High-Rate Quantum Low-Density Parity-Check Codes Assisted by Reliable Qubits
Abstract
Quantum error correction is an important building block for reliable quantum information processing. A challenging hurdle in the theory of quantum error correction is that it is significantly more difficult to design error-correcting codes with desirable properties for quantum information processing than for traditional digital communications and computation. A typical obstacle to constructing a variety of strong quantum error-correcting codes is the complicated restrictions imposed on the structure of a code. Recently, promising solutions to this problem have been proposed in quantum information science, where in principle any binary linear code can be turned into a quantum error-correcting code by assuming a small number of reliable quantum bits. This paper studies how best to take advantage of these latest ideas to construct desirable quantum error-correcting codes of very high information rate. Our methods exploit structured high-rate low-density parity-check codes available in the classical domain and provide quantum analogues that inherit their characteristic low decoding complexity and high error correction performance even at moderate code lengths. Our approach to designing high-rate quantum error-correcting codes also allows for making direct use of other major syndrome decoding methods for linear codes, making it possible to deal with a situation where promising quantum analogues of low-density parity-check codes are difficult to find.
Additional Information
© 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. Date of Publication : 30 January 2015. Early Access Article. This work was supported by JSPS (Y.F.), LGFG Baden-Württemberg (A.G.), and FWO (P.V.). The third author is support by a PhD fellowship of the Research Foundation - Flanders (FWO). The authors would like to thank the anonymous referees and Associate Editor Alexei Ashikhmin for their careful reading of the manuscript and valuable suggestions.Attached Files
Published - 07027863.pdf
Submitted - 1309.5587v1.pdf
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Additional details
- Eprint ID
- 54366
- Resolver ID
- CaltechAUTHORS:20150204-101038094
- Japan Society for the Promotion of Science (JSPS)
- LGFG Baden-Württemberg
- FWO (Belgium)
- FWO-Flanders (Belgium)
- Created
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2015-02-04Created from EPrint's datestamp field
- Updated
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2021-11-10Created from EPrint's last_modified field