Physics – Quantum Physics
Scientific paper
1999-04-09
Physics
Quantum Physics
Latex, 21 pages, no figures, simplification of the proof
Scientific paper
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{k\pi\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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