The DOI matches its Crossref record; 69 of the 71 references it cites were found in a registry or an index.
Direct Randomized Benchmarking for Multiqubit Devices
Open accessAbstract
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. 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.
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“Existing works have already proposed to adopt randomly generated benchmarks for evaluating the error rates of diferent gate operations regarding a particular NISQ device [83, 84, 106].”
From QASMBench: A Low-Level Quantum Benchmark Suite for NISQ Evaluation and Simulation (2023) · cites this paper as [106]
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“however, detailed modeling predicts that the SPAM error is dominated by measurement error for 171 Yb þ [47,48].”
From A Race-Track Trapped-Ion Quantum Processor (2023) · cites this paper as [48]
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Cites
Superconducting quantum circuits at the surface code threshold for fault tolerance
Barends, R., Kelly, J., Megrant, A., Veitia, A., Sank, D., Jeffrey, E., White, T. C., Mutus, J., Fowler, A. G., Campbell, B., et al. (2014) · Nature · doi:10.1038/nature13171 · Cited by 1,733
Improved simulation of stabilizer circuits
Aaronson, S., & Gottesman, D. (2004) · Physical Review A · doi:10.1103/physreva.70.052328 · Cited by 1,515
Quantum computing with realistically noisy devices
Knill, E. (2005) · Nature · doi:10.1038/nature03350 · Cited by 1,184 · cited 1×
“Assume that the gate errors are stochastic, which can be enforced to a good approximation by, e.g., Pauli-frame randomization [51–53] or by following each layer in DRB with a random n -qubit Pauli gate.”
MethodSekino, Y., & Susskind, L. (2008) · Journal of High Energy Physics · doi:10.1088/1126-6708/2008/10/065 · Cited by 1,112
Randomized benchmarking of quantum gates
Knill, E., Leibfried, D., Reichle, R., Britton, J., Blakestad, R. B., Jost, J. D., Langer, C., Ozeri, R., Seidelin, S., & Wineland, D. J. (2008) · Physical Review A · doi:10.1103/physreva.77.012307 · Cited by 1,019
An addressable quantum dot qubit with fault-tolerant control-fidelity
Veldhorst, M., Hwang, J. C. C., Yang, C. H., Leenstra, A., de Ronde, B., Dehollain, J. P., Muhonen, J. T., Hudson, F. E., Itoh, K. M., Morello, A., et al. (2014) · Nature Nanotechnology · doi:10.1038/nnano.2014.216 · Cited by 957
State preservation by repetitive error detection in a superconducting quantum circuit
Kelly, J., Barends, R., Fowler, A. G., Megrant, A., Jeffrey, E. R., White, T., Sank, D., Mutus, J., Campbell, B., Chen, Y., et al. (2015) · Nature · doi:10.1038/nature14270 · Cited by 933
A quantum-dot spin qubit with coherence limited by charge noise and fidelity higher than 99.9%
Yoneda, J., Takeda, K., Otsuka, T., Nakajima, T., Delbecq, M. R., Allison, G., Honda, T., Kodera, T., Oda, S., Hoshi, Y., et al. (2017) · Nature Nanotechnology · doi:10.1038/s41565-017-0014-x · Cited by 906
Scalable and Robust Randomized Benchmarking of Quantum Processes
Magesan, E., Gambetta, J., & Emerson, J. (2011) · Physical Review Letters · doi:10.1103/physrevlett.106.180504 · Cited by 797
A programmable two-qubit quantum processor in silicon
Watson, T. F., Philips, S. G. J., Kawakami, E., Ward, D. R., Scarlino, P., Veldhorst, M., Savage, D. E., Lagally, M. G., Friesen, M. G., Coppersmith, S. N., et al. (2018) · Nature · doi:10.1038/nature25766 · Cited by 739
Resonantly driven CNOT gate for electron spins
Zajac, D. M., Sigillito, A. J., Rimbach-Russ, M., Borjans, F., Taylor, J. M., Burkard, G., & Petta, J. R. (2017) · Science · doi:10.1126/science.aao5965 · Cited by 563
Noise tailoring for scalable quantum computation via randomized compiling
Wallman, J. J., & Emerson, J. (2016) · Physical Review A · doi:10.1103/physreva.94.052325 · Cited by 535
Experimental comparison of two quantum computing architectures
Linke, N. M., Maslov, D., Roetteler, M., Debnath, S., Figgatt, C., Landsman, K. A., Wright, K., & Monroe, C. (2017) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1618020114 · Cited by 508
Scalable noise estimation with random unitary operators
Emerson, J., Alicki, R., & Życzkowski, K. (2005) · Journal of Optics B: Quantum and Semiclassical Optics · doi:10.1088/1464-4266/7/10/021 · Cited by 502
Corcoles, A. D., Magesan, E., Srinivasan, S. J., Cross, A. W., Steffen, M., Gambetta, J., & Chow, J. M. (2015) · Nature Communications · doi:10.1038/ncomms7979 · Cited by 495
A blueprint for demonstrating quantum supremacy with superconducting qubits
Neill, C., Roushan, P., Kechedzhi, K., Boixo, S., Isakov, S. V., Smelyanskiy, V., Megrant, A., Chiaro, B., Dunsworth, A., Arya, K., et al. (2018) · Science · doi:10.1126/science.aao4309 · Cited by 468
10-Qubit Entanglement and Parallel Logic Operations with a Superconducting Circuit
Song, C., Xu, K., Liu, W., Yang, C., Zheng, S., Deng, H., Xie, Q., Huang, K., Guo, Q., Zhang, L., et al. (2017) · Physical Review Letters · doi:10.1103/physrevlett.119.180511 · Cited by 465
Characterizing quantum gates via randomized benchmarking
Magesan, E., Gambetta, J. M., & Emerson, J. (2012) · Physical Review A · doi:10.1103/physreva.85.042311 · Cited by 464
Efficient Measurement of Quantum Gate Error by Interleaved Randomized Benchmarking
Magesan, E., Gambetta, J., Johnson, B., Ryan, C. A., Chow, J. M., Merkel, S., Silva, M. P. D., Keefe, G., Rothwell, M. B., Ohki, T., et al. (2012) · Physical Review Letters · doi:10.1103/physrevlett.109.080505 · Cited by 456
Blume-Kohout, R., Gamble, J. K., Nielsen, E., Rudinger, K., Mizrahi, J., Fortier, K., & Maunz, P. (2017) · Nature Communications · doi:10.1038/ncomms14485 · Cited by 429
Self-citationLocal Random Quantum Circuits are Approximate Polynomial-Designs
Brandão, F. G. S. L., Harrow, A. W., & Horodecki, M. (2016) · Communications in Mathematical Physics · doi:10.1007/s00220-016-2706-8 · Cited by 404
Observation of Entangled States of a Fully Controlled 20-Qubit System
Friis, N., Marty, O., Maier, C., Hempel, C., Holzäpfel, M., Jurcevic, P., Plenio, M. B., Huber, M., Roos, C., Blatt, R., et al. (2018) · Physical Review X · doi:10.1103/physrevx.8.021012 · Cited by 354
Characterization of Addressability by Simultaneous Randomized Benchmarking
Gambetta, J., Corcoles, A. D., Merkel, S., Johnson, B., Smolin, J. A., Chow, J. M., Ryan, C. A., Rigetti, C. T., Poletto, S., Ohki, T., et al. (2012) · Physical Review Letters · doi:10.1103/physrevlett.109.240504 · Cited by 313
Self-consistent quantum process tomography
Merkel, S., Gambetta, J., Smolin, J. A., Poletto, S., Corcoles, A. D., Johnson, B., Ryan, C. A., & Steffen, M. (2013) · Physical Review A · doi:10.1103/physreva.87.062119 · Cited by 308
Measuring and Suppressing Quantum State Leakage in a Superconducting Qubit
Chen, Z., Kelly, J., Quintana, C., Barends, R., Campbell, B., Chen, Y., Chiaro, B., Dunsworth, A., Fowler, A. G., Lucero, E. A., et al. (2016) · Physical Review Letters · doi:10.1103/physrevlett.116.020501 · Cited by 270
Unsupervised Machine Learning on a Hybrid Quantum Computer
Otterbach, J. S., Manenti, R., Alidoust, N., Bestwick, A., Block, M., Bloom, B., Caldwell, S., Didier, N., Fried, E. S., Hong, S., et al. (2017) · arXiv · doi:10.48550/arxiv.1712.05771 · Cited by 263
Symmetrized Characterization of Noisy Quantum Processes
Emerson, J., Silva, M. P. D., Moussa, O., Ryan, C. A., Laforest, M., Baugh, J., Cory, D. G., & Laflamme, R. (2007) · Science · doi:10.1126/science.1145699 · Cited by 259
Optimal Quantum Control Using Randomized Benchmarking
Kelly, J., Barends, R., Campbell, B., Chen, Y., Chen, Z., Chiaro, B., Dunsworth, A., Fowler, A. G., Hoi, I.-C., Jeffrey, E. R., et al. (2014) · Physical Review Letters · doi:10.1103/physrevlett.112.240504 · Cited by 257
Complete 3-Qubit Grover search on a programmable quantum computer
Figgatt, C., Maslov, D. A., Landsman, K. A., Linke, N. M., Debnath, S., & Monroe, C. R. (2017) · Nature Communications · doi:10.1038/s41467-017-01904-7 · Cited by 250
Randomized Benchmarking of Single-Qubit Gates in a 2D Array of Neutral-Atom Qubits
Xia, T., Lichtman, M., Maller, K., Carr, A. W., Piotrowicz, M. J., Isenhower, L., & Saffman, M. (2015) · Physical Review Letters · doi:10.1103/physrevlett.114.100503 · Cited by 249
Introduction to Quantum Gate Set TomographyPreprint
Greenbaum, D. (2015) · arXiv (Cornell University) · doi:10.48550/arxiv.1509.02921 · Cited by 225
Process verification of two-qubit quantum gates by randomized benchmarking
Corcoles, A. D., Gambetta, J., Chow, J. M., Smolin, J. A., Ware, M., Strand, J., Plourde, B. L. T., & Steffen, M. (2013) · Physical Review A · doi:10.1103/physreva.87.030301 · Cited by 218
High-fidelity entangling gate for double-quantum-dot spin qubits
Nichol, J. M., Orona, L., Harvey, S. P., Fallahi, S., Gardner, G. C., Manfra, M. J., & Yacoby, A. (2017) · npj Quantum Information · doi:10.1038/s41534-016-0003-1 · Cited by 217
Estimating the coherence of noise
Wallman, J. J., Granade, C., Harper, R., & Flammia, S. T. (2015) · New Journal of Physics · doi:10.1088/1367-2630/17/11/113020 · Cited by 212
Optimal synthesis of linear reversible circuits
Patel, K. N., Markov, I., & Hayes, J. (2008) · Quantum information & computation · doi:10.26421/qic8.3-4-4 · Cited by 208
Quantification and characterization of leakage errors
Wood, C. J., & Gambetta, J. (2018) · Physical Review A · doi:10.1103/physreva.97.032306 · Cited by 185
Clifford group, stabilizer states, and linear and quadratic operations over GF(2)
Dehaene, J., & De Moor, B. (2003) · Physical Review A · doi:10.1103/physreva.68.042318 · Cited by 183 · cited 4×
“S and v pairs define a valid Clifford – given any S, half of the possible vectors define a valid Clifford [74, 75]).”
BackgroundMethodInfluentialCharacterizing errors on qubit operations via iterative randomized benchmarking
Sheldon, S., Bishop, L. S., Magesan, E., Filipp, S., Chow, J. M., & Gambetta, J. (2016) · Physical Review A · doi:10.1103/physreva.93.012301 · Cited by 161
Three-Qubit Randomized Benchmarking
McKay, D. C., Sheldon, S., Smolin, J. A., Chow, J. M., & Gambetta, J. M. (2019) · Physical Review Letters · doi:10.1103/physrevlett.122.200502 · Cited by 156
Muhonen, J. T., Laucht, A., Simmons, S., Dehollain, J. P., Kalra, R., Hudson, F. E., Freer, S., Itoh, K. M., Jamieson, D. N., McCallum, J. C., et al. (2015) · Journal of Physics Condensed Matter · doi:10.1088/0953-8984/27/15/154205 · Cited by 153
Robust calibration of a universal single-qubit gate set via robust phase estimation
Kimmel, S., Low, G. H., & Yoder, T. J. (2015) · Physical Review A · doi:10.1103/physreva.92.062315 · Cited by 152
Experimental quantum compressed sensing for a seven-qubit system
Riofrío, C. A., Gross, D., Flammia, S. T., Monz, T., Nigg, D., Blatt, R., & Eisert, J. (2017) · Nature Communications · doi:10.1038/ncomms15305 · Cited by 144
Investigating the limits of randomized benchmarking protocols
Epstein, J. M., Cross, A. W., Magesan, E., & Gambetta, J. (2014) · Physical Review A · doi:10.1103/physreva.89.062321 · Cited by 142
What Randomized Benchmarking Actually Measures
Proctor, T. J., Rudinger, K., Young, K. C., Sarovar, M., & Blume-Kohout, R. (2017) · Physical Review Letters · doi:10.1103/physrevlett.119.130502 · Cited by 140
Self-citationStabilizer states and Clifford operations for systems of arbitrary dimensions and modular arithmetic
Hostens, E., Dehaene, J., & Moor, B. D. (2005) · Physical Review A · doi:10.1103/physreva.71.042315 · Cited by 137
Ryan, C. A., Laforest, M., & Laflamme, R. (2009) · New Journal of Physics · doi:10.1088/1367-2630/11/1/013034 · Cited by 123
Randomized benchmarking with gate-dependent noise
Wallman, J. J. (2018) · Quantum · doi:10.22331/q-2018-01-29-47 · Cited by 121
An experimental microarchitecture for a superconducting quantum processor
Fu, X., Rol, M. A., Bultink, C. C., van Someren, J., Khammassi, N., Ashraf, I., Vermeulen, R. F. L., de Sterke, J. C., Vlothuizen, W., Schouten, R. N., et al. (2017) · IEEE/ACM International Symposium on Microarchitecture (MICRO) · doi:10.1145/3123939.3123952 · Cited by 104
Characterizing universal gate sets via dihedral benchmarking
Carignan-Dugas, A., Wallman, J. J., & Emerson, J. (2015) · Physical Review A · doi:10.1103/physreva.92.060302 · Cited by 102
Self-citationHow to efficiently select an arbitrary Clifford group element
König, R., & Smolin, J. A. (2014) · Journal of Mathematical Physics · doi:10.1063/1.4903507 · Cited by 97
Decoupling with Random Quantum Circuits
Brown, W., & Fawzi, O. (2015) · Communications in Mathematical Physics · doi:10.1007/s00220-015-2470-1 · Cited by 96
Scalable randomised benchmarking of non-Clifford gates
Cross, A. W., Magesan, E., Bishop, L. S., Smolin, J. A., & Gambetta, J. M. (2016) · npj Quantum Information · doi:10.1038/npjqi.2016.12 · Cited by 96
Restless Tuneup of High-Fidelity Qubit Gates
Rol, M. A., Bultink, C. C., O’Brien, T. E., de Jong, S. R., Theis, L. S., Fu, X., Luthi, F., Vermeulen, R. F. L., de Sterke, J. C., Bruno, A., et al. (2017) · Physical Review Applied · doi:10.1103/physrevapplied.7.041001 · Cited by 79
Hashagen, A. K., Flammia, S. T., Gross, D., & Wallman, J. J. (2018) · Quantum · doi:10.22331/q-2018-08-22-85 · Cited by 65
Experimental Pauli-frame randomization on a superconducting qubit
Ware, M., Ribeill, G. J., Ristè, D., Ryan, C. A., Johnson, B., & Silva, M. P. D. (2021) · Physical Review A · doi:10.1103/physreva.103.042604 · Cited by 61
Multiqubit randomized benchmarking using few samples
Helsen, J., Wallman, J. J., Flammia, S. T., & Wehner, S. (2019) · Physical Review A · doi:10.1103/physreva.100.032304 · Cited by 57
Efficient Synthesis of Linear Reversible CircuitsPreprint
Patel, K. N., Markov, I., & Hayes, J. (2003) · arXiv (Cornell University) · doi:10.48550/arxiv.quant-ph/0302002 · Cited by 54
Estimating the Coherence of Noise in Quantum Control of a Solid-State Qubit
Feng, G., Wallman, J. J., Buonacorsi, B., Cho, F. H., Park, D. K., Xin, T., Lu, D., Baugh, J., & Laflamme, R. (2016) · Physical Review Letters · doi:10.1103/physrevlett.117.260501 · Cited by 50
Hashagen, A.-L. K., Flammia, S. T., Gross, D., & Wallman, J. J. (2018) · Kölner Universitäts PublikationsServer (Universität zu Köln) · Cited by 49
Robust Characterization of Loss Rates
Wallman, J. J., Barnhill, M., & Emerson, J. (2015) · Physical Review Letters · doi:10.1103/physrevlett.115.060501 · Cited by 46
Randomized benchmarking with restricted gate sets
Brown, W., & Eastin, B. (2018) · Physical Review A · doi:10.1103/physreva.97.062323 · Cited by 44
Estimating the fidelity of T gates using standard interleaved randomized benchmarking
Harper, R., & Flammia, S. T. (2017) · Quantum Science and Technology · doi:10.1088/2058-9565/aa5f8d · Cited by 42
Complete randomized benchmarking protocol accounting for leakage errors
Chasseur, T., & Wilhelm, F. K. (2015) · Physical Review A · doi:10.1103/physreva.92.042333 · Cited by 41
Experimental Demonstration of a Cheap and Accurate Phase Estimation
Rudinger, K., Kimmel, S., Lobser, D., & Maunz, P. (2017) · Physical Review Letters · doi:10.1103/physrevlett.118.190502 · Cited by 40
Self-citationCarignan-Dugas, A., Boone, K., Wallman, J. J., & Emerson, J. (2018) · New Journal of Physics · doi:10.1088/1367-2630/aadcc7 · Cited by 33
Self-citationDirect digital synthesis of microwave waveforms for quantum computingPreprint
Raftery, J. J., Vrajitoarea, A., Zhang, G., Leng, Z., Srinivasan, S. J., & Houck, A. (2017) · arXiv (Cornell University) · doi:10.48550/arxiv.1703.00942 · Cited by 23
Hybrid benchmarking of arbitrary quantum gates
Chasseur, T., Reich, D. M., Koch, C. P., & Wilhelm, F. K. (2017) · Physical Review A · doi:10.1103/physreva.95.062335 · Cited by 21
Engineering superconducting qubit arrays for Quantum Supremacy
Kelly, J. (2018) · Bulletin of the American Physical Society · Cited by 14
Research works printed but not linked: 1
- J. Kelly, 2018, Bull. Am. Phys. Soc.
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Metadata
- Authors
- Proctor, T. J., Carignan-Dugas, A., Rudinger, K., Nielsen, E., Blume-Kohout, R., & Young, K.
- Affiliations
- Sandia National Laboratories California (US)
- University of Waterloo (CA)
- Sandia National Laboratories (US)
- ORCID
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2019-07-19
- Volume
- 123
- Issue
- 3
- Pages
- 030503-030503
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2884175209
- Cited by
- 118
- References
- 71
- Citations by year
- 2026: 8 · 2025: 11 · 2024: 9 · 2023: 19 · 2022: 21 · 2021: 24 · 2020: 22 · 2019: 4
- FWCI
- 8.10
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Licence
- Locations
- Physical Review Letters (publishedVersion)
- arXiv (Cornell University) (publishedVersion)
- PubMed (publishedVersion)
- OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) (submittedVersion)
- arXiv (Cornell University)
- Funders
- U.S. Department of Energy (DE-NA0003525)
- Office of the Director of National Intelligence
- Intelligence Advanced Research Projects Activity
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Information and Cryptography
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Keywords
- randomized benchmarking, gate error rates, IBM Quantum Experience, quantum hardware characterization, exponential decay
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