Natural Majorization of the Quantum Fourier Transformation in Phase-Estimation Algorithms

作     者：Orus, Roman Latorre, Jose I. Martin-Delgado, Miguel A. 

作者机构：Univ Barcelona Dept Estructura & Constituents Mat E-08028 Barcelona Spain Univ Complutense Dept Fis Teor 1 E-28040 Madrid Spain 

出 版 物：《QUANTUM INFORMATION PROCESSING》 (量子信息处理)

年 卷 期：2002年第1卷第4期

页      面：283-302页

核心收录：

学科分类：07[理学] 070201[理学-理论物理] 0702[理学-物理学] 

基　　金：AEN99-0766 19999GR-00097 IST-1999-11053 PB98-0685 BFM2000-1320-C02-01 

主　　题：majorization quantum Fourier transformation quantum phase-estimation quantum algorithms 

摘      要：We prove that majorization relations hold step by step in the Quantum Fourier Transformation (QFT) for phase-estimation algorithms. Our result relies on the fact that states which are mixed by Hadamard operators at any stage of the computation only differ by a phase. This property is a consequence of the structure of the initial state and of the QFT, based on controlled-phase operators and a single action of a Hadamard gate per qubit. The detail of our proof shows that Hadamard gates sort the probability distribution associated to the quantum state, whereas controlled-phase operators carry all the entanglement but are immaterial to majorization. We also prove that majorization in phase-estimation algorithms follows in a most natural way from unitary evolution, unlike its counterpart in Grover s algorithm.