Mathematical formulation of quantum-classical hybrid algorithm in open system and its application for search problem

2018 Fiscal Year Final Research Report

• Project/Area Number: 16K00025
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Theory of informatics
• Research Institution: Tokyo University of Science
• Principal Investigator: Iriyama Satoshi 東京理科大学, 理工学部情報科学科, 准教授 (10385528)
• Co-Investigator(Kenkyū-buntansha): 田畑 耕治 東京理科大学, 理工学部情報科学科, 准教授 (30453814)
• Project Period (FY): 2016-04-01 – 2019-03-31
• Keywords: 量子アルゴリズム / 開放系 / GKSLマスター方程式 / 光合成過程

Outline of Final Research Achievements

In this project, the quantum-classical hybrid algorithm in open systems was formulated, and its application for search problem was found. We studied the multi-qubits quantum algorithm with environmental noise in open systems where precise parameter condition for efficient algorithm was found. The adiabatic quantum algorithm was discussed in the open systems where the error probability is related to the quantum noise. We provided mathematical framework to treat with the complex system with special parameter. The computational complexity of the hybrid quantum algorithm for the general type search problem which is belongs to NP-hard class. The result of this project will be a important role to develop a real quantum computer in the room temperature with several types of noise.

Free Research Field

量子アルゴリズム，暗号理論

Academic Significance and Societal Importance of the Research Achievements

本研究課題の達成により，次のような効果が期待される．(1)理想化された閉じた系でなく，開放系での量子アルゴリズムの記述がなされることによる，量子計算機の実現に向けての大きな貢献．(2)環境系との相互作用を積極的に利用する新たな計算の数理モデルの構築が行われ，雑音のある系における量子計算機の基礎が構成される．(3)生命現象の数理についての数学的基礎が発展し，化学的ネットワークだけでなく，物理的相互作用を土台とした生命理解が深められる．