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Cross-Platform Verification of Intermediate Scale Quantum Devices
Open accessAbstract
We describe a protocol for cross-platform verification of quantum simulators and quantum computers. We show how to measure directly the overlap Tr[ρ_{1}ρ_{2}] and the purities Tr[ρ_{1,2}^{2}], and thus a fidelity of two, possibly mixed, quantum states ρ_{1} and ρ_{2} prepared in separate experimental platforms. We require only local measurements in randomized product bases, which are communicated classically. As a proof of principle, we present the measurement of experiment-theory fidelities for entangled 10-qubit quantum states in a trapped ion quantum simulator.
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“Alternatively, one can use randomized measurements to measure the overlap Tr ( ρ 1 ρ 2 ) of two density matrices ρ 1 , ρ 2 (Elben et al. , 2020, 2019; van Enk and Beenakker, 2012).”
From Noisy intermediate-scale quantum algorithms (2022) · cites this paper as Elben et al., 2020
In the citing paper
“Using randomized measurements (Elben et al. , 2020), the kernel can be computed in a time that scales linearly with the dataset size D , which allows for processing large datasets with quantum computers (Haug et al. , 2021c).”
From Noisy intermediate-scale quantum algorithms (2022) · cites this paper as Elben et al. , 2020
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Cites
Quantum Computing in the NISQ era and beyond
Preskill, J. (2018) · Quantum · doi:10.22331/q-2018-08-06-79 · Cited by 8,830
A leisurely look at the bootstrap, the jackknife, and cross-validation
Efron, B., & Gong, G. (1983) · The American Statistician · doi:10.1080/00031305.1983.10483087 · Cited by 3,229
Haake, F. (2010) · Springer series in synergetics · doi:10.1007/978-3-642-05428-0 · Cited by 2,072
Fidelity for Mixed Quantum States
Jozsa, R. (1994) · Journal of Modern Optics · doi:10.1080/09500349414552171 · Cited by 1,911
The Theory of Quantum Information
Watrous, J. (2018) · doi:10.1017/9781316848142 · Cited by 1,325
Scalable multiparticle entanglement of trapped ions
Häffner, H., Hänsel, W., Roos, C. F., Benhelm, J., Chek-al-kar, D., Chwalla, M., Körber, T., Rapol, U. D., Riebe, M., Schmidt, P. O., et al. (2005) · Nature · doi:10.1038/nature04279 · Cited by 1,249
Self-citationMeasuring entanglement entropy in a quantum many-body system
Islam, R., Ma, R., Preiss, P. M., Tai, M. E., Lukin, A., Rispoli, M., & Greiner, M. (2015) · Nature · doi:10.1038/nature15750 · Cited by 1,209
Quantum State Tomography via Compressed Sensing
Gross, D., Liu, Y.-K., Flammia, S. T., Becker, S., & Eisert, J. (2010) · Physical Review Letters · doi:10.1103/physrevlett.105.150401 · Cited by 1,133
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
Neural-network quantum state tomography
Torlai, G., Mazzola, G., Carrasquilla, J., Troyer, M., Melko, R. G., & Carleo, G. (2018) · Nature Physics · doi:10.1038/s41567-018-0048-5 · Cited by 906
Exact and approximate unitary 2-designs and their application to fidelity estimation
Dankert, C., Cleve, R., Emerson, J., & Livine, E. R. (2009) · Physical Review A · doi:10.1103/physreva.80.012304 · Cited by 683
Probing Rényi entanglement entropy via randomized measurements
Brydges, T., Elben, A., Jurcevic, P., Vermersch, B., Maier, C., Lanyon, B. P., Zoller, P., Blatt, R., & Roos, C. F. (2019) · Science · doi:10.1126/science.aau4963 · Cited by 636
Self-citationNew Light on the Correlation Coefficient and its Transforms
Hotelling, H. (1953) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/j.2517-6161.1953.tb00135.x · Cited by 546
Chaos and complexity by design
Roberts, D. A., & Yoshida, B. (2017) · Journal of High Energy Physics · doi:10.1007/jhep04(2017)121 · Cited by 521
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
Direct Fidelity Estimation from Few Pauli Measurements
Flammia, S. T., & Liu, Y.-K. (2011) · Physical Review Letters · doi:10.1103/physrevlett.106.230501 · Cited by 449
Measuring Entanglement Growth in Quench Dynamics of Bosons in an Optical Lattice
Daley, A. J., Pichler, H., Schachenmayer, J., & Zoller, P. (2012) · Physical Review Letters · doi:10.1103/physrevlett.109.020505 · Cited by 393
Self-citationEvenly distributed unitaries: On the structure of unitary designs
Gross, D., Audenaert, K., & Eisert, J. (2007) · Journal of Mathematical Physics · doi:10.1063/1.2716992 · Cited by 358
Practical Characterization of Quantum Devices without Tomography
Silva, M. P. D., Landon-Cardinal, O., & Poulin, D. (2011) · Physical Review Letters · doi:10.1103/physrevlett.107.210404 · Cited by 340
Out-of-time-order correlation for many-body localization
Fan, R., Zhang, P., Shen, H., & Zhai, H. (2017) · 中国科学通报:英文版 · doi:10.1016/j.scib.2017.04.011 · Cited by 322
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
Rényi Entropies from Random Quenches in Atomic Hubbard and Spin Models
Elben, A., Vermersch, B., Dalmonte, M., Cirac, J. I., & Zoller, P. (2018) · Physical Review Letters · doi:10.1103/physrevlett.120.050406 · Cited by 258
Self-citationOut‐of‐time‐ordered correlators in many‐body localized systems
Huang, Y., Zhang, Y., & Chen, X. (2016) · Annalen der Physik · doi:10.1002/andp.201600318 · Cited by 248
Efficient tomography of a quantum many-body system
Lanyon, B. P., Maier, C., Holzäpfel, M., Baumgratz, T., Hempel, C., Jurcevic, P., Dhand, I., Buyskikh, A. S., Daley, A. J., Cramer, M., et al. (2017) · Nature Physics · doi:10.1038/nphys4244 · Cited by 243
Self-citationQuantum fidelity measures for mixed states
Liang, Y.-C., Yeh, Y.-H., Mendonça, P. E. M. F., Teh, R. Y., Reid, M. D., & Drummond, P. D. (2019) · Reports on Progress in Physics · doi:10.1088/1361-6633/ab1ca4 · Cited by 203
Out‐of‐time‐order correlations in many‐body localized and thermal phases
Chen, X., Zhou, T., Huse, D. A., & Fradkin, E. (2016) · Annalen der Physik · doi:10.1002/andp.201600332 · Cited by 190
Elben, A., Vermersch, B., Roos, C. F., & Zoller, P. (2019) · Physical Review A · doi:10.1103/physreva.99.052323 · Cited by 168
Self-citation(2012) · doi:10.1103/physrevlett.108.110503 · Cited by 153
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
Self-citationProbing Scrambling Using Statistical Correlations between Randomized Measurements
Vermersch, B., Elben, A., Sieberer, L. M., Yao, N. Y., & Zoller, P. (2019) · Physical Review X · doi:10.1103/physrevx.9.021061 · Cited by 121
Self-citationMeasuring the Rényi entropy of a two-site Fermi-Hubbard model on a trapped ion quantum computer
Linke, N. M., Johri, S., Figgatt, C., Landsman, K. A., Matsuura, A. Y., & Monroe, C. R. (2018) · Physical Review A · doi:10.1103/physreva.98.052334 · Cited by 115
Vermersch, B., Elben, A., Dalmonte, M., Cirac, J. I., & Zoller, P. (2018) · Physical Review A · doi:10.1103/physreva.97.023604 · Cited by 109
Self-citationEfficient Quantum Pseudorandomness with Nearly Time-Independent Hamiltonian Dynamics
Nakata, Y., Hirche, C., Koashi, M., & Winter, A. (2017) · Physical Review X · doi:10.1103/physrevx.7.021006 · Cited by 107
Experimental Estimation of Average Fidelity of a Clifford Gate on a 7-Qubit Quantum Processor
Lu, D., Li, H., Trottier, D., Li, J., Brodutch, A., Krismanich, A. P., Ghavami, A., Dmitrienko, G. I., Long, G., Baugh, J., et al. (2015) · Physical Review Letters · doi:10.1103/physrevlett.114.140505 · Cited by 65
Loschmidt echo in many-body localized phases
Serbyn, M., & Abanin, D. A. (2017) · Physical review. B./Physical review. B · doi:10.1103/physrevb.96.014202 · Cited by 42
Joint quantum-state and measurement tomography with incomplete measurements
Keith, A. C., Baldwin, C. H., Glancy, S., & Knill, E. H. (2018) · Physical Review A · doi:10.1103/physreva.98.042318 · Cited by 35
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Noisy intermediate-scale quantum algorithms
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Practical quantum advantage in quantum simulation
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Self-citation
Metadata
- Authors
- Elben, A., Vermersch, B., van Bijnen, R., Kokail, C., Brydges, T., Maier, C., Joshi, M. K., Blatt, R., Roos, C. F., & Zoller, P.
- Affiliations
- Austrian Academy of Sciences (AT)
- ORCID
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2020-01-06
- Volume
- 124
- Issue
- 1
- Pages
- 010504-010504
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2971898467
- Cited by
- 151
- References
- 37
- Citations by year
- 2026: 11 · 2025: 28 · 2024: 27 · 2023: 21 · 2022: 26 · 2021: 22 · 2020: 16
- FWCI
- 8.35
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review Letters (publishedVersion)
- arXiv (Cornell University) (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University)
- Funders
- H2020 European Research Council
- Horizon 2020 Framework Programme (741541, 817482, 731473)
- Simons Foundation (651440)
- Austrian Science Fund
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › 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
- quantum fidelity, quantum state purity, quantum simulators, quantum computing hardware, entangled states, trapped-ion quantum simulator
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