Approximating Fractional Time Quantum Evolution

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dc.creatorSheridan, L.
dc.creatorMaslov, D.
dc.creatorMosca, M.
dc.date2008-10-21
dc.date2009-04-24
dc.date.accessioned2026-07-07T13:07:36Z
dc.date.available2026-07-07T13:07:36Z
dc.descriptionAn 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.
dc.description13 pages, 2 figures
dc.identifierhttps://arxiv.org/abs/0810.3843
dc.identifierhttp://arxiv.org/abs/0810.3843
dc.identifierJ. Phys. A: Math. Theor. 42 (2009) 185302
dc.identifierdoi:10.1088/1751-8113/42/18/185302
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/228141
dc.subjectQuantum Physics
dc.titleApproximating Fractional Time Quantum Evolution
dc.typetext

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