利用并行性能加速迭代量子搜索
Speedup of iterated quantum search by parallel performance
摘要：
给定布尔函数序列$f_1 (x_1), f_2 (x_1, x_2), ..., f_k (x_1, ..., x_k)$，每个$f_i$在形式为$x_1^0, x_2^0, ..., x_i^0, i=1,2,..., k$的单个点上取值1。所有$x_i^0$的长度为$n, N=2^n$。它显示了如何使用\frac{kπ\sqrt{N}}{4\sqrt{2}} $ simultaneous evaluations of functions of the form $ f_i，f_{i+1} $ with an error probability of order $ k/ \sqrt{N} $ which is $ \sqrt{2} $ times as fast as by the $ k $ sequential applications of Grover algorithm for the quantum search. Evolutions of amplitudes in parallel quantum computations are approximated by systems of linear differential equations. Some advantage of simultaneous evaluations of all $ f_1，. f_k$的关系。
英文摘要：
Given a sequence $f_1 (x_1), f_2 (x_1, x_2), ..., f_k (x_1, ..., x_k)$ of Boolean functions, each of which $f_i$ takes the value 1 in a single point of the form $x_1^0, x_2^0, ..., x_i^0, i=1,2,..., k$. A length of all $x_i^0$ is $n, N=2^n$. It is shown how to find $x_k^0 (k\geq 2)$ using \frac{kπ\sqrt{N}}{4\sqrt{2}}$ simultaneous evaluations of functions of the form $f_i, f_{i+1}$ with an error probability of order $k/\sqrt{N}$ which is $\sqrt{2}$ times as fast as by the $k$ sequential applications of Grover algorithm for the quantum search. Evolutions of amplitudes in parallel quantum computations are approximated by systems of linear differential equations. Some advantage of simultaneous evaluations of all $f_1 ,... f_k$ are discussed.
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