{"id":314006,"date":"2018-11-06T17:09:23","date_gmt":"2018-11-07T01:09:23","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/?post_type=msr-research-item&#038;p=314006"},"modified":"2018-11-06T17:09:23","modified_gmt":"2018-11-07T01:09:23","slug":"engineering-functional-quantum-algorithms","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/engineering-functional-quantum-algorithms\/","title":{"rendered":"Engineering Functional Quantum Algorithms"},"content":{"rendered":"<p><span style=\"font-family: Palatino Linotype;\">Suppose that a quantum circuit with K elementary gates is known for a unitary matrix U, and assume that U^m is a scalar matrix for some positive integer m. We show that a function of U can be realized on a quantum computer with at most O(mK+m^2log m) elementary gates. The functions of U are realized by a generic quantum circuit, which has a particularly simple structure. Among other results, we obtain efficient circuits for the fractional Fourier transform. <\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Suppose that a quantum circuit with K elementary gates is known for a unitary matrix U, and assume that U^m is a scalar matrix for some positive integer m. We show that a function of U can be realized on a quantum computer with at most O(mK+m^2log m) elementary gates. The functions of U are 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