Exact quantum dynamics for two-level systems with time-dependent driving

doi:10.1088/1674-1056/ad8a4c

中国物理B ›› 2024, Vol. 33 ›› Issue (12): 120310-120310.doi: 10.1088/1674-1056/ad8a4c

Exact quantum dynamics for two-level systems with time-dependent driving

Zhi-Cheng He(贺郅程)¹, Yi-Xuan Wu(吴奕璇)¹, and Zheng-Yuan Xue(薛正远)^1,2,3,†

1 Key Laboratory of Atomic and Subatomic Structure and Quantum Control (Ministry of Education), Guangdong Basic Research Center of Excellence for Structure and Fundamental Interactions of Matter, and School of Physics, South China Normal University, Guangzhou 510006, China;
2 Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, Guangdong-Hong Kong Joint Laboratory of Quantum Matter, and Frontier Research Institute for Physics, South China Normal University, Guangzhou 510006, China;
3 Hefei National Laboratory, Hefei 230088, China

收稿日期:2024-09-01 修回日期:2024-10-19 接受日期:2024-10-23 出版日期:2024-12-15 发布日期:2024-11-29
通讯作者: Zheng-Yuan Xue E-mail:zyxue83@163.com
基金资助:
This work was supported by the National Natural Science Foundation of China (Grant No. 12275090), the Guangdong Provincial Quantum Science Strategic Initiative (Grant No. GDZX2203001), and the Innovation Program for Quantum Science and Technology (Grant No. 2021ZD0302303).

Exact quantum dynamics for two-level systems with time-dependent driving

Zhi-Cheng He(贺郅程)¹, Yi-Xuan Wu(吴奕璇)¹, and Zheng-Yuan Xue(薛正远)^1,2,3,†

1 Key Laboratory of Atomic and Subatomic Structure and Quantum Control (Ministry of Education), Guangdong Basic Research Center of Excellence for Structure and Fundamental Interactions of Matter, and School of Physics, South China Normal University, Guangzhou 510006, China;
2 Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, Guangdong-Hong Kong Joint Laboratory of Quantum Matter, and Frontier Research Institute for Physics, South China Normal University, Guangzhou 510006, China;
3 Hefei National Laboratory, Hefei 230088, China

Received:2024-09-01 Revised:2024-10-19 Accepted:2024-10-23 Online:2024-12-15 Published:2024-11-29
Contact: Zheng-Yuan Xue E-mail:zyxue83@163.com
Supported by:
This work was supported by the National Natural Science Foundation of China (Grant No. 12275090), the Guangdong Provincial Quantum Science Strategic Initiative (Grant No. GDZX2203001), and the Innovation Program for Quantum Science and Technology (Grant No. 2021ZD0302303).

摘要/Abstract

摘要： It is well known that the time-dependent Schrrödinger equation can only be solved exactly in very rare cases, even for two-level quantum systems. Thus, finding the exact quantum dynamics under a time-dependent Hamiltonian is not only fundamentally important in quantum physics but also facilitates active quantum manipulations for quantum information processing. In this work, we present a method for generating nearly infinite analytically assisted solutions to the Schrödinger equation for a qubit under time-dependent driving. These analytically assisted solutions feature free parameters with only boundary restrictions, making them applicable in a variety of precise quantum manipulations. Due to the general form of the time-dependent Hamiltonian in our approach, it can be readily implemented in various experimental setups involving qubits. Consequently, our scheme offers new solutions to the Schrödinger equation, providing an alternative analytical framework for precise control over qubits.

关键词: quantum computation, quantum control, analytical solution

Abstract: It is well known that the time-dependent Schrrödinger equation can only be solved exactly in very rare cases, even for two-level quantum systems. Thus, finding the exact quantum dynamics under a time-dependent Hamiltonian is not only fundamentally important in quantum physics but also facilitates active quantum manipulations for quantum information processing. In this work, we present a method for generating nearly infinite analytically assisted solutions to the Schrödinger equation for a qubit under time-dependent driving. These analytically assisted solutions feature free parameters with only boundary restrictions, making them applicable in a variety of precise quantum manipulations. Due to the general form of the time-dependent Hamiltonian in our approach, it can be readily implemented in various experimental setups involving qubits. Consequently, our scheme offers new solutions to the Schrödinger equation, providing an alternative analytical framework for precise control over qubits.

Key words: quantum computation, quantum control, analytical solution

中图分类号: (Quantum computation architectures and implementations)

03.67.Lx

03.67.Hk (Quantum communication)

Zhi-Cheng He(贺郅程), Yi-Xuan Wu(吴奕璇), and Zheng-Yuan Xue(薛正远). Exact quantum dynamics for two-level systems with time-dependent driving[J]. 中国物理B, 2024, 33(12): 120310-120310.

Zhi-Cheng He(贺郅程), Yi-Xuan Wu(吴奕璇), and Zheng-Yuan Xue(薛正远). Exact quantum dynamics for two-level systems with time-dependent driving[J]. Chin. Phys. B, 2024, 33(12): 120310-120310.

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Exact quantum dynamics for two-level systems with time-dependent driving

Exact quantum dynamics for two-level systems with time-dependent driving

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