A simple formula for the average gate fidelity of a quantum dynamical operation
Open accessThe claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
The average fidelity depends only on the noise operator and can be expressed in a known form.
“Due to the invariance of the Fubini-Study measure the average fidelity depends only on the noise operator and can been expressed in the form [9, 10, 11]”
From Scalable noise estimation with random unitary operators (2005) · cites this paper as [11]
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Cites
<i>Quantum Computation and Quantum Information</i>
Nielsen, M. A., Chuang, I., & Grover, L. K. (2002) · American Journal of Physics · doi:10.1119/1.1463744 · Cited by 21,895 · see citing works
Self-citationQuantum computation and quantum information
Law, J. (2001) · ACM SIGSOFT Software Engineering Notes · doi:10.1145/505482.505499 · Cited by 20,449 · see citing works
Measuring the Quantum State of Light
Leonhardt, U., & Beck, M. (1998) · American Journal of Physics · doi:10.1119/1.18900 · Cited by 976 · see citing works
General teleportation channel, singlet fraction, and quasidistillation
Horodecki, M., Horodecki, P., & Horodecki, R. (1999) · Physical Review A · doi:10.1103/physreva.60.1888 · Cited by 965 · see citing works
Prescription for experimental determination of the dynamics of a quantum black box
Chuang, I. L., & Nielsen, M. A. (1997) · Journal of Modern Optics · doi:10.1080/09500349708231894 · Cited by 949 · see citing works
Self-citationSending entanglement through noisy quantum channels
Schumacher, B. W. (1996) · Physical Review A · doi:10.1103/physreva.54.2614 · Cited by 824 · see citing works
Complete Characterization of a Quantum Process: The Two-Bit Quantum Gate
Poyatos, J. F., Cirac, J. I., & Zoller, P. (1997) · Physical Review Letters · doi:10.1103/physrevlett.78.390 · Cited by 694 · see citing works
Complete quantum teleportation using nuclear magnetic resonance
Nielsen, M. A., Knill, E., & Laflamme, R. (1998) · Nature · doi:10.1038/23891 · Cited by 548 · see citing works
Self-citationComplete quantum teleportation using nuclear magnetic resonance
Nielsen, M. A., Knill, E., & Laflamme, R. (1998) · RePEc: Research Papers in Economics · Cited by 437 · see citing works
Self-citationFortunato, E. M., Pravia, M. A., Boulant, N., Teklemariam, G., Havel, T. F., & Cory, D. G. (2002) · The Journal of Chemical Physics · doi:10.1063/1.1465412 · Cited by 243 · see citing works
Realization of quantum process tomography in NMR
Childs, A. M., Chuang, I. L., & Leung, D. W. (2001) · Physical Review A · doi:10.1103/physreva.64.012314 · Cited by 205 · see citing works
Bowdrey, M. D., Oi, D. K. L., Short, A. J., Banaszek, K., & Jones, J. A. (2002) · Physics Letters A · doi:10.1016/s0375-9601(02)00069-5 · Cited by 172 · see citing works
Measuring the Quantum State of Light
Chakraborty, A. K. (1998) · Journal of Optics · doi:10.1007/bf03549337 · Cited by 166 · see citing works
Implementation of universal control on a decoherence-free qubit
Fortunato, E. M., Viola, L., Hodges, J. S., Teklemariam, G., & Cory, D. G. (2002) · New Journal of Physics · doi:10.1088/1367-2630/4/1/305 · Cited by 105 · see citing works
Implementation of Universal Control on a Decoherence-Free Qubit
Fortunato, E. M., Viola, L., Hodges, J. S., Teklemariam, G., & Cory, D. G. (2001) · CERN Document Server (European Organization for Nuclear Research) · Cited by 67 · see citing works
Flagged first, then by citations
Cited by
Sorted by citations
NMR techniques for quantum control and computation
Vandersypen, L. M. K., & Chuang, I. L. (2005) · Reviews of Modern Physics · doi:10.1103/revmodphys.76.1037 · Cited by 1,217 · see citing works
Hybrid Quantum-Classical Algorithms and Quantum Error Mitigation
Endo, S., Cai, Z., Benjamin, S. C., & Yuan, X. (2021) · Journal of the Physical Society of Japan · doi:10.7566/jpsj.90.032001 · Cited by 566 · see citing works
Demonstration of the trapped-ion quantum CCD computer architecture
Pino, J. M., Dreiling, J. M., Figgatt, C., Gaebler, J. P., Moses, S. A., Allman, M. S., Baldwin, C. H., Foss-Feig, M., Hayes, D., Mayer, K., et al. (2021) · Nature · doi:10.1038/s41586-021-03318-4 · Cited by 547 · see citing works
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 · see citing works
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 · see citing works
Real-time quantum error correction beyond break-even
Sivak, V. V., Eickbusch, A., Royer, B., Singh, S., Tsioutsios, I., Ganjam, S., Miano, A., Brock, B. L., Ding, A. Z., Frunzio, L., et al. (2023) · Nature · doi:10.1038/s41586-023-05782-6 · Cited by 407 · see citing works
Quantum-assisted quantum compiling
Khatri, S., LaRose, R., Poremba, A., Cincio, L., Sornborger, A. T., & Coles, P. J. (2019) · Quantum · doi:10.22331/q-2019-05-13-140 · Cited by 382 · see citing works
A Race-Track Trapped-Ion Quantum Processor
Moses, S. A., Baldwin, C. H., Allman, M. S., Ancona, R., Ascarrunz, L., Barnes, C., Bartolotta, J., Bjork, B., Blanchard, P., Bohn, M., et al. (2023) · Physical Review X · doi:10.1103/physrevx.13.041052 · Cited by 391 · see citing works
A Survey on Quantum Channel Capacities
Gyongyosi, L., Imre, S., & Nguyen, H. V. (2018) · IEEE Communications Surveys & Tutorials · doi:10.1109/comst.2017.2786748 · Cited by 337 · see citing works
Variational fast forwarding for quantum simulation beyond the coherence time
Cîrstoiu, C., Holmes, Z., Iosue, J., Cincio, L., Coles, P. J., & Sornborger, A. (2020) · npj Quantum Information · doi:10.1038/s41534-020-00302-0 · Cited by 232 · see citing works
“Specifically, it can be shown [44, 45] that”
Noise resilience of variational quantum compiling
Sharma, K., Khatri, S., Cerezo, M., & Coles, P. J. (2020) · New Journal of Physics · doi:10.1088/1367-2630/ab784c · Cited by 196 · see citing works
Fast universal control of an oscillator with weak dispersive coupling to a qubit
Eickbusch, A., Sivak, V., Ding, A. Z., Elder, S. S., Jha, S. R., Venkatraman, J., Royer, B., Girvin, S. M., Schoelkopf, R. J., & Devoret, M. H. (2022) · Nature Physics · doi:10.1038/s41567-022-01776-9 · Cited by 173 · see citing works
Measuring the capabilities of quantum computers
Proctor, T., Rudinger, K., Young, K., Nielsen, E., & Blume-Kohout, R. (2022) · Nature Physics · doi:10.1038/s41567-021-01409-7 · Cited by 146 · see citing works
Average fidelity between random quantum states
Życzkowski, K., & Sommers, H.-J. (2005) · Physical Review A · doi:10.1103/physreva.71.032313 · Cited by 135 · see citing works
Midcircuit Operations Using the <i>omg</i> Architecture in Neutral Atom Arrays
Lis, J. W., Senoo, A., McGrew, W. F., Rönchen, F., Jenkins, A., & Kaufman, A. M. (2023) · Physical Review X · doi:10.1103/physrevx.13.041035 · Cited by 113 · see citing works
Experimental quantum process tomography of non-trace-preserving maps
Bongioanni, I., Sansoni, L., Sciarrino, F., Vallone, G., & Mataloni, P. (2010) · Physical Review A · doi:10.1103/physreva.82.042307 · Cited by 79 · see citing works
Noise analysis for high-fidelity quantum entangling gates in an anharmonic linear Paul trap
Wu, Y., Wang, S.-T., & Duan, L.-M. (2018) · Physical Review A · doi:10.1103/physreva.97.062325 · Cited by 69 · see citing works
Experimental Time-Optimal Universal Control of Spin Qubits in Solids
Geng, J., Wu, Y., Wang, X., Xu, K., Shi, F., Xie, Y., Rong, X., & Du, J. (2016) · Physical Review Letters · doi:10.1103/physrevlett.117.170501 · Cited by 68 · see citing works
Quantum error correction of qudits beyond break-even
Brock, B. L., Singh, S., Eickbusch, A., Sivak, V. V., Ding, A. Z., Frunzio, L., Girvin, S. M., & Devoret, M. H. (2025) · Nature · doi:10.1038/s41586-025-08899-y · Cited by 64 · see citing works
Gate fidelity fluctuations and quantum process invariants
Magesan, E., Blume-Kohout, R., & Emerson, J. (2011) · Physical Review A · doi:10.1103/physreva.84.012309 · Cited by 60 · see citing works
High-fidelity teleportation of a logical qubit using transversal gates and lattice surgery
Ryan-Anderson, C., Brown, N. C., Baldwin, C. H., Dreiling, J. M., Foltz, C., Gaebler, J. P., Gatterman, T. M., Hewitt, N., Holliman, C., Horst, C. V., et al. (2024) · Science · doi:10.1126/science.adp6016 · Cited by 52 · see citing works
The prospects of Monte Carlo antibody loop modelling on a fault-tolerant quantum computer
Allcock, J., Vangone, A., Meyder, A., Adaszewski, S., Strahm, M., Hsieh, C.-Y., & Zhang, S. (2022) · Frontiers in Drug Discovery · doi:10.3389/fddsv.2022.908870 · Cited by 12 · see citing works
A 98-qubit trapped-ion quantum computer with all-to-all connectivity
Ransford, A., Allman, M. S., Arkinstall, J., Campora, J. P., Cooper, S. F., Delaney, R. D., Dreiling, J. M., Estey, B., Figgatt, C., Hall, A., et al. (2026) · Nature · doi:10.1038/s41586-026-10676-4 · Cited by 16 · see citing works
“To see whether the results are consistent with our component benchmarks, we first compute an effective 2Q gate error ϵ eff,2Q from the n m = 0 data, using in which the factor 5/4 comes from the conversion between process and average fidelity 99 .”
- Authors
- Nielsen, M. A.
- Affiliations
- The University of Queensland (AU)
- Corresponding author
- Nielsen, Michael A
- ORCID
- Nielsen, Michael A
- Venue
- Physics Letters A
- Publisher
- Elsevier BV
- Published
- 2002-10
- Volume
- 303
- Issue
- 4
- Pages
- 249-252
- ISSN
- 0375-9601 (ISSN-L)
- OpenAlex
- W2030467629
- Cited by
- 725
- References
- 15
- Citations by year
- 2026: 64 · 2025: 80 · 2024: 72 · 2023: 86 · 2022: 51 · 2021: 66 · 2020: 48 · 2019: 32 · 2018: 30 · 2017: 23 · 2016: 20 · 2015: 17 · 2014: 25 · 2013: 13 · 2012: 14
- FWCI
- 4.84
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physics Letters A (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Keywords
- average gate fidelity, quantum operations, qudits, entanglement fidelity, quantum dynamical systems
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review