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 »
- Authors:
-
- Sandia National Lab. (SNL-CA), Livermore, CA (United States)
- Univ. of Waterloo, Waterloo, ON (Canada)
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
- Publication Date:
- Research Org.:
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Sandia National Lab. (SNL-CA), 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. https://doi.org/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. https://doi.org/10.1103/PhysRevLett.123.030503. https://www.osti.gov/servlets/purl/1544805.
@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}
}
Free Publicly Available Full Text
Publisher's Version of Record
Other availability
Search WorldCat to find libraries that may hold this journal
Cited by: 7 works
Citation information provided by
Web of Science
Web of Science
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.
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
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
Optimal Quantum Control Using Randomized Benchmarking
journal, June 2014
- Kelly, J.; Barends, R.; Campbell, B.
- Physical Review Letters, Vol. 112, Issue 24
Robust Characterization of Loss Rates
journal, August 2015
- Wallman, Joel J.; Barnhill, Marie; Emerson, Joseph
- Physical Review Letters, Vol. 115, Issue 6
Hybrid benchmarking of arbitrary quantum gates
journal, June 2017
- Chasseur, Tobias; Reich, Daniel M.; Koch, Christiane P.
- Physical Review A, Vol. 95, Issue 6
Self-consistent quantum process tomography
journal, June 2013
- Merkel, Seth T.; Gambetta, Jay M.; Smolin, John A.
- Physical Review A, Vol. 87, Issue 6
What Randomized Benchmarking Actually Measures
journal, September 2017
- Proctor, Timothy; Rudinger, Kenneth; Young, Kevin
- Physical Review Letters, Vol. 119, Issue 13
Stabilizer states and Clifford operations for systems of arbitrary dimensions and modular arithmetic
journal, April 2005
- Hostens, Erik; Dehaene, Jeroen; De Moor, Bart
- Physical Review A, Vol. 71, Issue 4
Randomized benchmarking of quantum gates
journal, January 2008
- Knill, E.; Leibfried, D.; Reichle, R.
- Physical Review A, Vol. 77, Issue 1
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
Noise tailoring for scalable quantum computation via randomized compiling
journal, November 2016
- Wallman, Joel J.; Emerson, Joseph
- Physical Review A, Vol. 94, Issue 5
Quantifying the quantum gate fidelity of single-atom spin qubits in silicon by randomized benchmarking
journal, March 2015
- Muhonen, J. T.; Laucht, A.; Simmons, S.
- Journal of Physics: Condensed Matter, Vol. 27, Issue 15
Superconducting quantum circuits at the surface code threshold for fault tolerance
journal, April 2014
- Barends, R.; Kelly, J.; Megrant, A.
- Nature, Vol. 508, Issue 7497
Characterizing errors on qubit operations via iterative randomized benchmarking
journal, January 2016
- Sheldon, Sarah; Bishop, Lev S.; Magesan, Easwar
- Physical Review A, Vol. 93, Issue 1
Improved simulation of stabilizer circuits
journal, November 2004
- Aaronson, Scott; Gottesman, Daniel
- Physical Review A, Vol. 70, Issue 5
Scalable and Robust Randomized Benchmarking of Quantum Processes
journal, May 2011
- Magesan, Easwar; Gambetta, J. M.; Emerson, Joseph
- Physical Review Letters, Vol. 106, Issue 18
Fast scramblers
journal, October 2008
- Sekino, Yasuhiro; Susskind, L.
- Journal of High Energy Physics, Vol. 2008, Issue 10
Randomized benchmarking with gate-dependent noise
journal, January 2018
- Wallman, Joel J.
- Quantum, Vol. 2
Investigating the limits of randomized benchmarking protocols
journal, June 2014
- Epstein, Jeffrey M.; Cross, Andrew W.; Magesan, Easwar
- Physical Review A, Vol. 89, Issue 6
Complete randomized benchmarking protocol accounting for leakage errors
journal, October 2015
- Chasseur, T.; Wilhelm, F. K.
- Physical Review A, Vol. 92, Issue 4
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
Randomized benchmarking of single- and multi-qubit control in liquid-state NMR quantum information processing
journal, January 2009
- Ryan, C. A.; Laforest, M.; Laflamme, R.
- New Journal of Physics, Vol. 11, Issue 1
Efficient Measurement of Quantum Gate Error by Interleaved Randomized Benchmarking
journal, August 2012
- Magesan, Easwar; Gambetta, Jay M.; Johnson, B. R.
- Physical Review Letters, Vol. 109, Issue 8
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
Clifford group, stabilizer states, and linear and quadratic operations over GF(2)
journal, October 2003
- Dehaene, Jeroen; De Moor, Bart
- Physical Review A, Vol. 68, Issue 4
Symmetrized Characterization of Noisy Quantum Processes
journal, September 2007
- Emerson, J.; Silva, M.; Moussa, O.
- Science, Vol. 317, Issue 5846
Characterizing universal gate sets via dihedral benchmarking
journal, December 2015
- Carignan-Dugas, Arnaud; Wallman, Joel J.; Emerson, Joseph
- Physical Review A, Vol. 92, Issue 6
Characterization of Addressability by Simultaneous Randomized Benchmarking
journal, December 2012
- Gambetta, Jay M.; Córcoles, A. D.; Merkel, S. T.
- Physical Review Letters, Vol. 109, Issue 24
A quantum-dot spin qubit with coherence limited by charge noise and fidelity higher than 99.9%
journal, December 2017
- Yoneda, Jun; Takeda, Kenta; Otsuka, Tomohiro
- Nature Nanotechnology, Vol. 13, Issue 2
State preservation by repetitive error detection in a superconducting quantum circuit
journal, March 2015
- Kelly, J.; Barends, R.; Fowler, A. G.
- Nature, Vol. 519, Issue 7541
Three-Qubit Randomized Benchmarking
journal, May 2019
- McKay, David C.; Sheldon, Sarah; Smolin, John A.
- Physical Review Letters, Vol. 122, Issue 20
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
Complete 3-Qubit Grover search on a programmable quantum computer
journal, December 2017
- Figgatt, C.; Maslov, D.; Landsman, K. A.
- Nature Communications, Vol. 8, Issue 1
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
Randomized Benchmarking of Single-Qubit Gates in a 2D Array of Neutral-Atom Qubits
journal, March 2015
- Xia, T.; Lichtman, M.; Maller, K.
- Physical Review Letters, Vol. 114, Issue 10
Measuring and Suppressing Quantum State Leakage in a Superconducting Qubit
journal, January 2016
- Chen, Zijun; Kelly, Julian; Quintana, Chris
- Physical Review Letters, Vol. 116, Issue 2
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
Estimating the fidelity of T gates using standard interleaved randomized benchmarking
journal, March 2017
- Harper, Robin; Flammia, Steven T.
- Quantum Science and Technology, Vol. 2, Issue 1
Experimental Demonstration of a Cheap and Accurate Phase Estimation
journal, May 2017
- Rudinger, Kenneth; Kimmel, Shelby; Lobser, Daniel
- Physical Review Letters, Vol. 118, Issue 19
Restless Tuneup of High-Fidelity Qubit Gates
journal, April 2017
- Rol, M. A.; Bultink, C. C.; O’Brien, T. E.
- Physical Review Applied, Vol. 7, Issue 4
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
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
Robust calibration of a universal single-qubit gate set via robust phase estimation
journal, December 2015
- Kimmel, Shelby; Low, Guang Hao; Yoder, Theodore J.
- Physical Review A, Vol. 92, Issue 6
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
Quantum computing with realistically noisy devices
journal, March 2005
- Knill, E.
- Nature, Vol. 434, Issue 7029
Observation of Entangled States of a Fully Controlled 20-Qubit System
journal, April 2018
- Friis, Nicolai; Marty, Oliver; Maier, Christine
- Physical Review X, Vol. 8, Issue 2
Randomized benchmarking with restricted gate sets
journal, June 2018
- Brown, Winton G.; Eastin, Bryan
- Physical Review A, Vol. 97, Issue 6
Resonantly driven CNOT gate for electron spins
journal, December 2017
- Zajac, D. M.; Sigillito, A. J.; Russ, M.
- Science, Vol. 359, Issue 6374
Estimating the coherence of noise
journal, November 2015
- Wallman, Joel; Granade, Chris; Harper, Robin
- New Journal of Physics, Vol. 17, Issue 11
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
Decoupling with Random Quantum Circuits
journal, September 2015
- Brown, Winton; Fawzi, Omar
- Communications in Mathematical Physics, Vol. 340, Issue 3
Estimating the Coherence of Noise in Quantum Control of a Solid-State Qubit
journal, December 2016
- Feng, Guanru; Wallman, Joel J.; Buonacorsi, Brandon
- Physical Review Letters, Vol. 117, Issue 26
Real Randomized Benchmarking
journal, August 2018
- Hashagen, A. K.; Flammia, S. T.; Gross, D.
- Quantum, Vol. 2
Characterizing quantum gates via randomized benchmarking
journal, April 2012
- Magesan, Easwar; Gambetta, Jay M.; Emerson, Joseph
- Physical Review A, Vol. 85, Issue 4
Process verification of two-qubit quantum gates by randomized benchmarking
journal, March 2013
- Córcoles, A. D.; Gambetta, Jay M.; Chow, Jerry M.
- Physical Review A, Vol. 87, Issue 3
Quantification and characterization of leakage errors
journal, March 2018
- Wood, Christopher J.; Gambetta, Jay M.
- Physical Review A, Vol. 97, Issue 3
A blueprint for demonstrating quantum supremacy with superconducting qubits
journal, April 2018
- Neill, C.; Roushan, P.; Kechedzhi, K.
- Science, Vol. 360, Issue 6385
10-Qubit Entanglement and Parallel Logic Operations with a Superconducting Circuit
journal, November 2017
- Song, Chao; Xu, Kai; Liu, Wuxin
- Physical Review Letters, Vol. 119, Issue 18
Bootstrapping quantum process tomography via a perturbative ansatz
journal, February 2020
- Govia, L. C. G.; Ribeill, G. J.; Ristè, D.
- Nature Communications, Vol. 11, Issue 1
Demonstration of non-Markovian process characterisation and control on a quantum processor
journal, December 2020
- White, G. A. L.; Hill, C. D.; Pollock, F. A.
- Nature Communications, Vol. 11, Issue 1
Single ion qubit with estimated coherence time exceeding one hour
journal, January 2021
- Wang, Pengfei; Luan, Chun-Yang; Qiao, Mu
- Nature Communications, Vol. 12, Issue 1
Quantum random number generators with entanglement for public randomness testing
journal, January 2020
- Jacak, Janusz E.; Jacak, Witold A.; Donderowicz, Wojciech A.
- Scientific Reports, Vol. 10, Issue 1
Works referencing / citing this record:
Methods for Measuring Magnetic Flux Crosstalk between Tunable Transmons
journal, December 2019
- Abrams, Deanna M.; Didier, Nicolas; Caldwell, Shane A.
- Physical Review Applied, Vol. 12, Issue 6
A polar decomposition for quantum channels (with applications to bounding error propagation in quantum circuits)
journal, August 2019
- Carignan-Dugas, Arnaud; Alexander, Matthew; Emerson, Joseph
- Quantum, Vol. 3