{"id":313955,"date":"2018-11-06T17:09:32","date_gmt":"2018-11-07T01:09:32","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/?post_type=msr-research-item&#038;p=313955"},"modified":"2018-11-06T17:09:32","modified_gmt":"2018-11-07T01:09:32","slug":"optimal-quantum-codes","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/optimal-quantum-codes\/","title":{"rendered":"On Optimal Quantum Codes"},"content":{"rendered":"<p><span style=\"font-family: Palatino Linotype;\">We present families of quantum error-correcting codes which are optimal in the sense that the minimum distance is maximal. These maximum distance separable (MDS) codes are defined over q-dimensional quantum systems, where q is an arbitrary prime power. It is shown that codes with parameters [[n,n-2d+2,d]]_q exist for all 3 <= n <= q and 1< = d <= n\/2+1. We also present quantum MDS codes with parameters [[q^2,q^2-2d+2,d]]_q for 1 <= d <= q which additionally give rise to shortened codes [[q^2-s,q^2-2d+2-s,d]]_q for some s. <\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>We present families of quantum error-correcting codes which are optimal in the sense that the minimum distance is maximal. These maximum distance separable (MDS) codes are defined over q-dimensional quantum systems, where q is an arbitrary prime power. It is shown that codes with parameters [[n,n-2d+2,d]]_q exist for all 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