Entanglement-assisted quantum low-density parity-check codes

This article develops a general method for constructing entanglement-assisted quantum low-density parity-check (LDPC) codes, which is based on combinatorial design theory. Explicit constructions are given for entanglement-assisted quantum error-correcting codes with many desirable properties. These...

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Bibliographic Details
Published in:Physical review. A, Atomic, molecular, and optical physics Atomic, molecular, and optical physics, 2010-10, Vol.82 (4)
Main Authors: Fujiwara, Yuichiro, Clark, David, Tonchev, Vladimir D., Vandendriessche, Peter, De Boeck, Maarten
Format: Article
Language:English
Subjects:
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
CORRECTIONS
DENSITY
ERRORS
MECHANICS
PARITY
PARTICLE PROPERTIES
PHYSICAL PROPERTIES
QUANTUM ENTANGLEMENT
QUANTUM MECHANICS
QUANTUM STATES
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Summary:This article develops a general method for constructing entanglement-assisted quantum low-density parity-check (LDPC) codes, which is based on combinatorial design theory. Explicit constructions are given for entanglement-assisted quantum error-correcting codes with many desirable properties. These properties include the requirement of only one initial entanglement bit, high error-correction performance, high rates, and low decoding complexity. The proposed method produces several infinite families of codes with a wide variety of parameters and entanglement requirements. Our framework encompasses the previously known entanglement-assisted quantum LDPC codes having the best error-correction performance and many other codes with better block error rates in simulations over the depolarizing channel. We also determine important parameters of several well-known classes of quantum and classical LDPC codes for previously unsettled cases.
ISSN:1050-2947
1094-1622
DOI:10.1103/PHYSREVA.82.042338