Approximating Fractional Time Quantum Evolution

Abstract

An algorithm is presented for approximating arbitrary powers of a black box unitary operation, Ut, where t is a real number, and U is a black box implementing an unknown unitary. The complexity of this algorithm is calculated in terms of the number of calls to the black box, the errors in the approximation, and a certain `gap' parameter. For general U and large t, one should apply U a total of t times followed by our procedure for approximating the fractional power Ut- t . An example is also given where for large integers t this method is more efficient than direct application of t copies of U. Further applications and related algorithms are also discussed.

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