{"id":313187,"date":"2018-11-06T17:11:29","date_gmt":"2018-11-07T01:11:29","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/?post_type=msr-research-item&#038;p=313187"},"modified":"2018-11-06T17:11:29","modified_gmt":"2018-11-07T01:11:29","slug":"encoders-quantum-convolutional-codes","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/encoders-quantum-convolutional-codes\/","title":{"rendered":"On Encoders For Quantum Convolutional Codes"},"content":{"rendered":"<p><span style=\"font-family: Palatino Linotype;\">We consider the problem of computing an encoding circuit for a quantum convolutional code given by a polynomial stabilizer matrix S(D) = (X(D) | Z(D)). We present an algorithm that is very similar to a polynomial-time algorithm for computing the Smith form of a polynomial matrix. This is a step towards the conjecture that any quantum convolutional code has an encoder with polynomially bounded depth. <\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>We consider the problem of computing an encoding circuit for a quantum convolutional code given by a polynomial stabilizer matrix S(D) = (X(D) | Z(D)). We present an algorithm that is very similar to a polynomial-time algorithm for computing the Smith form of a polynomial matrix. This is a step towards the conjecture that any 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