Direct Randomized Benchmarking for Multiqubit Devices

Proctor, Timothy J.; Carignan-Dugas, Arnaud; Rudinger, Kenneth; Nielsen, Erik; Blume-Kohout, Robin; Young, Kevin

doi:10.1103/PhysRevLett.123.030503

Direct Randomized Benchmarking for Multiqubit Devices

Journal Article · Fri Jul 19 00:00:00 EDT 2019 · Physical Review Letters

DOI:https://doi.org/10.1103/PhysRevLett.123.030503· OSTI ID:1544805

Proctor, Timothy J. ^[1]; Carignan-Dugas, Arnaud ^[2]; Rudinger, Kenneth ^[3]; Nielsen, Erik ^[3]; Blume-Kohout, Robin ^[3]; Young, Kevin ^[1]

Sandia National Lab. (SNL-CA), Livermore, CA (United States)
Univ. of Waterloo, Waterloo, ON (Canada)
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

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.

View Accepted Manuscript (DOE)

Research Organization:: Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States); Sandia National Laboratories, Livermore, CA (United States)

Sponsoring Organization:: IARPA; USDOE

Grant/Contract Number:: AC04-94AL85000; NA0003525

OSTI ID:: 1544805

Alternate ID(s):: OSTI ID: 1543176

Report Number(s):: SAND--2019-7860J; 677251

Journal Information:: Physical Review Letters, Journal Name: Physical Review Letters Journal Issue: 3 Vol. 123; ISSN 0031-9007; ISSN PRLTAO

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

References (88)

Decoupling with Random Quantum Circuits Brown, Winton; Fawzi, Omar Communications in Mathematical Physics, Vol. 340, Issue 3 https://doi.org/10.1007/s00220-015-2470-1	journal	September 2015
Local Random Quantum Circuits are Approximate Polynomial-Designs Brandão, Fernando G. S. L.; Harrow, Aram W.; Horodecki, Michał Communications in Mathematical Physics, Vol. 346, Issue 2 https://doi.org/10.1007/s00220-016-2706-8	journal	August 2016
Quantum computing with realistically noisy devices Knill, E. Nature, Vol. 434, Issue 7029 https://doi.org/10.1038/nature03350	journal	March 2005
Superconducting quantum circuits at the surface code threshold for fault tolerance Barends, R.; Kelly, J.; Megrant, A. Nature, Vol. 508, Issue 7497 https://doi.org/10.1038/nature13171	journal	April 2014
State preservation by repetitive error detection in a superconducting quantum circuit Kelly, J.; Barends, R.; Fowler, A. G. Nature, Vol. 519, Issue 7541 https://doi.org/10.1038/nature14270	journal	March 2015
A programmable two-qubit quantum processor in silicon Watson, T. F.; Philips, S. G. J.; Kawakami, E. Nature, Vol. 555, Issue 7698 https://doi.org/10.1038/nature25766	journal	February 2018
Demonstration of qubit operations below a rigorous fault tolerance threshold with gate set tomography Blume-Kohout, Robin; Gamble, John King; Nielsen, Erik Nature Communications, Vol. 8, Issue 1 https://doi.org/10.1038/ncomms14485	journal	February 2017
Experimental quantum compressed sensing for a seven-qubit system Riofrío, C. A.; Gross, D.; Flammia, S. T. Nature Communications, Vol. 8, Issue 1 https://doi.org/10.1038/ncomms15305	journal	May 2017
Demonstration of a quantum error detection code using a square lattice of four superconducting qubits Córcoles, A. D.; Magesan, Easwar; Srinivasan, Srikanth J. Nature Communications, Vol. 6, Issue 1 https://doi.org/10.1038/ncomms7979	journal	April 2015
An addressable quantum dot qubit with fault-tolerant control-fidelity Veldhorst, M.; Hwang, J. C. C.; Yang, C. H. Nature Nanotechnology, Vol. 9, Issue 12 https://doi.org/10.1038/nnano.2014.216	journal	October 2014
Scalable randomised benchmarking of non-Clifford gates Cross, Andrew W.; Magesan, Easwar; Bishop, Lev S. npj Quantum Information, Vol. 2, Issue 1 https://doi.org/10.1038/npjqi.2016.12	journal	April 2016
Complete 3-Qubit Grover search on a programmable quantum computer Figgatt, C.; Maslov, D.; Landsman, K. A. Nature Communications, Vol. 8, Issue 1 https://doi.org/10.1038/s41467-017-01904-7	journal	December 2017
Bootstrapping quantum process tomography via a perturbative ansatz Govia, L. C. G.; Ribeill, G. J.; Ristè, D. Nature Communications, Vol. 11, Issue 1 https://doi.org/10.1038/s41467-020-14873-1	journal	February 2020
Demonstration of non-Markovian process characterisation and control on a quantum processor White, G. A. L.; Hill, C. D.; Pollock, F. A. Nature Communications, Vol. 11, Issue 1 https://doi.org/10.1038/s41467-020-20113-3	journal	December 2020
Single ion qubit with estimated coherence time exceeding one hour Wang, Pengfei; Luan, Chun-Yang; Qiao, Mu Nature Communications, Vol. 12, Issue 1 https://doi.org/10.1038/s41467-020-20330-w	journal	January 2021
High-fidelity entangling gate for double-quantum-dot spin qubits Nichol, John M.; Orona, Lucas A.; Harvey, Shannon P. npj Quantum Information, Vol. 3, Issue 1 https://doi.org/10.1038/s41534-016-0003-1	journal	January 2017
A quantum-dot spin qubit with coherence limited by charge noise and fidelity higher than 99.9% Yoneda, Jun; Takeda, Kenta; Otsuka, Tomohiro Nature Nanotechnology, Vol. 13, Issue 2 https://doi.org/10.1038/s41565-017-0014-x	journal	December 2017
Quantum random number generators with entanglement for public randomness testing Jacak, Janusz E.; Jacak, Witold A.; Donderowicz, Wojciech A. Scientific Reports, Vol. 10, Issue 1 https://doi.org/10.1038/s41598-019-56706-2	journal	January 2020
How to efficiently select an arbitrary Clifford group element Koenig, Robert; Smolin, John A. Journal of Mathematical Physics, Vol. 55, Issue 12 https://doi.org/10.1063/1.4903507	journal	December 2014
Experimental comparison of two quantum computing architectures Linke, Norbert M.; Maslov, Dmitri; Roetteler, Martin Proceedings of the National Academy of Sciences, Vol. 114, Issue 13 https://doi.org/10.1073/pnas.1618020114	journal	March 2017
Quantifying the quantum gate fidelity of single-atom spin qubits in silicon by randomized benchmarking Muhonen, J. T.; Laucht, A.; Simmons, S. Journal of Physics: Condensed Matter, Vol. 27, Issue 15 https://doi.org/10.1088/0953-8984/27/15/154205	journal	March 2015
Fast scramblers Sekino, Yasuhiro; Susskind, L. Journal of High Energy Physics, Vol. 2008, Issue 10 https://doi.org/10.1088/1126-6708/2008/10/065	journal	October 2008
Randomized benchmarking of single- and multi-qubit control in liquid-state NMR quantum information processing Ryan, C. A.; Laforest, M.; Laflamme, R. New Journal of Physics, Vol. 11, Issue 1 https://doi.org/10.1088/1367-2630/11/1/013034	journal	January 2009
Estimating the coherence of noise Wallman, Joel; Granade, Chris; Harper, Robin New Journal of Physics, Vol. 17, Issue 11 https://doi.org/10.1088/1367-2630/17/11/113020	journal	November 2015
From randomized benchmarking experiments to gate-set circuit fidelity: how to interpret randomized benchmarking decay parameters Carignan-Dugas, Arnaud; Boone, Kristine; Wallman, Joel J. New Journal of Physics, Vol. 20, Issue 9 https://doi.org/10.1088/1367-2630/aadcc7	journal	September 2018
Scalable noise estimation with random unitary operators Emerson, Joseph; Alicki, Robert; Życzkowski, Karol Journal of Optics B: Quantum and Semiclassical Optics, Vol. 7, Issue 10 https://doi.org/10.1088/1464-4266/7/10/021	journal	September 2005
Estimating the fidelity of T gates using standard interleaved randomized benchmarking Harper, Robin; Flammia, Steven T. Quantum Science and Technology, Vol. 2, Issue 1 https://doi.org/10.1088/2058-9565/aa5f8d	journal	March 2017
Clifford group, stabilizer states, and linear and quadratic operations over GF(2) Dehaene, Jeroen; De Moor, Bart Physical Review A, Vol. 68, Issue 4 https://doi.org/10.1103/PhysRevA.68.042318	journal	October 2003
Improved simulation of stabilizer circuits Aaronson, Scott; Gottesman, Daniel Physical Review A, Vol. 70, Issue 5 https://doi.org/10.1103/PhysRevA.70.052328	journal	November 2004
Stabilizer states and Clifford operations for systems of arbitrary dimensions and modular arithmetic Hostens, Erik; Dehaene, Jeroen; De Moor, Bart Physical Review A, Vol. 71, Issue 4 https://doi.org/10.1103/PhysRevA.71.042315	journal	April 2005
Randomized benchmarking of quantum gates Knill, E.; Leibfried, D.; Reichle, R. Physical Review A, Vol. 77, Issue 1 https://doi.org/10.1103/PhysRevA.77.012307	journal	January 2008
Characterizing quantum gates via randomized benchmarking Magesan, Easwar; Gambetta, Jay M.; Emerson, Joseph Physical Review A, Vol. 85, Issue 4 https://doi.org/10.1103/PhysRevA.85.042311	journal	April 2012
Process verification of two-qubit quantum gates by randomized benchmarking Córcoles, A. D.; Gambetta, Jay M.; Chow, Jerry M. Physical Review A, Vol. 87, Issue 3 https://doi.org/10.1103/PhysRevA.87.030301	journal	March 2013
Self-consistent quantum process tomography Merkel, Seth T.; Gambetta, Jay M.; Smolin, John A. Physical Review A, Vol. 87, Issue 6 https://doi.org/10.1103/PhysRevA.87.062119	journal	June 2013
Investigating the limits of randomized benchmarking protocols Epstein, Jeffrey M.; Cross, Andrew W.; Magesan, Easwar Physical Review A, Vol. 89, Issue 6 https://doi.org/10.1103/PhysRevA.89.062321	journal	June 2014
Complete randomized benchmarking protocol accounting for leakage errors Chasseur, T.; Wilhelm, F. K. Physical Review A, Vol. 92, Issue 4 https://doi.org/10.1103/PhysRevA.92.042333	journal	October 2015
Characterizing universal gate sets via dihedral benchmarking Carignan-Dugas, Arnaud; Wallman, Joel J.; Emerson, Joseph Physical Review A, Vol. 92, Issue 6 https://doi.org/10.1103/PhysRevA.92.060302	journal	December 2015
Robust calibration of a universal single-qubit gate set via robust phase estimation Kimmel, Shelby; Low, Guang Hao; Yoder, Theodore J. Physical Review A, Vol. 92, Issue 6 https://doi.org/10.1103/PhysRevA.92.062315	journal	December 2015
Characterizing errors on qubit operations via iterative randomized benchmarking Sheldon, Sarah; Bishop, Lev S.; Magesan, Easwar Physical Review A, Vol. 93, Issue 1 https://doi.org/10.1103/PhysRevA.93.012301	journal	January 2016
Noise tailoring for scalable quantum computation via randomized compiling Wallman, Joel J.; Emerson, Joseph Physical Review A, Vol. 94, Issue 5 https://doi.org/10.1103/PhysRevA.94.052325	journal	November 2016
Hybrid benchmarking of arbitrary quantum gates Chasseur, Tobias; Reich, Daniel M.; Koch, Christiane P. Physical Review A, Vol. 95, Issue 6 https://doi.org/10.1103/PhysRevA.95.062335	journal	June 2017
Quantification and characterization of leakage errors Wood, Christopher J.; Gambetta, Jay M. Physical Review A, Vol. 97, Issue 3 https://doi.org/10.1103/PhysRevA.97.032306	journal	March 2018
Randomized benchmarking with restricted gate sets Brown, Winton G.; Eastin, Bryan Physical Review A, Vol. 97, Issue 6 https://doi.org/10.1103/PhysRevA.97.062323	journal	June 2018
Restless Tuneup of High-Fidelity Qubit Gates Rol, M. A.; Bultink, C. C.; O’Brien, T. E. Physical Review Applied, Vol. 7, Issue 4 https://doi.org/10.1103/PhysRevApplied.7.041001	journal	April 2017
Scalable and Robust Randomized Benchmarking of Quantum Processes Magesan, Easwar; Gambetta, J. M.; Emerson, Joseph Physical Review Letters, Vol. 106, Issue 18 https://doi.org/10.1103/PhysRevLett.106.180504	journal	May 2011
Efficient Measurement of Quantum Gate Error by Interleaved Randomized Benchmarking Magesan, Easwar; Gambetta, Jay M.; Johnson, B. R. Physical Review Letters, Vol. 109, Issue 8 https://doi.org/10.1103/PhysRevLett.109.080505	journal	August 2012
Characterization of Addressability by Simultaneous Randomized Benchmarking Gambetta, Jay M.; Córcoles, A. D.; Merkel, S. T. Physical Review Letters, Vol. 109, Issue 24 https://doi.org/10.1103/PhysRevLett.109.240504	journal	December 2012
Optimal Quantum Control Using Randomized Benchmarking Kelly, J.; Barends, R.; Campbell, B. Physical Review Letters, Vol. 112, Issue 24 https://doi.org/10.1103/PhysRevLett.112.240504	journal	June 2014
Randomized Benchmarking of Single-Qubit Gates in a 2D Array of Neutral-Atom Qubits Xia, T.; Lichtman, M.; Maller, K. Physical Review Letters, Vol. 114, Issue 10 https://doi.org/10.1103/PhysRevLett.114.100503	journal	March 2015
Robust Characterization of Loss Rates Wallman, Joel J.; Barnhill, Marie; Emerson, Joseph Physical Review Letters, Vol. 115, Issue 6 https://doi.org/10.1103/PhysRevLett.115.060501	journal	August 2015
Measuring and Suppressing Quantum State Leakage in a Superconducting Qubit Chen, Zijun; Kelly, Julian; Quintana, Chris Physical Review Letters, Vol. 116, Issue 2 https://doi.org/10.1103/PhysRevLett.116.020501	journal	January 2016
Estimating the Coherence of Noise in Quantum Control of a Solid-State Qubit Feng, Guanru; Wallman, Joel J.; Buonacorsi, Brandon Physical Review Letters, Vol. 117, Issue 26 https://doi.org/10.1103/PhysRevLett.117.260501	journal	December 2016
Experimental Demonstration of a Cheap and Accurate Phase Estimation Rudinger, Kenneth; Kimmel, Shelby; Lobser, Daniel Physical Review Letters, Vol. 118, Issue 19 https://doi.org/10.1103/PhysRevLett.118.190502	journal	May 2017
What Randomized Benchmarking Actually Measures Proctor, Timothy; Rudinger, Kenneth; Young, Kevin Physical Review Letters, Vol. 119, Issue 13 https://doi.org/10.1103/PhysRevLett.119.130502	journal	September 2017
10-Qubit Entanglement and Parallel Logic Operations with a Superconducting Circuit Song, Chao; Xu, Kai; Liu, Wuxin Physical Review Letters, Vol. 119, Issue 18 https://doi.org/10.1103/PhysRevLett.119.180511	journal	November 2017
Three-Qubit Randomized Benchmarking McKay, David C.; Sheldon, Sarah; Smolin, John A. Physical Review Letters, Vol. 122, Issue 20 https://doi.org/10.1103/PhysRevLett.122.200502	journal	May 2019
Observation of Entangled States of a Fully Controlled 20-Qubit System Friis, Nicolai; Marty, Oliver; Maier, Christine Physical Review X, Vol. 8, Issue 2 https://doi.org/10.1103/PhysRevX.8.021012	journal	April 2018
Symmetrized Characterization of Noisy Quantum Processes Emerson, J.; Silva, M.; Moussa, O. Science, Vol. 317, Issue 5846 https://doi.org/10.1126/science.1145699	journal	September 2007
A blueprint for demonstrating quantum supremacy with superconducting qubits Neill, C.; Roushan, P.; Kechedzhi, K. Science, Vol. 360, Issue 6385 https://doi.org/10.1126/science.aao4309	journal	April 2018
Resonantly driven CNOT gate for electron spins Zajac, D. M.; Sigillito, A. J.; Russ, M. Science, Vol. 359, Issue 6374 https://doi.org/10.1126/science.aao5965	journal	December 2017
Randomized benchmarking with gate-dependent noise Wallman, Joel J. Quantum, Vol. 2 https://doi.org/10.22331/q-2018-01-29-47	journal	January 2018
Real Randomized Benchmarking Hashagen, A. K.; Flammia, S. T.; Gross, D. Quantum, Vol. 2 https://doi.org/10.22331/q-2018-08-22-85	journal	August 2018
Randomized Benchmarking of Quantum Gates Knill, E.; Leibfried, D.; Reichle, R. arXiv https://doi.org/10.48550/arxiv.0707.0963	text	January 2007
Fast Scramblers Sekino, Yasuhiro; Susskind, Leonard arXiv https://doi.org/10.48550/arxiv.0808.2096	text	January 2008
Self-Consistent Quantum Process Tomography Merkel, Seth T.; Gambetta, Jay M.; Smolin, John A. arXiv https://doi.org/10.48550/arxiv.1211.0322	text	January 2012
Optimal quantum control using randomized benchmarking Kelly, J.; Barends, R.; Campbell, B. arXiv https://doi.org/10.48550/arxiv.1403.0035	text	January 2014
How to efficiently select an arbitrary Clifford group element Koenig, Robert; Smolin, John A. arXiv https://doi.org/10.48550/arxiv.1406.2170	text	January 2014
An addressable quantum dot qubit with fault-tolerant control fidelity Veldhorst, M.; Hwang, J. C. C.; Yang, C. H. arXiv https://doi.org/10.48550/arxiv.1407.1950	text	January 2014
State preservation by repetitive error detection in a superconducting quantum circuit Kelly, J.; Barends, R.; Fowler, A. G. arXiv https://doi.org/10.48550/arxiv.1411.7403	text	January 2014
Randomized benchmarking of single qubit gates in a 2D array of neutral atom qubits Xia, T.; Lichtman, M.; Maller, K. arXiv https://doi.org/10.48550/arxiv.1501.02041	text	January 2015
Estimating the Coherence of Noise Wallman, Joel J.; Granade, Christopher; Harper, Robin arXiv https://doi.org/10.48550/arxiv.1503.07865	text	January 2015
Measuring and Suppressing Quantum State Leakage in a Superconducting Qubit Chen, Zijun; Kelly, Julian; Quintana, Chris arXiv https://doi.org/10.48550/arxiv.1509.05470	text	January 2015
Noise tailoring for scalable quantum computation via randomized compiling Wallman, Joel J.; Emerson, Joseph arXiv https://doi.org/10.48550/arxiv.1512.01098	text	January 2015
Estimating the coherence of noise in quantum control of a solid-state qubit Feng, Guanru; Wallman, Joel J.; Buonacorsi, Brandon arXiv https://doi.org/10.48550/arxiv.1603.03761	text	January 2016
Demonstration of qubit operations below a rigorous fault tolerance threshold with gate set tomography Blume-Kohout, Robin; Gamble, John King; Nielsen, Erik arXiv https://doi.org/10.48550/arxiv.1605.07674	text	January 2016
Hybrid benchmarking of arbitrary quantum gates Chasseur, Tobias; Reich, Daniel M.; Koch, Christiane P. arXiv https://doi.org/10.48550/arxiv.1606.03927	text	January 2016
High-fidelity entangling gate for double-quantum-dot spin qubits Nichol, John M.; Orona, Lucas A.; Harvey, Shannon P. arXiv https://doi.org/10.48550/arxiv.1608.04258	preprint	January 2016
Restless Tuneup of High-Fidelity Qubit Gates Rol, M. A.; Bultink, C. C.; O'Brien, T. E. arXiv https://doi.org/10.48550/arxiv.1611.04815	text	January 2016
Experimental demonstration of cheap and accurate phase estimation Rudinger, Kenneth; Kimmel, Shelby; Lobser, Daniel arXiv https://doi.org/10.48550/arxiv.1702.01763	text	January 2017
Complete 3-Qubit Grover Search on a Programmable Quantum Computer Figgatt, C.; Maslov, D.; Landsman, K. A. arXiv https://doi.org/10.48550/arxiv.1703.10535	text	January 2017
A programmable two-qubit quantum processor in silicon Watson, T. F.; Philips, S. G. J.; Kawakami, E. arXiv https://doi.org/10.48550/arxiv.1708.04214	text	January 2017
A blueprint for demonstrating quantum supremacy with superconducting qubits Neill, C.; Roushan, P.; Kechedzhi, K. arXiv https://doi.org/10.48550/arxiv.1709.06678	text	January 2017
Observation of Entangled States of a Fully Controlled 20-Qubit System Friis, Nicolai; Marty, Oliver; Maier, Christine arXiv https://doi.org/10.48550/arxiv.1711.11092	text	January 2017
Three Qubit Randomized Benchmarking McKay, David C.; Sheldon, Sarah; Smolin, John A. arXiv https://doi.org/10.48550/arxiv.1712.06550	text	January 2017
Real Randomized Benchmarking Hashagen, A. K.; Flammia, S. T.; Gross, D. arXiv https://doi.org/10.48550/arxiv.1801.06121	text	January 2018
The Clifford group, stabilizer states, and linear and quadratic operations over GF(2) Dehaene, Jeroen; De Moor, Bart arXiv https://doi.org/10.48550/arxiv.quant-ph/0304125	text	January 2003
Stabilizer states and Clifford operations for systems of arbitrary dimensions, and modular arithmetic Hostens, Erik; Dehaene, Jeroen; De Moor, Bart arXiv https://doi.org/10.48550/arxiv.quant-ph/0408190	text	January 2004
Scalable Noise Estimation with Random Unitary Operators Emerson, Joseph; Alicki, Robert; Zyczkowski, Karol arXiv https://doi.org/10.48550/arxiv.quant-ph/0503243	text	January 2005

Cited By (4)

Methods for Measuring Magnetic Flux Crosstalk between Tunable Transmons Abrams, Deanna M.; Didier, Nicolas; Caldwell, Shane A. Physical Review Applied, Vol. 12, Issue 6 https://doi.org/10.1103/physrevapplied.12.064022	journal	December 2019
A polar decomposition for quantum channels (with applications to bounding error propagation in quantum circuits) Carignan-Dugas, Arnaud; Alexander, Matthew; Emerson, Joseph Quantum, Vol. 3 https://doi.org/10.22331/q-2019-08-12-173	journal	August 2019
A polar decomposition for quantum channels (with applications to bounding error propagation in quantum circuits) Carignan-Dugas, Arnaud; Alexander, Matthew; Emerson, Joseph arXiv https://doi.org/10.48550/arxiv.1904.08897	text	January 2019
Methods for Measuring Magnetic Flux Crosstalk Between Tunable Transmons Abrams, Deanna M.; Didier, Nicolas; Caldwell, Shane A. arXiv https://doi.org/10.48550/arxiv.1908.11856	text	January 2019