Quantum ``hyperbicycle'' low-stabilizer-weight finite-rate error correction codes
ORAL
Abstract
We construct a large family of finite-rate quantum error correcting codes (QECCs) which interpolate between the hypergraph-product [1] and generalized bicycle codes [2]. The construction allows for the lower and upper bounds on the distance which generally scale as a square root of the block size; in several important cases the two bounds coincide. The constructed QECCs include several new classes of codes with low stabilizer weights; they can offer an advantage compared to the toric codes. \\[0.2em] [1] J.-P. Tillich and G. Z\'emor, in Proc. IEEE Int. Symp. Inf. Th., 2009 (ISIT 2009), pp. 799-803.\\[0em] [2] D. MacKay, G. Mitchison, and P. McFadden, IEEE Trans. on Inf. Th., {\bf 50}, 2315 (2004).
*This research was supported in part by the U.S. Army Research Office under Grant No. W911NF-11-1-0027, and by the NSF under Grant No. 1018935.
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