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Achieving the Heisenberg limit in quantum metrology using quantum error correction

Zhou, Sisi and Zhang, Mengzhen and Preskill, John and Jiang, Liang (2018) Achieving the Heisenberg limit in quantum metrology using quantum error correction. Nature Communications, 9 . Art. No. 78. ISSN 2041-1723. PMCID PMC5758555. doi:10.1038/s41467-017-02510-3.

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Quantum metrology has many important applications in science and technology, ranging from frequency spectroscopy to gravitational wave detection. Quantum mechanics imposes a fundamental limit on measurement precision, called the Heisenberg limit, which can be achieved for noiseless quantum systems, but is not achievable in general for systems subject to noise. Here we study how measurement precision can be enhanced through quantum error correction, a general method for protecting a quantum system from the damaging effects of noise. We find a necessary and sufficient condition for achieving the Heisenberg limit using quantum probes subject to Markovian noise, assuming that noiseless ancilla systems are available, and that fast, accurate quantum processing can be performed. When the sufficient condition is satisfied, a quantum error-correcting code can be constructed that suppresses the noise without obscuring the signal; the optimal code, achieving the best possible precision, can be found by solving a semidefinite program.

Item Type:Article
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URLURL TypeDescription CentralArticle Paper
Preskill, John0000-0002-2421-4762
Jiang, Liang0000-0002-0000-9342
Additional Information:© 2018 Macmillan Publishers Limited, part of Springer Nature. 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 Received: 07 June 2017; Accepted: 05 December 2017; Published online: 08 January 2018. We thank Fernando Brandão, Yanbei Chen, Steve Girvin, Linshu Li, Mikhail Lukin, Changling Zou for inspiring discussions. We acknowledge support from the ARL-CDQI (W911NF-15-2-0067), ARO (W911NF-14-1-0011, W911NF-14-1-0563), ARO MURI (W911NF-16-1-0349), AFOSR MURI (FA9550-14-1-0052, FA9550-15-1-0015), NSF (EFMA-1640959), Alfred P. Sloan Foundation (BR2013-049), and Packard Foundation (2013-39273). The Institute for Quantum Information and Matter is an NSF Physics Frontiers Center with support from the Gordon and Betty Moore Foundation. Author Contributions: J.P. and L.J. conceived this project. S.Z. proved linear scaling of the QFI and constructed the QEC code. S.Z., M.Z. and L.J. formulated the QEC condition. S.Z., J.P. and L.J. wrote the manuscript. The authors declare no competing financial interests.
Group:Institute for Quantum Information and Matter
Funding AgencyGrant Number
Army Research Office (ARO)W911NF-15-2-0067
Army Research Office (ARO)W911NF-14-1-0011
Army Research Office (ARO)W911NF-14-1-0563
Army Research Office (ARO)W911NF-16-1-0349
Air Force Office of Scientific Research (AFOSR)FA9550-14-1-0052
Air Force Office of Scientific Research (AFOSR)FA9550-15-1-0015
Alfred P. Sloan FoundationBR2013-049
David and Lucile Packard Foundation2013-39273
Gordon and Betty Moore FoundationUNSPECIFIED
PubMed Central ID:PMC5758555
Record Number:CaltechAUTHORS:20170720-172112488
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:79259
Deposited By: Joy Painter
Deposited On:21 Jul 2017 16:04
Last Modified:18 Mar 2022 19:10

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