Gate Set Tomography

Nielsen, Erik; Gamble, John King; Rudinger, Kenneth; Scholten, Travis; Young, Kevin; Blume-Kohout, Robin

doi:10.22331/q-2021-10-05-557

Gate Set Tomography

Journal Article · 05 October 2021 · Quantum

DOI:https://doi.org/10.22331/q-2021-10-05-557· OSTI ID:1828793

Nielsen, Erik ^[1]; Gamble, John King ^[2]; Rudinger, Kenneth ^[1]; Scholten, Travis ^[3]; Young, Kevin ^[1]; Blume-Kohout, Robin ^[1]

Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Microsoft Research, Redmond, WA (United States)
IBM, Yorktown Heights, NY (United States). Thomas J. Watson Research Center

Gate set tomography (GST) is a protocol for detailed, predictive characterization of logic operations (gates) on quantum computing processors. Early versions of GST emerged around 2012-13, and since then it has been refined, demonstrated, and used in a large number of experiments. This paper presents the foundations of GST in comprehensive detail. The most important feature of GST, compared to older state and process tomography protocols, is that it is calibration-free . GST does not rely on pre-calibrated state preparations and measurements. Instead, it characterizes all the operations in a gate set simultaneously and self-consistently, relative to each other. Long sequence GST can estimate gates with very high precision and efficiency, achieving Heisenberg scaling in regimes of practical interest. In this paper, we cover GST's intellectual history, the techniques and experiments used to achieve its intended purpose, data analysis, gauge freedom and fixing, error bars, and the interpretation of gauge-fixed estimates of gate sets. Our focus is fundamental mathematical aspects of GST, rather than implementation details, but we touch on some of the foundational algorithmic tricks used in the pyGSTi implementation.

View Accepted Manuscript (DOE)

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

Sponsoring Organization:: USDOE Laboratory Directed Research and Development (LDRD) Program; USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

Grant/Contract Number:: NA0003525

OSTI ID:: 1828793

Report Number(s):: SAND--2021-10706J; 699056

Journal Information:: Quantum, Journal Name: Quantum Vol. 5; ISSN 2521-327X

Publisher:: Quantum Science Open CommunityCopyright Statement

Country of Publication:: United States

Language:: English

References (172)

Accomplishments, malfeasances, misfeasances and nonfeasances Ferrie, Jane E. International Journal of Epidemiology, Vol. 45, Issue 2 https://doi.org/10.1093/ije/dyw068	journal	April 2016
Machine Learning of Noise-Resilient Quantum Circuits Cincio, Lukasz; Rudinger, Kenneth; Sarovar, Mohan PRX Quantum, Vol. 2, Issue 1 https://doi.org/10.1103/prxquantum.2.010324	journal	February 2021
Focus on quantum tomography Banaszek, K.; Cramer, M.; Gross, D. Universität Ulm https://doi.org/10.18725/oparu-46943	other	January 2013
On discrete structures in finite Hilbert spaces Bengtsson, Ingemar; Zyczkowski, Karol arXiv https://doi.org/10.48550/arxiv.1701.07902	preprint	January 2017
Detecting and tracking drift in quantum information processors Proctor, Timothy; Revelle, Melissa; Nielsen, Erik arXiv https://doi.org/10.48550/arxiv.1907.13608	text	January 2019
Robust and efficient algorithms for high-dimensional black-box quantum optimization Leng, Zhaoqi; Mundada, Pranav; Ghadimi, Saeed arXiv https://doi.org/10.48550/arxiv.1910.03591	preprint	January 2019
States, Effects, and Operations Fundamental Notions of Quantum Theory Kraus, Karl; Böhm, A.; Dollard, J. D. https://doi.org/10.1007/3-540-12732-1	book	January 1983
On the generators of quantum dynamical semigroups Lindblad, G. Communications in Mathematical Physics, Vol. 48, Issue 2 https://doi.org/10.1007/BF01608499	journal	June 1976
Quantum Tomography under Prior Information Heinosaari, Teiko; Mazzarella, Luca; Wolf, Michael M. Communications in Mathematical Physics, Vol. 318, Issue 2 https://doi.org/10.1007/s00220-013-1671-8	journal	February 2013
How to best sample a periodic probability distribution, or on the accuracy of Hamiltonian finding strategies Ferrie, Christopher; Granade, Christopher E.; Cory, D. G. Quantum Information Processing, Vol. 12, Issue 1 https://doi.org/10.1007/s11128-012-0407-6	journal	April 2012
Completely positive linear maps on complex matrices Choi, Man-Duen Linear Algebra and its Applications, Vol. 10, Issue 3 https://doi.org/10.1016/0024-3795(75)90075-0	journal	June 1975
Linear transformations which preserve trace and positive semidefiniteness of operators Jamiołkowski, A. Reports on Mathematical Physics, Vol. 3, Issue 4 https://doi.org/10.1016/0034-4877(72)90011-0	journal	December 1972
Benchmarking gate-based quantum computers Michielsen, Kristel; Nocon, Madita; Willsch, Dennis Computer Physics Communications, Vol. 220 https://doi.org/10.1016/j.cpc.2017.06.011	journal	November 2017
Pauli semigroups and unistochastic quantum channels Puchała, Zbigniew; Rudnicki, Łukasz; Życzkowski, Karol Physics Letters A, Vol. 383, Issue 20 https://doi.org/10.1016/j.physleta.2019.04.057	journal	July 2019
Convex Optimization Boyd, Stephen; Vandenberghe, Lieven https://doi.org/10.1017/CBO9780511804441	book	January 2004
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
Quantum control and process tomography of a semiconductor quantum dot hybrid qubit Kim, Dohun; Shi, Zhan; Simmons, C. B. Nature, Vol. 511, Issue 7507 https://doi.org/10.1038/nature13407	journal	July 2014
Demonstration of a small programmable quantum computer with atomic qubits Debnath, S.; Linke, N. M.; Figgatt, C. Nature, Vol. 536, Issue 7614 https://doi.org/10.1038/nature18648	journal	August 2016
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
A trapped-ion-based quantum byte with 10−5 next-neighbour cross-talk Piltz, C.; Sriarunothai, T.; Varón, A. F. Nature Communications, Vol. 5, Issue 1 https://doi.org/10.1038/ncomms5679	journal	August 2014
Nuclear spin effects in semiconductor quantum dots Chekhovich, E. A.; Makhonin, M. N.; Tartakovskii, A. I. Nature Materials, Vol. 12, Issue 6 https://doi.org/10.1038/nmat3652	journal	May 2013
Self-consistent measurement and state tomography of an exchange-only spin qubit Medford, J.; Beil, J.; Taylor, J. M. Nature Nanotechnology, Vol. 8, Issue 9 https://doi.org/10.1038/nnano.2013.168	journal	September 2013
Microwave-driven coherent operation of a semiconductor quantum dot charge qubit Kim, Dohun; Ward, D. R.; Simmons, C. B. Nature Nanotechnology, Vol. 10, Issue 3 https://doi.org/10.1038/nnano.2014.336	journal	February 2015
Tomography of quantum detectors Lundeen, J. S.; Feito, A.; Coldenstrodt-Ronge, H. Nature Physics, Vol. 5, Issue 1 https://doi.org/10.1038/nphys1133	journal	November 2008
Quantum process tomography of a universal entangling gate implemented with Josephson phase qubits Bialczak, R. C.; Ansmann, M.; Hofheinz, M. Nature Physics, Vol. 6, Issue 6 https://doi.org/10.1038/nphys1639	journal	April 2010
Experimental quantum Hamiltonian learning Wang, Jianwei; Paesani, Stefano; Santagati, Raffaele Nature Physics, Vol. 13, Issue 6 https://doi.org/10.1038/nphys4074	journal	March 2017
Characterizing large-scale quantum computers via cycle benchmarking Erhard, Alexander; Wallman, Joel J.; Postler, Lukas Nature Communications, Vol. 10, Issue 1 https://doi.org/10.1038/s41467-019-13068-7	journal	November 2019
Benchmarking an 11-qubit quantum computer Wright, K.; Beck, K. M.; Debnath, S. Nature Communications, Vol. 10, Issue 1 https://doi.org/10.1038/s41467-019-13534-2	journal	November 2019
Error-mitigated quantum gates exceeding physical fidelities in a trapped-ion system Zhang, Shuaining; Lu, Yao; Zhang, Kuan Nature Communications, Vol. 11, Issue 1 https://doi.org/10.1038/s41467-020-14376-z	journal	January 2020
Detecting and tracking drift in quantum information processors Proctor, Timothy; Revelle, Melissa; Nielsen, Erik Nature Communications, Vol. 11, Issue 1 https://doi.org/10.1038/s41467-020-19074-4	journal	October 2020
Density-matrix simulation of small surface codes under current and projected experimental noise O’Brien, T. E.; Tarasinski, B.; DiCarlo, L. npj Quantum Information, Vol. 3, Issue 1 https://doi.org/10.1038/s41534-017-0039-x	journal	September 2017
Experimental quantum verification in the presence of temporally correlated noise Mavadia, S.; Edmunds, C. L.; Hempel, C. npj Quantum Information, Vol. 4, Issue 1 https://doi.org/10.1038/s41534-017-0052-0	journal	February 2018
Spectral quantum tomography Helsen, Jonas; Battistel, Francesco; Terhal, Barbara M. npj Quantum Information, Vol. 5, Issue 1 https://doi.org/10.1038/s41534-019-0189-0	journal	September 2019
Quantum chemistry as a benchmark for near-term quantum computers McCaskey, Alexander J.; Parks, Zachary P.; Jakowski, Jacek npj Quantum Information, Vol. 5, Issue 1 https://doi.org/10.1038/s41534-019-0209-0	journal	November 2019
Characterizing quantum supremacy in near-term devices Boixo, Sergio; Isakov, Sergei V.; Smelyanskiy, Vadim N. Nature Physics, Vol. 14, Issue 6 https://doi.org/10.1038/s41567-018-0124-x	journal	April 2018
Predicting many properties of a quantum system from very few measurements Huang, Hsin-Yuan; Kueng, Richard; Preskill, John Nature Physics, Vol. 16, Issue 10 https://doi.org/10.1038/s41567-020-0932-7	journal	June 2020
Fidelity benchmarks for two-qubit gates in silicon Huang, W.; Yang, C. H.; Chan, K. W. Nature, Vol. 569, Issue 7757 https://doi.org/10.1038/s41586-019-1197-0	journal	May 2019
Quantum supremacy using a programmable superconducting processor Arute, Frank; Arya, Kunal; Babbush, Ryan Nature, Vol. 574, Issue 7779 https://doi.org/10.1038/s41586-019-1666-5	journal	October 2019
Decoherence and control of a qubit in spin baths: an exact master equation study Jing, Jun; Wu, Lian-Ao Scientific Reports, Vol. 8, Issue 1 https://doi.org/10.1038/s41598-018-19977-9	journal	January 2018
Quantum process tomography of the quantum Fourier transform Weinstein, Yaakov S.; Havel, Timothy F.; Emerson, Joseph The Journal of Chemical Physics, Vol. 121, Issue 13 https://doi.org/10.1063/1.1785151	journal	October 2004
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
Prescription for experimental determination of the dynamics of a quantum black box Chuang, Isaac L.; Nielsen, M. A. Journal of Modern Optics, Vol. 44, Issue 11-12 https://doi.org/10.1080/09500349708231894	journal	November 1997
Experimental Hamiltonian Learning of an 11-Qubit Solid-State Quantum Spin Register ^* Hou, P. -Y.; He, L.; Wang, F. Chinese Physics Letters, Vol. 36, Issue 10 https://doi.org/10.1088/0256-307X/36/10/100303	journal	October 2019
Tight informationally complete quantum measurements Scott, A. J. Journal of Physics A: Mathematical and General, Vol. 39, Issue 43 https://doi.org/10.1088/0305-4470/39/43/009	journal	October 2006
Optimal, reliable estimation of quantum states Blume-Kohout, Robin New Journal of Physics, Vol. 12, Issue 4 https://doi.org/10.1088/1367-2630/12/4/043034	journal	April 2010
Robust online Hamiltonian learning Granade, Christopher E.; Ferrie, Christopher; Wiebe, Nathan New Journal of Physics, Vol. 14, Issue 10 https://doi.org/10.1088/1367-2630/14/10/103013	journal	October 2012
Self-calibrating quantum state tomography Brańczyk, A. M.; Mahler, D. H.; Rozema, L. A. New Journal of Physics, Vol. 14, Issue 8 https://doi.org/10.1088/1367-2630/14/8/085003	journal	August 2012
Self-calibration for self-consistent tomography Mogilevtsev, D.; Řeháček, J.; Hradil, Z. New Journal of Physics, Vol. 14, Issue 9 https://doi.org/10.1088/1367-2630/14/9/095001	journal	September 2012
Quantum tomography via compressed sensing: error bounds, sample complexity and efficient estimators Flammia, Steven T.; Gross, David; Liu, Yi-Kai New Journal of Physics, Vol. 14, Issue 9 https://doi.org/10.1088/1367-2630/14/9/095022	journal	September 2012
Optimal error regions for quantum state estimation Shang, Jiangwei; Ng, Hui Khoon; Sehrawat, Arun New Journal of Physics, Vol. 15, Issue 12 https://doi.org/10.1088/1367-2630/15/12/123026	journal	December 2013
Focus on quantum tomography Banaszek, K.; Cramer, M.; Gross, D. New Journal of Physics, Vol. 15, Issue 12 https://doi.org/10.1088/1367-2630/15/12/125020	journal	December 2013
Randomized benchmarking with confidence Wallman, Joel J.; Flammia, Steven T. New Journal of Physics, Vol. 16, Issue 10 https://doi.org/10.1088/1367-2630/16/10/103032	journal	October 2014
High posterior density ellipsoids of quantum states Ferrie, Christopher New Journal of Physics, Vol. 16, Issue 2 https://doi.org/10.1088/1367-2630/16/2/023006	journal	February 2014
Hamiltonian tomography: the quantum (system) measurement problem Cole, Jared H. New Journal of Physics, Vol. 17, Issue 10 https://doi.org/10.1088/1367-2630/17/10/101001	journal	September 2015
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
Hamiltonian tomography for quantum many-body systems with arbitrary couplings Wang, Sheng-Tao; Deng, Dong-Ling; Duan, L-M New Journal of Physics, Vol. 17, Issue 9 https://doi.org/10.1088/1367-2630/17/9/093017	journal	September 2015
Optimization of a solid-state electron spin qubit using gate set tomography Dehollain, Juan P.; Muhonen, Juha T.; Blume-Kohout, Robin New Journal of Physics, Vol. 18, Issue 10 https://doi.org/10.1088/1367-2630/18/10/103018	journal	October 2016
Practical Bayesian tomography Granade, Christopher; Combes, Joshua; Cory, D. G. New Journal of Physics, Vol. 18, Issue 3 https://doi.org/10.1088/1367-2630/18/3/033024	journal	March 2016
Robust characterization of leakage errors Wallman, Joel J.; Barnhill, Marie; Emerson, Joseph New Journal of Physics, Vol. 18, Issue 4 https://doi.org/10.1088/1367-2630/18/4/043021	journal	April 2016
Behavior of the maximum likelihood in quantum state tomography Scholten, Travis L.; Blume-Kohout, Robin New Journal of Physics, Vol. 20, Issue 2 https://doi.org/10.1088/1367-2630/aaa7e2	journal	February 2018
On the freedom in representing quantum operations Lin, Junan; Buonacorsi, Brandon; Laflamme, Raymond New Journal of Physics, Vol. 21, Issue 2 https://doi.org/10.1088/1367-2630/ab075a	journal	February 2019
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
Stochastic estimation of dynamical variables Krastanov, Stefan; Zhou, Sisi; Flammia, Steven T. Quantum Science and Technology, Vol. 4, Issue 3 https://doi.org/10.1088/2058-9565/ab18d5	journal	May 2019
Probing quantum processor performance with pyGSTi Nielsen, Erik; Rudinger, Kenneth; Proctor, Timothy Quantum Science and Technology, Vol. 5, Issue 4 https://doi.org/10.1088/2058-9565/ab8aa4	journal	July 2020
Nonparametric estimates of standard error: The jackknife, the bootstrap and other methods Efron, Bradley Biometrika, Vol. 68, Issue 3 https://doi.org/10.1093/biomet/68.3.589	journal	January 1981
Machine Learning of Noise-Resilient Quantum Circuits Cincio, Lukasz; Rudinger, Kenneth; Sarovar, Mohan PRX Quantum, Vol. 2, Issue 1 https://doi.org/10.1103/PRXQuantum.2.010324	journal	February 2021
Determination of the Quantum State by Measurements Gale, W.; Guth, E.; Trammell, G. T. Physical Review, Vol. 165, Issue 5 https://doi.org/10.1103/PhysRev.165.1434	journal	January 1968
Validating quantum computers using randomized model circuits Cross, Andrew W.; Bishop, Lev S.; Sheldon, Sarah Physical Review A, Vol. 100, Issue 3 https://doi.org/10.1103/PhysRevA.100.032328	journal	September 2019
Detector tomography on IBM quantum computers and mitigation of an imperfect measurement Chen, Yanzhu; Farahzad, Maziar; Yoo, Shinjae Physical Review A, Vol. 100, Issue 5 https://doi.org/10.1103/PhysRevA.100.052315	journal	November 2019
Demonstration of a parametrically activated entangling gate protected from flux noise Hong, Sabrina S.; Papageorge, Alexander T.; Sivarajah, Prasahnt Physical Review A, Vol. 101, Issue 1 https://doi.org/10.1103/PhysRevA.101.012302	journal	January 2020
Experimental Pauli-frame randomization on a superconducting qubit Ware, Matthew; Ribeill, Guilhem; Ristè, Diego Physical Review A, Vol. 103, Issue 4 https://doi.org/10.1103/PhysRevA.103.042604	journal	April 2021
Quantum-state estimation Hradil, Z. Physical Review A, Vol. 55, Issue 3 https://doi.org/10.1103/PhysRevA.55.R1561	journal	March 1997
Maximum-likelihood estimation of quantum processes Fiurášek, Jaromír; Hradil, Zdeněk Physical Review A, Vol. 63, Issue 2 https://doi.org/10.1103/PhysRevA.63.020101	journal	January 2001
Realization of quantum process tomography in NMR Childs, Andrew M.; Chuang, Isaac L.; Leung, Debbie W. Physical Review A, Vol. 64, Issue 1 https://doi.org/10.1103/PhysRevA.64.012314	journal	June 2001
Maximum-likelihood estimation of quantum measurement Fiurášek, Jaromír Physical Review A, Vol. 64, Issue 2 https://doi.org/10.1103/PhysRevA.64.024102	journal	July 2001
Measurement of qubits James, Daniel F. V.; Kwiat, Paul G.; Munro, William J. Physical Review A, Vol. 64, Issue 5 https://doi.org/10.1103/PhysRevA.64.052312	journal	October 2001
Experimental Hamiltonian identification for controlled two-level systems Schirmer, S. G.; Kolli, A.; Oi, D. K. L. Physical Review A, Vol. 69, Issue 5 https://doi.org/10.1103/PhysRevA.69.050306	journal	May 2004
Identifying an experimental two-state Hamiltonian to arbitrary accuracy Cole, Jared H.; Schirmer, Sonia G.; Greentree, Andrew D. Physical Review A, Vol. 71, Issue 6 https://doi.org/10.1103/PhysRevA.71.062312	journal	June 2005
Efficient error characterization in quantum information processing Lévi, Benjamin; López, Cecilia C.; Emerson, Joseph Physical Review A, Vol. 75, Issue 2 https://doi.org/10.1103/PhysRevA.75.022314	journal	February 2007
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
Fibonacci scheme for fault-tolerant quantum computation Aliferis, Panos; Preskill, John Physical Review A, Vol. 79, Issue 1 https://doi.org/10.1103/PhysRevA.79.012332	journal	January 2009
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-calibrating tomography for angular Schmidt modes in spontaneous parametric down-conversion Straupe, S. S.; Ivanov, D. P.; Kalinkin, A. A. Physical Review A, Vol. 87, Issue 4 https://doi.org/10.1103/PhysRevA.87.042109	journal	April 2013
Self-calibrating tomography for multidimensional systems Quesada, Nicolás; Brańczyk, Agata M.; James, Daniel F. V. Physical Review A, Vol. 87, Issue 6 https://doi.org/10.1103/PhysRevA.87.062118	journal	June 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
Tomography of a spin qubit in a double quantum dot Takahashi, Maki; Bartlett, Stephen D.; Doherty, Andrew C. Physical Review A, Vol. 88, Issue 2 https://doi.org/10.1103/PhysRevA.88.022120	journal	August 2013
Optimization of quantum state tomography in the presence of experimental constraints Mohammadi, Mohammadreza; Brańczyk, Agata M. Physical Review A, Vol. 89, Issue 1 https://doi.org/10.1103/PhysRevA.89.012113	journal	January 2014
Self-consistent tomography of the state-measurement Gram matrix Stark, Cyril Physical Review A, Vol. 89, Issue 5 https://doi.org/10.1103/PhysRevA.89.052109	journal	May 2014
Detecting correlated errors in state-preparation-and-measurement tomography Jackson, Christopher; van Enk, S. J. Physical Review A, Vol. 92, Issue 4 https://doi.org/10.1103/PhysRevA.92.042312	journal	October 2015
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
Compressed sensing for Hamiltonian reconstruction Rudinger, Kenneth; Joynt, Robert Physical Review A, Vol. 92, Issue 5 https://doi.org/10.1103/PhysRevA.92.052322	journal	November 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
Experimental demonstration of loop state-preparation-and-measurement tomography McCormick, A. F.; van Enk, S. J.; Beck, M. Physical Review A, Vol. 95, Issue 4 https://doi.org/10.1103/PhysRevA.95.042329	journal	April 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
Joint quantum-state and measurement tomography with incomplete measurements Keith, Adam C.; Baldwin, Charles H.; Glancy, Scott Physical Review A, Vol. 98, Issue 4 https://doi.org/10.1103/PhysRevA.98.042318	journal	October 2018
Quantum process fidelity bounds from sets of input states Mayer, Karl; Knill, Emanuel Physical Review A, Vol. 98, Issue 5 https://doi.org/10.1103/PhysRevA.98.052326	journal	November 2018
Scalar quantum field theories as a benchmark for near-term quantum computers Yeter-Aydeniz, Kübra; Dumitrescu, Eugene F.; McCaskey, Alex J. Physical Review A, Vol. 99, Issue 3 https://doi.org/10.1103/PhysRevA.99.032306	journal	March 2019
Generative model benchmarks for superconducting qubits Hamilton, Kathleen E.; Dumitrescu, Eugene F.; Pooser, Raphael C. Physical Review A, Vol. 99, Issue 6 https://doi.org/10.1103/PhysRevA.99.062323	journal	June 2019
Suppression of Qubit Crosstalk in a Tunable Coupling Superconducting Circuit Mundada, Pranav; Zhang, Gengyan; Hazard, Thomas Physical Review Applied, Vol. 12, Issue 5 https://doi.org/10.1103/PhysRevApplied.12.054023	journal	November 2019
Self-Consistent Calibration of Quantum-Gate Sets Cerfontaine, Pascal; Otten, René; Bluhm, Hendrik Physical Review Applied, Vol. 13, Issue 4 https://doi.org/10.1103/PhysRevApplied.13.044071	journal	April 2020
Performance Optimization for Drift-Robust Fidelity Improvement of Two-Qubit Gates White, G. A. L.; Hill, C. D.; Hollenberg, L. C. L. Physical Review Applied, Vol. 15, Issue 1 https://doi.org/10.1103/PhysRevApplied.15.014023	journal	January 2021
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
Selective and Efficient Estimation of Parameters for Quantum Process Tomography Bendersky, Ariel; Pastawski, Fernando; Paz, Juan Pablo Physical Review Letters, Vol. 100, Issue 19 https://doi.org/10.1103/PhysRevLett.100.190403	journal	May 2008
Optimal Control of a Qubit Coupled to a Non-Markovian Environment Rebentrost, P.; Serban, I.; Schulte-Herbrüggen, T. Physical Review Letters, Vol. 102, Issue 9 https://doi.org/10.1103/PhysRevLett.102.090401	journal	March 2009
Hamiltonian Tomography in an Access-Limited Setting without State Initialization Di Franco, C.; Paternostro, M.; Kim, M. S. Physical Review Letters, Vol. 102, Issue 18 https://doi.org/10.1103/PhysRevLett.102.187203	journal	May 2009
Quantum State Tomography via Compressed Sensing Gross, David; Liu, Yi-Kai; Flammia, Steven T. Physical Review Letters, Vol. 105, Issue 15 https://doi.org/10.1103/PhysRevLett.105.150401	journal	October 2010
Hedged Maximum Likelihood Quantum State Estimation Blume-Kohout, Robin Physical Review Letters, Vol. 105, Issue 20 https://doi.org/10.1103/PhysRevLett.105.200504	journal	November 2010
Permutationally Invariant Quantum Tomography Tóth, G.; Wieczorek, W.; Gross, D. Physical Review Letters, Vol. 105, Issue 25 https://doi.org/10.1103/PhysRevLett.105.250403	journal	December 2010
Efficient Measurement of Quantum Dynamics via Compressive Sensing Shabani, A.; Kosut, R. L.; Mohseni, M. Physical Review Letters, Vol. 106, Issue 10 https://doi.org/10.1103/PhysRevLett.106.100401	journal	March 2011
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
Direct Fidelity Estimation from Few Pauli Measurements Flammia, Steven T.; Liu, Yi-Kai Physical Review Letters, Vol. 106, Issue 23 https://doi.org/10.1103/PhysRevLett.106.230501	journal	June 2011
Practical Characterization of Quantum Devices without Tomography da Silva, Marcus P.; Landon-Cardinal, Olivier; Poulin, David Physical Review Letters, Vol. 107, Issue 21 https://doi.org/10.1103/PhysRevLett.107.210404	journal	November 2011
Efficient Method for Computing the Maximum-Likelihood Quantum State from Measurements with Additive Gaussian Noise Smolin, John A.; Gambetta, Jay M.; Smith, Graeme Physical Review Letters, Vol. 108, Issue 7 https://doi.org/10.1103/PhysRevLett.108.070502	journal	February 2012
Randomized Benchmarking of Multiqubit Gates Gaebler, J. P.; Meier, A. M.; Tan, T. R. Physical Review Letters, Vol. 108, Issue 26 https://doi.org/10.1103/PhysRevLett.108.260503	journal	June 2012
Practical Experimental Certification of Computational Quantum Gates Using a Twirling Procedure Moussa, Osama; da Silva, Marcus P.; Ryan, Colm A. Physical Review Letters, Vol. 109, Issue 7 https://doi.org/10.1103/PhysRevLett.109.070504	journal	August 2012
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
Reliable Quantum State Tomography Christandl, Matthias; Renner, Renato Physical Review Letters, Vol. 109, Issue 12 https://doi.org/10.1103/PhysRevLett.109.120403	journal	September 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
Adaptive Quantum State Tomography Improves Accuracy Quadratically Mahler, D. H.; Rozema, Lee A.; Darabi, Ardavan Physical Review Letters, Vol. 111, Issue 18 https://doi.org/10.1103/PhysRevLett.111.183601	journal	October 2013
Optimal Strategies for Estimating the Average Fidelity of Quantum Gates Reich, Daniel M.; Gualdi, Giulia; Koch, Christiane P. Physical Review Letters, Vol. 111, Issue 20 https://doi.org/10.1103/PhysRevLett.111.200401	journal	November 2013
Quantum Hamiltonian Identification from Measurement Time Traces Zhang, Jun; Sarovar, Mohan Physical Review Letters, Vol. 113, Issue 8 https://doi.org/10.1103/PhysRevLett.113.080401	journal	August 2014
Systematic Errors in Current Quantum State Tomography Tools Schwemmer, Christian; Knips, Lukas; Richart, Daniel Physical Review Letters, Vol. 114, Issue 8 https://doi.org/10.1103/PhysRevLett.114.080403	journal	February 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
Practical and Reliable Error Bars in Quantum Tomography Faist, Philippe; Renner, Renato Physical Review Letters, Vol. 117, Issue 1 https://doi.org/10.1103/PhysRevLett.117.010404	journal	July 2016
Experimental Demonstration of Self-Guided Quantum Tomography Chapman, Robert J.; Ferrie, Christopher; Peruzzo, Alberto Physical Review Letters, Vol. 117, Issue 4 https://doi.org/10.1103/PhysRevLett.117.040402	journal	July 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
Resilient Entangling Gates for Trapped Ions Webb, A. E.; Webster, S. C.; Collingbourne, S. Physical Review Letters, Vol. 121, Issue 18 https://doi.org/10.1103/PhysRevLett.121.180501	journal	November 2018
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
Direct Randomized Benchmarking for Multiqubit Devices Proctor, Timothy J.; Carignan-Dugas, Arnaud; Rudinger, Kenneth Physical Review Letters, Vol. 123, Issue 3 https://doi.org/10.1103/PhysRevLett.123.030503	journal	July 2019
Quantum Information Scrambling in a Trapped-Ion Quantum Simulator with Tunable Range Interactions Joshi, Manoj K.; Elben, Andreas; Vermersch, Benoît Physical Review Letters, Vol. 124, Issue 24 https://doi.org/10.1103/PhysRevLett.124.240505	journal	June 2020
Complete Characterization of a Quantum Process: The Two-Bit Quantum Gate Poyatos, J. F.; Cirac, J. I.; Zoller, P. Physical Review Letters, Vol. 78, Issue 2 https://doi.org/10.1103/PhysRevLett.78.390	journal	January 1997
Complete Characterization of Arbitrary Quantum Measurement Processes Luis, A.; Sánchez-Soto, L. L. Physical Review Letters, Vol. 83, Issue 18 https://doi.org/10.1103/PhysRevLett.83.3573	journal	November 1999
Quantum Tomography for Measuring Experimentally the Matrix Elements of an Arbitrary Quantum Operation D'Ariano, G. M.; Lo Presti, P. Physical Review Letters, Vol. 86, Issue 19 https://doi.org/10.1103/PhysRevLett.86.4195	journal	May 2001
Direct Estimations of Linear and Nonlinear Functionals of a Quantum State Ekert, Artur K.; Alves, Carolina Moura; Oi, Daniel K. L. Physical Review Letters, Vol. 88, Issue 21 https://doi.org/10.1103/PhysRevLett.88.217901	journal	May 2002
Ancilla-Assisted Quantum Process Tomography Altepeter, J. B.; Branning, D.; Jeffrey, E. Physical Review Letters, Vol. 90, Issue 19 https://doi.org/10.1103/PhysRevLett.90.193601	journal	May 2003
Quantum Process Tomography of a Controlled-NOT Gate O'Brien, J. L.; Pryde, G. J.; Gilchrist, A. Physical Review Letters, Vol. 93, Issue 8 https://doi.org/10.1103/PhysRevLett.93.080502	journal	August 2004
Direct Characterization of Quantum Dynamics Mohseni, M.; Lidar, D. A. Physical Review Letters, Vol. 97, Issue 17 https://doi.org/10.1103/PhysRevLett.97.170501	journal	October 2006
Process Tomography of Ion Trap Quantum Gates Riebe, M.; Kim, K.; Schindler, P. Physical Review Letters, Vol. 97, Issue 22 https://doi.org/10.1103/PhysRevLett.97.220407	journal	December 2006
Subsystem Fault Tolerance with the Bacon-Shor Code Aliferis, Panos; Cross, Andrew W. Physical Review Letters, Vol. 98, Issue 22 https://doi.org/10.1103/PhysRevLett.98.220502	journal	May 2007
Robust Extraction of Tomographic Information via Randomized Benchmarking Kimmel, Shelby; da Silva, Marcus P.; Ryan, Colm A. Physical Review X, Vol. 4, Issue 1 https://doi.org/10.1103/PhysRevX.4.011050	journal	March 2014
Implementing and Characterizing Precise Multiqubit Measurements Blumoff, J. Z.; Chou, K.; Shen, C. Physical Review X, Vol. 6, Issue 3 https://doi.org/10.1103/PhysRevX.6.031041	journal	September 2016
Quantum Chemistry Calculations on a Trapped-Ion Quantum Simulator Hempel, Cornelius; Maier, Christine; Romero, Jonathan Physical Review X, Vol. 8, Issue 3 https://doi.org/10.1103/PhysRevX.8.031022	journal	July 2018
Practical Quantum Error Mitigation for Near-Future Applications Endo, Suguru; Benjamin, Simon C.; Li, Ying Physical Review X, Vol. 8, Issue 3 https://doi.org/10.1103/PhysRevX.8.031027	journal	July 2018
Probing Context-Dependent Errors in Quantum Processors Rudinger, Kenneth; Proctor, Timothy; Langharst, Dylan Physical Review X, Vol. 9, Issue 2 https://doi.org/10.1103/PhysRevX.9.021045	journal	June 2019
Determination of quasiprobability distributions in terms of probability distributions for the rotated quadrature phase Vogel, K.; Risken, H. Physical Review A, Vol. 40, Issue 5 https://doi.org/10.1103/physreva.40.2847	journal	September 1989
Sample-optimal tomography of quantum states Haah, Jeongwan; Harrow, Aram W.; Ji, Zhengfeng IEEE Transactions on Information Theory https://doi.org/10.1109/TIT.2017.2719044	journal	January 2017
An invitation to quantum tomography Artiles, L. M.; Gill, R. D.; Guta, M. I. Journal of the Royal Statistical Society: Series B (Statistical Methodology), Vol. 67, Issue 1 https://doi.org/10.1111/j.1467-9868.2005.00491.x	journal	February 2005
Quantum computation with universal error mitigation on a superconducting quantum processor Song, Chao; Cui, Jing; Wang, H. Science Advances, Vol. 5, Issue 9 https://doi.org/10.1126/sciadv.aaw5686	journal	September 2019
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
Complete Characterization of Quantum-Optical Processes Lobino, M.; Korystov, D.; Kupchak, C. Science, Vol. 322, Issue 5901 https://doi.org/10.1126/science.1162086	journal	October 2008
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
Shadow tomography of quantum states Aaronson, Scott Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing - STOC 2018 https://doi.org/10.1145/3188745.3188802	conference	January 2018
The Large-Sample Distribution of the Likelihood Ratio for Testing Composite Hypotheses Wilks, S. S. The Annals of Mathematical Statistics, Vol. 9, Issue 1 https://doi.org/10.1214/aoms/1177732360	journal	March 1938
Holistic Quantum State and Process Tomography Quesada, Nicolás; Brańczyk, Agata M.; James, Daniel F. V. Frontiers in Optics 2013 https://doi.org/10.1364/FIO.2013.FW1C.6	conference	January 2013
Error-compensation measurements on polarization qubits Hou, Zhibo; Zhu, Huangjun; Xiang, Guo-Yong Journal of the Optical Society of America B, Vol. 33, Issue 6 https://doi.org/10.1364/JOSAB.33.001256	journal	January 2016
Self-calibrating tomography for non-unitary processes Quesada, Nicolás; Brańczyk, Agata M.; James, Daniel F. V. The Rochester Conferences on Coherence and Quantum Optics and the Quantum Information and Measurement meeting https://doi.org/10.1364/QIM.2013.W6.38	conference	January 2013
QInfer: Statistical inference software for quantum applications Granade, Christopher; Ferrie, Christopher; Hincks, Ian Quantum, Vol. 1 https://doi.org/10.22331/q-2017-04-25-5	journal	April 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
Gauge invariant information concerning quantum channels Rudnicki, Łukasz; Puchała, Zbigniew; Zyczkowski, Karol Quantum, Vol. 2 https://doi.org/10.22331/q-2018-04-11-60	journal	April 2018
Detecting crosstalk errors in quantum information processors Sarovar, Mohan; Proctor, Timothy; Rudinger, Kenneth Quantum, Vol. 4 https://doi.org/10.22331/q-2020-09-11-321	journal	September 2020
A volumetric framework for quantum computer benchmarks Blume-Kohout, Robin; Young, Kevin C. Quantum, Vol. 4 https://doi.org/10.22331/q-2020-11-15-362	journal	November 2020
Operational, gauge-free quantum tomography Di Matteo, Olivia; Gamble, John; Granade, Chris Quantum, Vol. 4 https://doi.org/10.22331/q-2020-11-17-364	journal	November 2020
Testing the context-independence of quantum gates Veitia, Andrzej; van Enk, Steven J. quantum Information and Computation, Vol. 20, Issue 15&16 https://doi.org/10.26421/QIC20.15-16-3	journal	December 2020
Quantum accuracy threshold for concatenated distance-3 code Aliferis, P.; Gottesman, D.; Preskill, J. Quantum Information and Computation, Vol. 6, Issue 2 https://doi.org/10.26421/QIC6.2-1	journal	March 2006
Quantum supremacy using a programmable superconducting processor Martinis, John; Boixo, Sergio; Neven, Hartmut Dryad https://doi.org/10.5061/dryad.k6t1rj8	dataset	January 2019
Detecting and Tracking Drift in Quantum Information Processors Proctor, Timothy; Revelle, Melissa; Nielsen, Erik Zenodo https://doi.org/10.5281/zenodo.4033077	dataset	January 2020
Quantum Information Scrambling in a Trapped-Ion Quantum Simulator with Tunable Range Interactions Joshi, Manoj K.; Elben, Andreas; Vermersch, Beno\^it Zenodo https://doi.org/10.5281/zenodo.4916120	dataset	January 2020

Similar Records

A volumetric framework for quantum computer benchmarks

Journal Article · 2020 · Quantum · OSTI ID:1725835

Error mitigation with Clifford quantum-circuit data

Journal Article · 2021 · Quantum · OSTI ID:1836985

Understanding the tool influence function during sub-aperture belt-on-wheel glass polishing

Journal Article · 2022 · Applied Optics · OSTI ID:2203635

Related Subjects

97 MATHEMATICS AND COMPUTING

Gate Set Tomography

Citation Formats

References (172)

Similar Records

Related Subjects