分数时间量子演化的近似
Approximating Fractional Time Quantum Evolution
摘要：
给出了一种近似计算黑箱酉运算$\mathcal{U}^t$任意幂的算法，其中$t$是实数，$\mathcal{U}$是实现未知酉运算的黑箱.该算法的复杂度是根据对黑盒的调用次数、近似误差和某个“间隙”参数来计算的。对于一般的$\mathcal{U}$和大的$t$，应该应用$\mathcal{U}$总共$\lfloor t \rfloor$次，然后是我们用于近似分数幂$\mathcal{U}^{t-\lfloor t \rfloor}$的过程。还给出了一个例子，其中对于大整数$t$，该方法比直接应用$\mathcal{U}$的$t$副本更有效。进一步的应用和相关的算法进行了讨论。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
