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arXiv · 0810.3843

Approximating Fractional Time Quantum Evolution

L. Sheridan·D. Maslov·M. Mosca
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Abstract

An algorithm is presented for approximating arbitrary powers of a black box unitary operation, $\mathcal{U}^t$, where $t$ is a real number, and $\mathcal{U}$ 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 $\mathcal{U}$ and large $t$, one should apply $\mathcal{U}$ a total of $\lfloor t \rfloor$ times followed by our procedure for approximating the fractional power $\mathcal{U}^{t-\lfloor t \rfloor}$. An example is also given where for large integers $t$ this method is more efficient than direct application of $t$ copies of $\mathcal{U}$. Further applications and related algorithms are also discussed.

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L. Sheridan, D. Maslov, M. Mosca. 2009-04-24. Approximating Fractional Time Quantum Evolution. https://doi.org/10.1088/1751-8113/42/18/185302

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