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Degenerate Quantum Codes for Pauli Channels

Smith, Graeme and Smolin, John A. (2007) Degenerate Quantum Codes for Pauli Channels. Physical Review Letters, 98 (3). Art. No. 030501. ISSN 0031-9007.

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A striking feature of quantum error correcting codes is that they can sometimes be used to correct more errors than they can uniquely identify. Such degenerate codes have long been known, but have remained poorly understood. We provide a heuristic for designing degenerate quantum codes for high noise rates, which is applied to generate codes that can be used to communicate over almost any Pauli channel at rates that are impossible for a nondegenerate code. The gap between nondegenerate and degenerate code performance is quite large, in contrast to the tiny magnitude of the only previous demonstration of this effect. We also identify a channel for which none of our codes outperform the best nondegenerate code and show that it is nevertheless quite unlike any channel for which nondegenerate codes are known to be optimal.

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Additional Information:©2007 The American Physical Society (Received 27 April 2006; revised 9 October 2006; published 16 January 2007) We are grateful to D.P. DiVincenzo, D. Leung, and M.B. Ruskai for valuable discussions. G.S. thanks NSF PHY-0456720 and NSERC of Canada. J.A.S. thanks ARO Contract No. DAAD19-01-C-0056.
Issue or Number:3
Record Number:CaltechAUTHORS:SMIprl07a
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:7222
Deposited By: Archive Administrator
Deposited On:18 Jan 2007
Last Modified:02 Oct 2019 23:40

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