On Comparison of Some Representations for the Evolution of Quantum Operators
On Comparison of Some Representations for the Evolution of Quantum Operators
复制标题
量子算子演化的一些表示的比较
DOI：
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发表时间：
2020
期刊：
影响因子：
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通讯作者：
Petr Zufan
中科院分区：
文献类型：
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作者：
Michal Bidlo;Petr Zufan
本文对酉矩阵形式的量子算符的进化设计进行了比较研究。三种不同的技术，允许生成的酉矩阵进行了研究，其参数通过进化算法进行调整。这样的问题可以被认为是一个数值优化任务，因为酉矩阵是由具有实值系数的复数表示的。具体来说，遗传算法和进化策略，每个在四个不同的设置，并评估三个案例研究：2-qubit受控非门，3-qubit纠缠算子和4-qubit检测器的元素与最大幅度。结合给定的表示技术的进化算法进行评估，以确定各种实验设置来解决给定的任务的能力。主要贡献是QR分解的利用，这是一种从理论上任何复数序列生成酉矩阵的技术，本文首次将其应用于量子算符的演化。它将被证明，QR分解表现出良好的性能，特别是在解决更复杂的量子算子相比，其他表示。
This paper presents a comparative study regarding the evolutionary design of quantum operators in the form of unitary matrices. Three different techniques allowing the generation of unitary matrices are investigated whose parameters are tuned by means of evolutionary algorithms. Such problem may be considered as a numerical optimisation task because the unitary matrices are represented by complex numbers with real-valued coefficients. Specifically, Genetic Algorithm and Evolution Strategy are applied, each in four different setups, and evaluated on three case studies: the 2-qubit Controlled-NOT gate, 3-qubit entanglement operator and 4-qubit detector of an element with the maximum amplitude. The evolutionary algorithms in combination with the given representation techniques are evaluated in order to determine the abilities of various experimental setups to solve the given tasks. The main contribution is the utilisation of QR decomposition, a technique for generating unitary matrices from theoretically any sequence of complex numbers, that has been applied for the first time in this paper for the evolution of quantum operators. It will be demonstrated that the QR decomposition exhibits a good performance especially in solving more complex quantum operators in comparison with other representations.