量子线路中的酉算子分解研究  

Research on the decomposition of unitary operators in quantum circuits

作　　者：王士琪 张可佳[1] 张淋萌 WANG Shiqi;ZHANG Kejia;ZHANG Linmeng(School of Mathematical Sciences,Heilongjiang University,Harbin 150080,China;School of Mathematics,Harbin Institute of Technology,Harbin 150001,China)

机构地区：[1]黑龙江大学数学科学学院,哈尔滨150080 [2]哈尔滨工业大学数学学院,哈尔滨150001

出　　处：《黑龙江大学自然科学学报》2020年第6期653-660,共8页Journal of Natural Science of Heilongjiang University

基　　金：国家自然科学基金资助项目(61802118);黑龙江省普通高校青年创新人才资助项目(UNPYSCT-2018015)。

摘　　要：由量子逻辑门构造的量子线路是实现量子计算的基础。从算子角度来看,量子逻辑门的数学本质是酉算子,研究任意量子门的酉算子分解问题是优化量子线路的关键。本文从Pauli门和Hadamard门这两类基本的逻辑门分析入手,首先拓展了Pauli门、Hadamard门与旋转算子的线路恒等式关系;随后基于具体的线路恒等式关系,对于量子线路中的任意单量子比特门分解结论,提出了更为直观、简便的证明方法。这些工作将有助于后续量子计算的数学本质刻画。As we know,the quantum circuit constructed by the basic quantum logic gates plays a key role in the realization of quantum computation.In the view of operator theory,quantum logic gates are described by unitary operators,studying the decomposition of any unitary operators in quantum circuit is significant to analyze quantum circuit optimization.In this paper,we firstly expand the line identity relation between Pauli gate,Hadamard gate and rotation operator with the analysis of the Pauli gate and Hadamard gate.Then some novel and intuitive proofs to the decomposition results of any single-qubit gate in quantum circuit are proposed based on the specific line identity relation above.These results will be helpful to further research on the mathematical characterization of quantum computation.

关 键 词：Pauli门 Hadamard门 旋转算子 线路恒等式 单量子比特门分解 

分 类 号：O151.23[理学—数学]