Ancilla-Free Quantum Error Correction Codes for Quantum Metrology

Layden, David; Zhou, Sisi; Cappellaro, Paola; Jiang, Liang

doi:10.1103/physrevlett.122.040502

Title: Ancilla-Free Quantum Error Correction Codes for Quantum Metrology

Journal Article · Wed Jan 30 00:00:00 EST 2019 · Physical Review Letters

DOI:https://doi.org/10.1103/physrevlett.122.040502· OSTI ID:1613222

Layden, David ^[1]; Zhou, Sisi ^[2]; Cappellaro, Paola ^[1]; Jiang, Liang ^[2]

Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
Yale Univ., New Haven, CT (United States)

Quantum error correction has recently emerged as a tool to enhance quantum sensing under Markovian noise. It works by correcting errors in a sensor while letting a signal imprint on the logical state. This approach typically requires a specialized error-correcting code, as most existing codes correct away both the dominant errors and the signal. To date, however, few such specialized codes are known, among which most require noiseless, controllable ancillas. We show here that such ancillas are not needed when the signal Hamiltonian and the error operators commute, a common limiting type of decoherence in quantum sensors. We give a semidefinite program for finding optimal ancilla-free sensing codes in general, as well as closed-form codes for two common sensing scenarios: qubits undergoing dephasing, and a lossy bosonic mode. Lastly, we analyze the sensitivity enhancement offered by the qubit code under arbitrary spatial noise correlations, beyond the ideal limit of orthogonal signal and noise operators.

View Accepted Manuscript (DOE)

Cite

Export

Save

Research Organization:: Yale Univ., New Haven, CT (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

Grant/Contract Number:: SC0019406

OSTI ID:: 1613222

Alternate ID(s):: OSTI ID: 1492913

Journal Information:: Physical Review Letters, Vol. 122, Issue 4; ISSN 0031-9007

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

Citation Metrics:

Cited by: 44 works

Citation information provided by
Web of Science

References (52)

Quantum Metrology Enhanced by Repetitive Quantum Error Correction Unden, Thomas; Balasubramanian, Priya; Louzon, Daniel Physical Review Letters, Vol. 116, Issue 23 https://doi.org/10.1103/PhysRevLett.116.230502	journal	June 2016
Quantum metrology with full and fast quantum control Sekatski, Pavel; Skotiniotis, Michalis; Kołodyński, Janek Quantum, Vol. 1 https://doi.org/10.22331/q-2017-09-06-27	journal	September 2017
Storing quantum information for 30 seconds in a nanoelectronic device Muhonen, Juha T.; Dehollain, Juan P.; Laucht, Arne Nature Nanotechnology, Vol. 9, Issue 12 https://doi.org/10.1038/nnano.2014.211	journal	October 2014
The nitrogen-vacancy colour centre in diamond Doherty, Marcus W.; Manson, Neil B.; Delaney, Paul Physics Reports, Vol. 528, Issue 1 https://doi.org/10.1016/j.physrep.2013.02.001	journal	July 2013
The minimum variance of estimates in quantum signal detection Helstrom, C. IEEE Transactions on Information Theory, Vol. 14, Issue 2 https://doi.org/10.1109/TIT.1968.1054108	journal	March 1968
Convex Optimization Boyd, Stephen; Vandenberghe, Lieven https://doi.org/10.1017/CBO9780511804441	book	January 2004
Achieving the Heisenberg limit in quantum metrology using quantum error correction Zhou, Sisi; Zhang, Mengzhen; Preskill, John Nature Communications, Vol. 9, Issue 1 https://doi.org/10.1038/s41467-017-02510-3	journal	January 2018
Theory of Quantum Error Correction for General Noise Knill, Emanuel; Laflamme, Raymond; Viola, Lorenza Physical Review Letters, Vol. 84, Issue 11 https://doi.org/10.1103/PhysRevLett.84.2525	journal	March 2000
Quantum Error Correction for Metrology Kessler, E. M.; Lovchinsky, I.; Sushkov, A. O. Physical Review Letters, Vol. 112, Issue 15 https://doi.org/10.1103/PhysRevLett.112.150802	journal	April 2014
Optimal adaptive control for quantum metrology with time-dependent Hamiltonians Pang, Shengshi; Jordan, Andrew N. Nature Communications, Vol. 8, Issue 1 https://doi.org/10.1038/ncomms14695	journal	March 2017
Increasing Sensing Resolution with Error Correction Arrad, G.; Vinkler, Y.; Aharonov, D. Physical Review Letters, Vol. 112, Issue 15 https://doi.org/10.1103/PhysRevLett.112.150801	journal	April 2014
Advances in quantum metrology Giovannetti, Vittorio; Lloyd, Seth; Maccone, Lorenzo Nature Photonics, Vol. 5, Issue 4 https://doi.org/10.1038/nphoton.2011.35	journal	March 2011
Improved Quantum Metrology Using Quantum Error Correction Dür, W.; Skotiniotis, M.; Fröwis, F. Physical Review Letters, Vol. 112, Issue 8 https://doi.org/10.1103/PhysRevLett.112.080801	journal	February 2014
Quantum Metrology Giovannetti, Vittorio; Lloyd, Seth; Maccone, Lorenzo Physical Review Letters, Vol. 96, Issue 1 https://doi.org/10.1103/PhysRevLett.96.010401	journal	January 2006
Adaptive Quantum Metrology under General Markovian Noise Demkowicz-Dobrzański, Rafał; Czajkowski, Jan; Sekatski, Pavel Physical Review X, Vol. 7, Issue 4 https://doi.org/10.1103/PhysRevX.7.041009	journal	October 2017
Quantum Computation and Quantum Information Nielsen, Michael A.; Chuang, Isaac L. Cambridge University Press https://doi.org/10.1017/CBO9780511976667	book	January 2011
Dephasing time of GaAs electron-spin qubits coupled to a nuclear bath exceeding 200 μs Bluhm, Hendrik; Foletti, Sandra; Neder, Izhar Nature Physics, Vol. 7, Issue 2 https://doi.org/10.1038/nphys1856	journal	December 2010
Bosonic quantum codes for amplitude damping Chuang, Isaac L.; Leung, Debbie W.; Yamamoto, Yoshihisa Physical Review A, Vol. 56, Issue 2 https://doi.org/10.1103/PhysRevA.56.1114	journal	August 1997
Mixed-state entanglement and quantum error correction Bennett, Charles H.; DiVincenzo, David P.; Smolin, John A. Physical Review A, Vol. 54, Issue 5 https://doi.org/10.1103/PhysRevA.54.3824	journal	November 1996
Optimized dynamical decoupling in a model quantum memory Biercuk, Michael J.; Uys, Hermann; VanDevender, Aaron P. Nature, Vol. 458, Issue 7241 https://doi.org/10.1038/nature07951	journal	April 2009
Completely positive dynamical semigroups of N-level systems Gorini, Vittorio Journal of Mathematical Physics, Vol. 17, Issue 5 https://doi.org/10.1063/1.522979	journal	January 1976
Quantum Estimation for Quantum Technology Paris, Matteo G. A. International Journal of Quantum Information, Vol. 07, Issue supp01 https://doi.org/10.1142/S0219749909004839	journal	January 2009
Quantum sensing Degen, C. L.; Reinhard, F.; Cappellaro, P. Reviews of Modern Physics, Vol. 89, Issue 3 https://doi.org/10.1103/RevModPhys.89.035002	journal	July 2017
Photon-echo technique for reducing the decoherence of a quantum bit Ban, Masashi Journal of Modern Optics, Vol. 45, Issue 11 https://doi.org/10.1080/09500349808231241	journal	November 1998
Flux qubits in a planar circuit quantum electrodynamics architecture: Quantum control and decoherence Orgiazzi, J. -L.; Deng, C.; Layden, D. Physical Review B, Vol. 93, Issue 10 https://doi.org/10.1103/PhysRevB.93.104518	journal	March 2016
Dynamical suppression of decoherence in two-state quantum systems Viola, Lorenza; Lloyd, Seth Physical Review A, Vol. 58, Issue 4 https://doi.org/10.1103/PhysRevA.58.2733	journal	October 1998
Improvement of Frequency Standards with Quantum Entanglement Huelga, S. F.; Macchiavello, C.; Pellizzari, T. Physical Review Letters, Vol. 79, Issue 20 https://doi.org/10.1103/PhysRevLett.79.3865	journal	November 1997
Dissipative quantum error correction and application to quantum sensing with trapped ions Reiter, F.; Sørensen, A. S.; Zoller, P. Nature Communications, Vol. 8, Issue 1 https://doi.org/10.1038/s41467-017-01895-5	journal	November 2017
Statistical distance and the geometry of quantum states Braunstein, Samuel L.; Caves, Carlton M. Physical Review Letters, Vol. 72, Issue 22 https://doi.org/10.1103/PhysRevLett.72.3439	journal	May 1994
Optimum quantum error recovery using semidefinite programming Fletcher, Andrew S.; Shor, Peter W.; Win, Moe Z. Physical Review A, Vol. 75, Issue 1 https://doi.org/10.1103/PhysRevA.75.012338	journal	January 2007
Spatial noise filtering through error correction for quantum sensing Layden, David; Cappellaro, Paola npj Quantum Information, Vol. 4, Issue 1 https://doi.org/10.1038/s41534-018-0082-2	journal	July 2018
Sequential Feedback Scheme Outperforms the Parallel Scheme for Hamiltonian Parameter Estimation Yuan, Haidong Physical Review Letters, Vol. 117, Issue 16 https://doi.org/10.1103/PhysRevLett.117.160801	journal	October 2016
Perturbative Quantum Error Correction Bény, Cédric Physical Review Letters, Vol. 107, Issue 8 https://doi.org/10.1103/PhysRevLett.107.080501	journal	August 2011
Quantum error correction via convex optimization Kosut, Robert L.; Lidar, Daniel A. Quantum Information Processing, Vol. 8, Issue 5 https://doi.org/10.1007/s11128-009-0120-2	journal	July 2009
Electron Spin Decoherence in Isotope-Enriched Silicon Witzel, Wayne M.; Carroll, Malcolm S.; Morello, Andrea Physical Review Letters, Vol. 105, Issue 18 https://doi.org/10.1103/PhysRevLett.105.187602	journal	October 2010
Theory of quantum error-correcting codes Knill, Emanuel; Laflamme, Raymond Physical Review A, Vol. 55, Issue 2 https://doi.org/10.1103/PhysRevA.55.900	journal	February 1997
New Class of Quantum Error-Correcting Codes for a Bosonic Mode Michael, Marios H.; Silveri, Matti; Brierley, R. T. Physical Review X, Vol. 6, Issue 3 https://doi.org/10.1103/PhysRevX.6.031006	journal	July 2016
Quantum computation and quantum information† Nagy, Marius; Akl, Selim G. International Journal of Parallel, Emergent and Distributed Systems, Vol. 21, Issue 1 https://doi.org/10.1080/17445760500355678	journal	February 2006
Quantum Error Correction Gottesman, Daniel The University of British Columbia https://doi.org/10.14288/1.0040931	text	January 2010
Optimized Dynamical Decoupling in a Model Quantum Memory Biercuk, Michael J.; Uys, Hermann; VanDevender, Aaron P. arXiv https://doi.org/10.48550/arxiv.0812.5095	text	January 2008
Advances in Quantum Metrology Giovannetti, Vittorio; Lloyd, Seth; Maccone, Lorenzo arXiv https://doi.org/10.48550/arxiv.1102.2318	text	January 2011
Perturbative quantum error correction Bény, Cédric arXiv https://doi.org/10.48550/arxiv.1102.3809	text	January 2011
Quantum Error Correction for Metrology Kessler, Eric M.; Lovchinsky, Igor; Sushkov, Alexander O. arXiv https://doi.org/10.48550/arxiv.1310.3260	text	January 2013
Improved quantum metrology using quantum error-correction Dür, W.; Skotiniotis, M.; Fröwis, F. arXiv https://doi.org/10.48550/arxiv.1310.3750	text	January 2013
Storing quantum information for 30 seconds in a nanoelectronic device Muhonen, Juha T.; Dehollain, Juan P.; Laucht, Arne arXiv https://doi.org/10.48550/arxiv.1402.7140	text	January 2014
Sequential feedback scheme outperforms the parallel scheme for Hamiltonian parameter estimation Yuan, Haidong arXiv https://doi.org/10.48550/arxiv.1601.04466	text	January 2016
Quantum metrology with full and fast quantum control Sekatski, Pavel; Skotiniotis, Michalis; Kołodyński, Janek arXiv https://doi.org/10.48550/arxiv.1603.08944	text	January 2016
Achieving the Heisenberg limit in quantum metrology using quantum error correction Zhou, Sisi; Zhang, Mengzhen; Preskill, John arXiv https://doi.org/10.48550/arxiv.1706.02445	text	January 2017
Quantum metrology Giovannetti, Vittorio; Lloyd, Seth; Maccone, Lorenzo arXiv https://doi.org/10.48550/arxiv.quant-ph/0509179	text	January 2005
Optimum Quantum Error Recovery using Semidefinite Programming Fletcher, Andrew S.; Shor, Peter W.; Win, Moe Z. arXiv https://doi.org/10.48550/arxiv.quant-ph/0606035	text	January 2006
Theory of Quantum Error Correction for General Noise Knill, Emanuel; Laflamme, Raymond; Viola, Lorenza arXiv https://doi.org/10.48550/arxiv.quant-ph/9908066	preprint	January 1999
Management of patients with Graves' orbitopathy: initial assessment, management outside specialized centres and referral pathways Orgiazzi, J. Clinical Endocrinology, Vol. 84, Issue 5 https://doi.org/10.1111/cen.13039	journal	March 2016

Cited By (14)

Tensor-network approach for quantum metrology in many-body quantum systems Chabuda, Krzysztof; Dziarmaga, Jacek; Osborne, Tobias J. Nature Communications, Vol. 11, Issue 1 https://doi.org/10.1038/s41467-019-13735-9	journal	January 2020
Quantum-error-correction-assisted quantum metrology without entanglement Tan, Kok Chuan; Omkar, S.; Jeong, Hyunseok Physical Review A, Vol. 100, Issue 2 https://doi.org/10.1103/physreva.100.022312	journal	August 2019
Efficient Quantum Error Correction of Dephasing Induced by a Common Fluctuator Layden, David; Chen, Mo; Cappellaro, Paola Physical Review Letters, Vol. 124, Issue 2 https://doi.org/10.1103/physrevlett.124.020504	journal	January 2020
Nanosystems, Edge Computing, and the Next Generation Computing Systems Passian, Ali; Imam, Neena Sensors, Vol. 19, Issue 18 https://doi.org/10.3390/s19184048	journal	September 2019
Tensor-network approach for quantum metrology in many-body quantum systems Chabuda, Krzysztof; Dziarmaga, Jacek; Osborne, Tobias J. London : Nature Publishing Group https://doi.org/10.15488/10595	other	January 2020
Fault-tolerant quantum metrology Kapourniotis, Theodoros; Datta, Animesh arXiv https://doi.org/10.48550/arxiv.1807.04267	text	January 2018
Quantum error correction assisted quantum metrology without entanglement Tan, K. C.; Omkar, S.; Jeong, H. arXiv https://doi.org/10.48550/arxiv.1901.03493	text	January 2019
Efficient quantum error correction of dephasing induced by a common fluctuator Layden, David; Chen, Mo; Cappellaro, Paola arXiv https://doi.org/10.48550/arxiv.1903.01046	text	January 2019
Optimal probes and error-correction schemes in multi-parameter quantum metrology Gorecki, Wojciech; Zhou, Sisi; Jiang, Liang arXiv https://doi.org/10.48550/arxiv.1901.00896	text	January 2019
Optimal approximate quantum error correction for quantum metrology Zhou, Sisi; Jiang, Liang arXiv https://doi.org/10.48550/arxiv.1910.08472	text	January 2019
Decoherence-Free Rotational Degrees of Freedom for Quantum Applications Pedernales, Julen S.; Cosco, Francesco; Plenio, Martin B. arXiv https://doi.org/10.48550/arxiv.2001.00826	text	January 2020
Fluctuation-enhanced quantum metrology Chen, Yu; Chen, Hongzhen; Liu, Jing arXiv https://doi.org/10.48550/arxiv.2003.13010	preprint	January 2020
Ancilla-assisted frequency estimation under phase covariant noises with Greenberger-Horne-Zeilinger states Cai, Rui-Jie; Zhong, Wei; Zhou, Lan arXiv https://doi.org/10.48550/arxiv.2006.11498	text	January 2020
Quantum Plasmonic Sensors Lee, Changhyoup; Lawrie, Benjamin; Pooser, Raphael arXiv https://doi.org/10.48550/arxiv.2012.01525	text	January 2020

Similar Records

Continuous quantum error correction for non-Markovian decoherence

Journal Article · Wed Aug 15 00:00:00 EDT 2007 · Physical Review. A · OSTI ID:1613222

Oreshkov, Ognyan; Brun, Todd A

Entanglement Purification and Protection in a Superconducting Quantum Network

Journal Article · Tue Feb 22 00:00:00 EST 2022 · Physical Review Letters · OSTI ID:1613222

Yan, Haoxiong; Zhong, Youpeng; Chang, Hung-Shen; +7 more

Repetitive Quantum Nondemolition Measurement and Soft Decoding of a Silicon Spin Qubit

Journal Article · Wed Apr 08 00:00:00 EDT 2020 · Physical Review. X · OSTI ID:1613222

Xue, Xiao; D’Anjou, Benjamin; Watson, Thomas F.; +8 more

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
Physics
Quantum error correction
Quantum metrology
Quantum sensing

Title: Ancilla-Free Quantum Error Correction Codes for Quantum Metrology

Citation Formats

References (52)

Cited By (14)

Similar Records

Related Subjects