Design and Verification of Quantum Controlled-Not Gate NMR Pulse Sequence

doi:10.3778/j.issn.1002-8331.2008-0399

Computer Engineering and Applications ›› 2021, Vol. 57 ›› Issue (18): 97-102.DOI: 10.3778/j.issn.1002-8331.2008-0399

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Design and Verification of Quantum Controlled-Not Gate NMR Pulse Sequence

PENG Yonggang

1.Department of Applied Physics, College of Science, Nanjing University of Posts and Telecommunications, Nanjing 210003, China
2.New Energy Technology Engineering Laboratory of Jiangsu Province, Nanjing 210003, China

Online:2021-09-15 Published:2021-09-13

量子控制非门核磁共振脉冲序列设计与验证

彭永刚

1.南京邮电大学理学院应用物理系，南京 210003
2.江苏省新能源技术工程实验室，南京 210003

Abstract

Abstract:

The single-body time-dependent Schr?dinger equation is solved under the condition of nuclear magnetic resonance, and the rotation operators of nuclear spin around[x]-axis and[y]-axis are given. According to the definition of quantum controlled-not gate, the nuclear magnetic resonance pulse sequence is designed to realize the quantum controlled-not gate. Using the condition that the interaction time between two nuclear spins is much shorter than the duration of radio frequency pulse, the two-body time-dependent Schrödinger equation in nuclear magnetic resonance is approximately solved in the rotating reference frame and parameter values of quantum controlled-not gate pulse sequence are given. According to the Suzuki symmetric product formula, the time-dependent Schrödinger equation is numerically calculated. The numerical results confirm the correctness of the design and parameter values of quantum controlled-not gate pulse sequence.

Key words: quantum controlled-not gate, NMR pulse sequence, approximate solution of time-dependent Schr?dinger equation, numerical calculation

摘要：

在核磁共振条件下解单体含时薛定谔方程，给出核自旋绕[x]轴和[y]轴转动[π/2]的单量子位转动门，根据量子控制非门的定义，设计出实现量子控制非门的核磁共振脉冲序列。利用两个核自旋之间的相互作用时间远小于射频脉冲作用时间这个条件，通过在旋转参考系中近似求解核磁共振时的两体含时薛定谔方程，给出量子控制非门核磁共振脉冲序参数取值。利用Suzuki对称乘积公式，对含时薛定谔方程进行数值计算，数值计算结果验证了量子控制非门脉冲序列设计与参数取值的正确性。

关键词: 量子控制非门, 核磁共振脉冲序列, 含时薛定谔方程近似求解, 数值计算

PENG Yonggang. Design and Verification of Quantum Controlled-Not Gate NMR Pulse Sequence[J]. Computer Engineering and Applications, 2021, 57(18): 97-102.

彭永刚. 量子控制非门核磁共振脉冲序列设计与验证[J]. 计算机工程与应用, 2021, 57(18): 97-102.

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Design and Verification of Quantum Controlled-Not Gate NMR Pulse Sequence

量子控制非门核磁共振脉冲序列设计与验证

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