Randomized benchmarking with gate-dependent noise
journal, January 2018


Investigating the limits of randomized benchmarking protocols
journal, June 2014


Complete randomized benchmarking protocol accounting for leakage errors
journal, October 2015


Local Random Quantum Circuits are Approximate Polynomial-Designs
journal, August 2016

  • Brandão, Fernando G. S. L.; Harrow, Aram W.; Horodecki, Michał
  • Communications in Mathematical Physics, Vol. 346, Issue 2
  • DOI: 10.1007/s00220-016-2706-8

Randomized benchmarking of single- and multi-qubit control in liquid-state NMR quantum information processing
journal, January 2009


Efficient Measurement of Quantum Gate Error by Interleaved Randomized Benchmarking
journal, August 2012


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

Clifford group, stabilizer states, and linear and quadratic operations over GF(2)
journal, October 2003


Symmetrized Characterization of Noisy Quantum Processes
journal, September 2007


Characterizing universal gate sets via dihedral benchmarking
journal, December 2015


Characterization of Addressability by Simultaneous Randomized Benchmarking
journal, December 2012


A quantum-dot spin qubit with coherence limited by charge noise and fidelity higher than 99.9%
journal, December 2017


State preservation by repetitive error detection in a superconducting quantum circuit
journal, March 2015


Three-Qubit Randomized Benchmarking
journal, May 2019


How to efficiently select an arbitrary Clifford group element
journal, December 2014

  • Koenig, Robert; Smolin, John A.
  • Journal of Mathematical Physics, Vol. 55, Issue 12
  • DOI: 10.1063/1.4903507

Complete 3-Qubit Grover search on a programmable quantum computer
journal, December 2017


High-fidelity entangling gate for double-quantum-dot spin qubits
journal, January 2017

  • Nichol, John M.; Orona, Lucas A.; Harvey, Shannon P.
  • npj Quantum Information, Vol. 3, Issue 1
  • DOI: 10.1038/s41534-016-0003-1

Randomized Benchmarking of Single-Qubit Gates in a 2D Array of Neutral-Atom Qubits
journal, March 2015


Measuring and Suppressing Quantum State Leakage in a Superconducting Qubit
journal, January 2016


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

Estimating the fidelity of T gates using standard interleaved randomized benchmarking
journal, March 2017


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


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


From randomized benchmarking experiments to gate-set circuit fidelity: how to interpret randomized benchmarking decay parameters
journal, September 2018

  • Carignan-Dugas, Arnaud; Boone, Kristine; Wallman, Joel J.
  • New Journal of Physics, Vol. 20, Issue 9
  • DOI: 10.1088/1367-2630/aadcc7

Demonstration of a quantum error detection code using a square lattice of four superconducting qubits
journal, April 2015

  • Córcoles, A. D.; Magesan, Easwar; Srinivasan, Srikanth J.
  • Nature Communications, Vol. 6, Issue 1
  • DOI: 10.1038/ncomms7979

Robust calibration of a universal single-qubit gate set via robust phase estimation
journal, December 2015


A programmable two-qubit quantum processor in silicon
journal, February 2018

  • Watson, T. F.; Philips, S. G. J.; Kawakami, E.
  • Nature, Vol. 555, Issue 7698
  • DOI: 10.1038/nature25766

Quantum computing with realistically noisy devices
journal, March 2005


Observation of Entangled States of a Fully Controlled 20-Qubit System
journal, April 2018


Randomized benchmarking with restricted gate sets
journal, June 2018


Resonantly driven CNOT gate for electron spins
journal, December 2017


Estimating the coherence of noise
journal, November 2015


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

Decoupling with Random Quantum Circuits
journal, September 2015


Estimating the Coherence of Noise in Quantum Control of a Solid-State Qubit
journal, December 2016


Real Randomized Benchmarking
journal, August 2018


Characterizing quantum gates via randomized benchmarking
journal, April 2012


Process verification of two-qubit quantum gates by randomized benchmarking
journal, March 2013


Quantification and characterization of leakage errors
journal, March 2018


A blueprint for demonstrating quantum supremacy with superconducting qubits
journal, April 2018


10-Qubit Entanglement and Parallel Logic Operations with a Superconducting Circuit
journal, November 2017