Title

Entanglement-assisted quantum low-density parity-check codes

Authors

Yuichiro Fujiwara, California Institute of Technology
David C. Clark, Michigan Technological University
Peter Vandendriessche, Ghent University
Maarten De Boeck, Ghent University
Vladimir Tonchev, Michigan Technological UniversityFollow

Document Type

Article

Publication Date

10-29-2010

Abstract

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.

Publisher's Statement

©2010 American Physical Society. Publisher’s version of record: https://doi.org/10.1103/PhysRevA.82.042338

Publication Title

Physical Review A

Recommended Citation

Fujiwara, Y., Clark, D. C., Vandendriessche, P., De Boeck, M., & Tonchev, V. (2010). Entanglement-assisted quantum low-density parity-check codes. Physical Review A, 82(4), 042338-1-042338-19. http://doi.org/10.1103/PhysRevA.82.042338
Retrieved from: https://digitalcommons.mtu.edu/math-fp/102

Version

Publisher's PDF