The DOI matches its Crossref record; 1 of the 1 references it cites were found in a registry or an index.
Quantum State Tomography via Compressed Sensing
Open accessAbstract
We establish methods for quantum state tomography based on compressed sensing. These methods are specialized for quantum states that are fairly pure, and they offer a significant performance improvement on large quantum systems. In particular, they are able to reconstruct an unknown density matrix of dimension d and rank r using O(rdlog²d) measurement settings, compared to standard methods that require d² settings. Our methods have several features that make them amenable to experimental implementation: they require only simple Pauli measurements, use fast convex optimization, are stable against noise, and can be applied to states that are only approximately low rank. The acquired data can be used to certify that the state is indeed close to pure, so no a priori assumptions are needed.
Overview
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.
Integrity signals
Registry
Cites
Statistics
Verification
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.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
Demonstration of an all-optical quantum controlled-NOT gate
O'Brien, J. L., Pryde, G. J., White, A. G., Ralph, T. C., & Branning, D. (2003) · Nature · doi:10.1038/nature02054 · Cited by 992
Cited by
Degen, C. L., Reinhard, F., & Cappellaro, P. (2017) · Reviews of Modern Physics · doi:10.1103/revmodphys.89.035002 · Cited by 4,045
Quantum principal component analysis
Lloyd, S., Mohseni, M., & Rebentrost, P. (2014) · Nature Physics · doi:10.1038/nphys3029 · Cited by 1,385
Multidimensional quantum entanglement with large-scale integrated optics
Wang, J., Paesani, S., Ding, Y., Santagati, R., Skrzypczyk, P., Salavrakos, A., Tura, J., Augusiak, R., Mančinska, L., Bacco, D., et al. (2018) · Science · doi:10.1126/science.aar7053 · Cited by 816
Quantum Algorithm for Data Fitting
Wiebe, N., Braun, D., & Lloyd, S. (2012) · Physical Review Letters · doi:10.1103/physrevlett.109.050505 · Cited by 528
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
Self-citationQuantum generalisation of feedforward neural networks
Wan, K. H., Dahlsten, O., Kristjánsson, H., Gardner, R., & Kim, M. S. (2017) · npj Quantum Information · doi:10.1038/s41534-017-0032-4 · Cited by 276
Elben, A., Vermersch, B., Roos, C. F., & Zoller, P. (2019) · Physical Review A · doi:10.1103/physreva.99.052323 · Cited by 168
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
Cross-Platform Verification of Intermediate Scale Quantum Devices
Elben, A., Vermersch, B., van Bijnen, R., Kokail, C., Brydges, T., Maier, C., Joshi, M. K., Blatt, R., Roos, C. F., & Zoller, P. (2020) · Physical Review Letters · doi:10.1103/physrevlett.124.010504 · Cited by 151
Error-protected qubits in a silicon photonic chip
Vigliar, C., Paesani, S., Ding, Y., Adcock, J. C., Wang, J., Morley-Short, S., Bacco, D., Oxenløwe, L. K., Thompson, M. G., Rarity, J. G., et al. (2021) · Nature Physics · doi:10.1038/s41567-021-01333-w · Cited by 118
Characterization of High-Dimensional Entangled Systems via Mutually Unbiased Measurements
Giovannini, D., Romero, J., Leach, J., Dudley, A., Forbes, A., & Padgett, M. J. (2013) · Physical Review Letters · doi:10.1103/physrevlett.110.143601 · Cited by 112
Banaszek, K., Cramer, M., & Gross, D. (2013) · New Journal of Physics · doi:10.1088/1367-2630/15/12/125020 · Cited by 105
Self-citationReliable quantum certification of photonic state preparations
Aolita, L., Gogolin, C., Kliesch, M., & Eisert, J. (2015) · Nature Communications · doi:10.1038/ncomms9498 · Cited by 98
Self-citationExperimental Estimation of Quantum State Properties from Classical Shadows
Struchalin, G. I., Zagorovskii, Y. A., Kovlakov, E. V., Straupe, S. S., & Kulik, S. P. (2021) · PRX Quantum · doi:10.1103/prxquantum.2.010307 · Cited by 94
Estimation of many-body quantum Hamiltonians via compressive sensing
Shabani, A., Mohseni, M., Lloyd, S., Kosut, R. L., & Rabitz, H. (2011) · Physical Review A · doi:10.1103/physreva.84.012107 · Cited by 78
Efficient quantum state tomography with convolutional neural networks
Schmale, T., Reh, M., & Gärttner, M. (2022) · npj Quantum Information · doi:10.1038/s41534-022-00621-4 · Cited by 76
Scalable on-chip quantum state tomography
Titchener, J. G., Gräfe, M., Heilmann, R., Solntsev, A. S., Szameit, A., & Sukhorukov, A. A. (2018) · npj Quantum Information · doi:10.1038/s41534-018-0063-5 · Cited by 61
“Some approaches seek to avoid unnecessary measurements by assuming that the system is in particular low-rank states, such as sparse states 14,15 or low dimensional matrix product states.”
BackgroundMiranowicz, A., Bartkiewicz, K., Peřina, J., Koashi, M., Imoto, N., & Nori, F. (2014) · Physical Review A · doi:10.1103/physreva.90.062123 · Cited by 57
Two-photon tomography using on-chip quantum walks
Titchener, J. G., Solntsev, A. S., & Sukhorukov, A. A. (2016) · Optics Letters · doi:10.1364/ol.41.004079 · Cited by 27
Entanglement quantification from collective measurements processed by machine learning
Roik, J., Bartkiewicz, K., Černoch, A., & Lemr, K. (2022) · Physics Letters A · doi:10.1016/j.physleta.2022.128270 · Cited by 26
Novelty, efficacy, and significance of weak measurements for quantum tomography
Gross, J. A., Dangniam, N., Ferrie, C., & Caves, C. M. (2015) · Physical Review A · doi:10.1103/physreva.92.062133 · Cited by 24
Partial randomized benchmarking
Dubovitskii, K., & Makhlin, Y. (2022) · Scientific Reports · doi:10.1038/s41598-022-13813-x · Cited by 1
Metadata
- Authors
- Gross, D., Liu, Y.-K., Flammia, S. T., Becker, S., & Eisert, J.
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2010-10-04
- Volume
- 105
- Issue
- 15
- Pages
- 150401-150401
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W1529624360
- Cited by
- 1,093
- References
- 1
- FWCI
- 46.25
- Type
- journal article
- Language
- en
- Open access
- green
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
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
