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Phys. Rev. A 73, 012340 (2006) [13 pages]

Operator quantum error-correcting subsystems for self-correcting quantum memories

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Dave Bacon
Department of Computer Science & Engineering, University of Washington, Seattle, Washington 98195, USA

Received 30 June 2005; published 30 January 2006

Themost general method for encoding quantum information is not toencode the information into a subspace of a Hilbert space,but to encode information into a subsystem of a Hilbertspace. Recently this notion has led to a more generalnotion of quantum error correction known as operator quantum errorcorrection. In standard quantum error-correcting codes, one requires the abilityto apply a procedure which exactly reverses on the error-correctingsubspace any correctable error. In contrast, for operator error-correcting subsystems,the correction procedure need not undo the error which hasoccurred, but instead one must perform corrections only modulo thesubsystem structure. This does not lead to codes which differfrom subspace codes, but does lead to recovery routines whichexplicitly make use of the subsystem structure. Here we presenttwo examples of such operator error-correcting subsystems. These examples aremotivated by simple spatially local Hamiltonians on square and cubiclattices. In three dimensions we provide evidence, in the forma simple mean field theory, that our Hamiltonian gives riseto a system which is self-correcting. Such a system willbe a natural high-temperature quantum memory, robust to noise withoutexternal intervening quantum error-correction procedures.

©2006 The American Physical Society

URL:	http://link.aps.org/doi/10.1103/PhysRevA.73.012340
DOI:	10.1103/PhysRevA.73.012340
PACS:	03.67.Lx; 75.10.Pq 03.67.Lx Quantum computation 75.10.Pq Spin chain models of magnetic ordering YEAR: 2006
KEYWORDS:	quantum computing, error correction, encoding, Hilbert spaces

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W. G. Unruh, Phys. Rev. A 51, 992 (1995).
P. W. Shor, Phys. Rev. A 52, R2493 (1995).
A. M. Steane, Phys. Rev. A 54, 4741 (1996).
E. Knill and R. Laflamme, Phys. Rev. A 55, 900 (1997).
C. H. Bennett, D. P. DiVincenzo, J. A. Smolin, and W. K. Wootters, Phys. Rev. A 54, 3824 (1996).
D. Gottesman, Phys. Rev. A 57, 127 (1998).
E. Knill, R. Laflamme, and L. Viola, Phys. Rev. Lett. 84, 2525 (2000).
J. Kempe, D. Bacon, D. A. Lidar, and K. B. Whaley, Phys. Rev. A 63, 042307 (2001).
P. Zanardi, Phys. Rev. A 63, 012301 (2001).
P. Zanardi and S. Lloyd, Phys. Rev. Lett. 90, 067902 (2003).
A. Shabani and D. Lidar, Phys. Rev. A 72, 042303 (2005).
L. Viola, E. Knill, and S. Lloyd, Phys. Rev. Lett. 85, 3520 (2000).
L. A. Wu and D. A. Lidar, Phys. Rev. Lett. 88, 207902 (2002).
D. Kribs, R. Laflamme, and D. Poulin, Phys. Rev. Lett. 94, 180501 (2005).
D. A. Lidar, I. L. Chuang, and K. B. Whaley, Phys. Rev. Lett. 81, 2594 (1998).
E. Dennis, A. Kitaev, A. Landahl, and J. Preskill, J. Math. Phys. 43, 4452 (2002).
B. Douçut, M. Feigel'man, L. Ioffe, and A. Ioselevich, Phys. Rev. B 71, 024505 (2005).
J. Dorier, F. Becca, and F. Mila, Phys. Rev. B 72, 024448 (2005).
J. P. Barnes and W. S. Warren, Phys. Rev. Lett. 85, 856 (2000).
C. Nayak and K. Shtengel, Phys. Rev. B 64, 064422 (2001).
D. Bacon, K. R. Brown, and K. B. Whaley, Phys. Rev. Lett. 87, 247902 (2001).
A. Hamma, P. Zanardi, and X. Wen, Phys. Rev. A 69, 062319 (2004).
M. Freedman, C. Nayak, and K. Shtengel, Phys. Rev. Lett. 94, 147205 (2004).
M. Freedman, C. Nayak, and K. Shtengel, Phys. Rev. Lett. 94, 066401 (2005).
L. M. Duan, E. Demler, and M. D. Lukin, Phys. Rev. Lett. 91, 090402 (2003).
G. Vidal, Phys. Rev. Lett. 91, 147902 (2003).
M. Reimpell and R. F. Werner, Phys. Rev. Lett. 94, 080501 (2005).

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