Quantum algorithms for implementing quantum operations and measurements on quantum systems evolving under Hamiltonian dynamics

2016 Fiscal Year Final Research Report

• Project/Area Number: 26330006
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Theory of informatics
• Research Institution: The University of Tokyo
• Principal Investigator: Murao Mio 東京大学, 大学院理学系研究科(理学部), 教授 (30322671)
• Co-Investigator(Renkei-kenkyūsha): SOEDA Akihito 東京大学, 大学院理学系研究科, 助教 (70707653)
• Project Period (FY): 2014-04-01 – 2017-03-31
• Keywords: 量子計算 / 量子アルゴリズム / 高階量子演算 / 超写像 / オラクル / 量子操作 / 量子制御 / 並列化

Outline of Final Research Achievements

We discover quantum random algorithm approximately implementing a supermap for controllization of Hamiltonian dynamics. Using this algorithm, we proposed a quantum algorithm for universally implementing a projective measurement on the energy eigenbasis of an unknown Hamiltonian system and analyze the accuracy and implementation costs. We also show parallelizability of quantum gates in an adiabatic quantum computation model. We define higher order quantum operations as supermaps implementable within quantum mechanics. We proposed quantum algorithms implementing controllization of unknown unitaries and unitary conjugation and analyzed the relationship among causality, parallelizability, and nonlocality in higher order quantum operations.

Free Research Field

量子情報理論