© 2023 American Physical Society.
\n\nThis errata corrects some typographical errors and adds some relevant details that were missing in the the paper [J. Bentley, H. I Nurdin, Y. Chen, X. Li and H. Miao, “Designing optimal linear detectors—a bottom-up approach,” Phys. Rev. Applied 19, 034009 (2023)].
\n\nWe would like to thank Denis Martynov, LIGO AIC, and QNWG for fruitful discussions. J.B. is supported by the STFC and School of Physics and Astronomy at the University of Birmingham. J.B. and H.M. acknowledge the additional support from the Birmingham Institute for Gravitational Wave Astronomy. H.M. has also been supported by UK STFC Ernest Rutherford Fellowship (Grant No. ST/M005844/11). Y.C. is supported by the Simons Foundation (Award No. 568762), and the National Science Foundation, through Grants No. PHY-1708212 and No. PHY-1708213.
", "abstract": "This paper develops a systematic approach to realizing linear detectors with an optimized sensitivity, allowing for the detection of extremely weak signals. First, general constraints are derived on a specific class of input-output transfer functions of a linear detector. Then a physical realization of transfer functions in that class is found using the quantum network synthesis technique, which allows for the inference of the physical setup directly from the input-output transfer function. By exploring a minimal realization which has the minimum number of internal modes, it is shown that the optimal such detectors are internal squeezing schemes. Then, investigating nonminimal realizations, which is motivated by parity-time symmetric systems, a quantum nondemolition measurement is systematically recovered.", "date": "2024-03-14", "date_type": "published", "publication": "Physical Review Applied", "volume": "21", "number": "3", "publisher": "American Physical Society", "pagerange": "Art. No. 039901", "issn": "2331-7019", "official_url": "https://authors.library.caltech.edu/records/k91bj-w2e15", "funders": { "items": [ { "agency": "Birmingham Institute for Gravitational Wave Astronomy" }, { "agency": "Science and Technology Facilities Council (STFC)", "grant_number": "ST/M005844/11" }, { "agency": "Simons Foundation", "grant_number": "568762" }, { "agency": "NSF", "grant_number": "PHY-1708212" }, { "agency": "NSF", "grant_number": "PHY-1708213" } ] }, "local_group": { "items": [ { "id": "Astronomy-Department" }, { "id": "LIGO" }, { "id": "TAPIR" }, { "id": "Walter-Burke-Institute-for-Theoretical-Physics" }, { "id": "Physics-Department" } ] }, "doi": "10.1103/PhysRevApplied.21.039901", "primary_object": { "basename": "PhysRevApplied.21.039901.pdf", "url": "https://authors.library.caltech.edu/records/k91bj-w2e15/files/PhysRevApplied.21.039901.pdf" }, "pub_year": "2024", "author_list": "Bentley, Joe; Nurdin, Hendra; et al." }, { "id": "https://authors.library.caltech.edu/records/ynhzn-84626", "eprint_status": "archive", "datestamp": "2024-02-29 21:18:58", "lastmod": "2026-03-10 03:34:07", "type": "publication_erratum", "metadata_visibility": "show", "creators": { "items": [ { "id": "Lewis-Laura", "name": { "family": "Lewis", "given": "Laura" } }, { "id": "Huang-Hsin-Yuan", "name": { "family": "Huang", "given": "Hsin-Yuan" }, "orcid": "0000-0001-5317-2613" }, { "id": "Tran-Viet-T", "name": { "family": "Tran", "given": "Viet T." } }, { "id": "Lehner-Sebastian", "name": { "family": "Lehner", "given": "Sebastian" }, "orcid": "0000-0002-7562-8172" }, { "id": "Kueng-Richard", "name": { "family": "Kueng", "given": "Richard" }, "orcid": "0000-0002-8291-648X" }, { "id": "Preskill-J", "name": { "family": "Preskill", "given": "John" }, "orcid": "0000-0002-2421-4762" } ] }, "title": "Author Correction: Improved machine learning algorithm for predicting ground state properties", "ispublished": "pub", "full_text_status": "public", "keywords": "General Physics and Astronomy; General Biochemistry, Genetics and Molecular Biology; General Chemistry; Multidisciplinary; Computer science; Quantum information; Quantum mechanics", "note": "© The Author(s) 2024. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.
\n\nThe authors thank Chi-Fang Chen, Sitan Chen, Johannes Jakob Meyer, and Spiros Michalakis for valuable input and inspiring discussions. We thank Emilio Onorati, Cambyse Rouzé, Daniel Stilck França, and James D. Watson for sharing a draft of their new results on efficiently predicting properties of states in thermal phases of matter with exponential decay of correlation and in quantum phases of matter with local topological quantum order82. LL is supported by Caltech Summer Undergraduate Research Fellowship (SURF), Barry M. Goldwater Scholarship, and Mellon Mays Undergraduate Fellowship. HH is supported by a Google PhD fellowship and a MediaTek Research Young Scholarship. JP acknowledges support from the U.S. Department of Energy Office of Science, Office of Advanced Scientific Computing Research (DE-NA0003525, DE-SC0020290), the U.S. Department of Energy, Office of Science, National Quantum Information Science Research Centers, Quantum Systems Accelerator, and the National Science Foundation (PHY-1733907). The Institute for Quantum Information and Matter is an NSF Physics Frontiers Center.
\nH.H. and J.P. conceived the project. L.L. and H.H. developed the mathematical aspects of this work. L.L., H.H., S.L., and V.T. conducted the numerical experiments and wrote the open-source code. L.L., H.H., R.K., and J.P. wrote the paper.
\n\nSource data are available for this paper. All data can be found or generated using the source code at https://github.com/lllewis234/improved-ml-algorithm83.
\n\nSource code for an efficient implementation of the proposed procedure is available at https://github.com/lllewis234/improved-ml-algorithm83.
\n\nThe authors declare no competing interests.
\nCorrection to: Nature Communications https://doi.org/10.1038/s41467-024-45014-7, published online 30 January 2024
\nThe original version of this Article incorrectly acknowledged Laura Lewis as a corresponding author instead of Hsin-Yuan Huang. This has now been corrected in both the PDF and HTML versions of the Article.
\nFinding the ground state of a quantum many-body system is a fundamental problem in quantum physics. In this work, we give a classical machine learning (ML) algorithm for predicting ground state properties with an inductive bias encoding geometric locality. The proposed ML model can efficiently predict ground state properties of an n-qubit gapped local Hamiltonian after learning from only \ud835\udcaa(log\u2061(n)) data about other Hamiltonians in the same quantum phase of matter. This improves substantially upon previous results that require \ud835\udcaa(n\u1d9c) data for a large constant c. Furthermore, the training and prediction time of the proposed ML model scale as \ud835\udcaa(n log n) in the number of qubits n. Numerical experiments on physical systems with up to 45 qubits confirm the favorable scaling in predicting ground state properties using a small training dataset.
", "date": "2024-02-26", "date_type": "published", "publication": "Nature Communications", "volume": "15", "publisher": "Nature Publishing Group", "pagerange": "1740", "issn": "2041-1723", "official_url": "https://authors.library.caltech.edu/records/ynhzn-84626", "funders": { "items": [ { "grant_number": "Summer Undergraduate Research Fellowship" }, { "grant_number": "Barry M. Goldwater Scholarship" }, { "grant_number": "Mellon Mays Undergraduate Fellowship" }, {}, {}, { "grant_number": "DE-NA0003525" }, { "grant_number": "DE-SC0020290" }, { "grant_number": "PHY-1733907" } ] }, "local_group": { "items": [ { "id": "AWS-Center-for-Quantum-Computing" }, { "id": "Walter-Burke-Institute-for-Theoretical-Physics" }, { "id": "IQIM" }, { "id": "Physics-Department" } ] }, "doi": "10.1038/s41467-024-46164-4", "primary_object": { "basename": "s41467-024-46164-4.pdf", "url": "https://authors.library.caltech.edu/records/ynhzn-84626/files/s41467-024-46164-4.pdf" }, "pub_year": "2024", "author_list": "Lewis, Laura; Huang, Hsin-Yuan; et al." }, { "id": "https://authors.library.caltech.edu/records/sqkeq-39m86", "eprint_status": "archive", "datestamp": "2024-02-29 22:11:19", "lastmod": "2026-03-10 03:34:30", "type": "publication_erratum", "metadata_visibility": "show", "creators": { "items": [ { "name": { "family": "Chen", "given": "Sitan" } }, { "name": { "family": "Cotler", "given": "Jordan" }, "orcid": "0000-0003-3161-9677" }, { "id": "Huang-Hsin-Yuan", "name": { "family": "Huang", "given": "Hsin-Yuan" }, "orcid": "0000-0001-5317-2613" }, { "id": "Li-Jerry", "name": { "family": "Li", "given": "Jerry" } } ] }, "title": "Publisher Correction: The complexity of NISQ", "ispublished": "pub", "full_text_status": "public", "keywords": "General Physics and Astronomy; General Biochemistry, Genetics and Molecular Biology; General Chemistry; Multidisciplinary; Computer science; Information theory and computation; Quantum information", "note": "\u00a9 The Author(s) 2023. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
\n\nWe would like to thank Isaac Chuang for valuable conversations on complexity classes for learning theory, John Preskill for inspiring discussions on NISQ and its complexity class formulation, and John Wright for bringing76 and related works to our attention. S.C. is supported by NSF Award 2103300. J.C. is supported by a Junior Fellowship from the Harvard Society of Fellows, as well as in part by the Department of Energy under grant DE-SC0007870. H.H. is supported by a Google Ph.D. fellowship.
\n\nS.C., J.C., H.H., and J.L. contributed equally to this work. All authors developed the theoretical aspects of this work and wrote the manuscript together.
\n\nThe authors declare no competing interests.
\n\nCorrection to: Nature Communications https://doi.org/10.1038/s41467-023-41217-6, published online 26 September 2023
\nIn the original pdf version of this Article, the text of Theorems 2.2 and 2.3 in the Results section was missing the \u228a symbol. The html version displayed the theorems in the correct form.
\nThis has now been corrected.
\nThe recent proliferation of NISQ devices has made it imperative to understand their power. In this work, we define and study the complexity class , which encapsulates problems that can be efficiently solved by a classical computer with access to noisy quantum circuits. We establish super-polynomial separations in the complexity among classical computation, , and fault-tolerant quantum computation to solve some problems based on modifications of Simon's problems. We then consider the power of for three well-studied problems. For unstructured search, we prove that cannot achieve a Grover-like quadratic speedup over classical computers. For the Bernstein-Vazirani problem, we show that only needs a number of queries logarithmic in what is required for classical computers. Finally, for a quantum state learning problem, we prove that is exponentially weaker than classical computers with access to noiseless constant-depth quantum circuits.
", "date": "2024-02-12", "date_type": "published", "publication": "Nature Communications", "volume": "15", "publisher": "Nature Publishing Group", "pagerange": "1308", "issn": "2041-1723", "official_url": "https://authors.library.caltech.edu/records/sqkeq-39m86", "funders": { "items": [ { "grant_number": "DMS-2103300" }, {}, { "grant_number": "DE-SC0007870" }, { "agency": "Google PhD Fellowship" } ] }, "local_group": { "items": [ { "id": "IQIM" }, { "id": "Physics-Department" } ] }, "doi": "10.1038/s41467-024-45799-7", "primary_object": { "basename": "s41467-024-45799-7.pdf", "url": "https://authors.library.caltech.edu/records/sqkeq-39m86/files/s41467-024-45799-7.pdf" }, "pub_year": "2024", "author_list": "Chen, Sitan; Cotler, Jordan; et al." } ]