Year: 2000
Type: article
Abstract: Quantum computers and their algorithm are now widely studied.We consider the prob- lem of making a superposition with an arbitrarily specified amplitudes.By modifying Grover's quantum search algorithm, we show that this can be done in time $O(\sqrt{N})$ with two simple operations, one is the Walsh-Hadamard transformation of $N\cross N$ -matrices where $N=2^{n}$ , the other is phase rotation of a state.If we see this problem in the classical computation model, it corresponds to the problem of making a sample with an arbitrarily specified distribution, where its time complexity is $\Omega(N)$ .By making a measurement on the result of our algorithm, it is possible to obtain a sample according to an arbitrarily specified probability distribution in $O(\sqrt{N})$ time.
Source: 数理解析研究所講究録
Author: Keisuke Tanaka
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W592250715