几何量子门的脉冲优化问题

OPTIMAL PULSE FOR GEOMETRICAL QUANTUM GATES

刘宝杰

11849476

博士

物理学

翁文康

2021

2021-05-27

哈尔滨工业大学

深圳

量子计算是利用量子纠缠和叠加等量子资源进行信息处理的一种新型计算模型。相对传统的经典计算, 量子计算具有强大的计算能力因此能更有效解决一些经典计算机难以解决的问题。然而实验上实现量子计算存在两个主要的问题：一是由于量子体系与外部环境的无法避免的相互作用引起的量子系统退相干；二是实验参数抖动造成的量子逻辑门保真度的降低。相比于动力学相位，几何相位仅取决于系统量子态演化轨迹的整体属性，因此基于几何相位的量子计算具有抵抗特定局部噪声的独特性质。在当前量子信息处理领域中，几何量子计算已是一个重要的研究课题。在非绝热几何量子计算框架的基础上，本文主要研究如何利用量子优化控制技术进一步提升传统几何量子门的性能，从而实现高保真度和鲁棒性的几何量子计算。主要研究内容如下：(1) 基于非绝热几何量子计算，研究了一种非循环非绝热几何量子计算新方案。与常规的方案相比，新方案不受循环条件的限制，可以减少构造量子逻辑门的操作时间。因此，该方案在抵抗环境退相干方面更具鲁棒性。另外，我们探索将上述新方案应用到里德堡原子中，理论结果证明我们可以利用里德堡原子之间的强偶极相互作用引起的大失谐来构建高保真度非平庸的两比特几何纠缠门。(2) 基于非绝热和乐 (非阿贝尔几何相位) 量子计算，研究了一种可优化的几何量子计算新方案 (NHQC+)，该方案可以同时对特定噪声保持鲁棒性。NHQC+ 打破了以往方案对不同能级之间耦合脉冲的严格限制，因此可以将许多成熟的最佳控制方法，如动力学解耦、复合脉冲和绝热捷径等技术结合到非绝热几何量子门的构造中，从而进一步提高几何量子门对系统噪声的鲁棒性。该方案可以应用于各种物理平台，例如超导、囚禁离子、金刚石色心以及里德堡原子等。为了验证NHQC+ 的可行性和对噪声的稳定性，我们联合实验组在超导量子体系中进行了实验演示。实验结果表明，通过对超导能级的控制可以实现对系统几何量子相位的精确调控，实现任意单比特鲁棒几何门。(3) 基于弱非线性的超导比特系统，研究了一种压制态泄露的非绝热和乐量子计算新方法。通过利用量子优化控制技术，我们可以抑制量子比特态泄漏到计算空间之外的态空间。与常规的基于超导比特系统的非绝热和乐量子计算方案相比，结果表明新方案可以把几何量子门的误差压制到0.001。此外，我们还探索通过实验去验证该方案的对泄露误差的压制效果。(4) 基于非绝热和乐量子计算，研究了一种具有时间优化的非常规几何量子计算 (B-NHQC)。B-NHQC利用时间优化控制技术，可以对所有非绝热和乐量子门进行时间优化，从而最大程度地减少环境退相干的影响。同时也可以解决传统非绝热和乐量子计算的局限性：即使对于小角度旋转，所有操作都能够以完全相同的时间执行。此外，新方案还可以与复合脉冲相结合，进一步增强了几何量子门对脉冲误差的鲁棒性。我们联合实验组，同样在超导量子体系中演示了B-NHQC方案。实验结果表明，该方案对控制噪声和环境噪声的都比较鲁棒。(5) 针对非绝热几何量子计算缺少对全局控制误差的鲁棒性的问题，首先研究了一个超鲁棒几何控制条件。在此基础上，我们进一步研究了基于超鲁棒几何控制条件实现非绝热和乐 (几何) 量子计算。理论结果表明该方案可以显著地提高非绝热几何量子门对实验控制误差的稳定性，并且不需要复杂脉冲序列。此外，为了在实验上证实超鲁棒非绝热和乐计算方案的可行性以及对全局控制误差的鲁棒性，我们研究利用超导量子线路系统进行了实验演示。结果表明基于超鲁棒几何控制条件的非绝热和乐量子门可以将全局实验控制误差压制到四阶。

Quantum computation is a new type of computing model that uses quantum resources such as quantum entanglement and superposition for information processing. Compared with traditional classical computation, quantum computation has powerful computing capabilities and can more effectively solve some problems that are difficult to be solved by classical computers. However, there are two main problems with quantum computation: one is that the interaction between the quantum system and the external environment causes decoherence of the quantum system; another one is that imprecise experimental manipulation reduces the fidelity of the quantum logic gates of quantum computation. On the other hand, the geometric phase only depends on the global properties of the evolution trajectory, so geometric quantum computation based on the geometric phase has the unique property of resisting certain local noise. Geometric quantum computation has been an important research topic in the field of quantum information processing. This dissertation mainly studies how to use quantum optimal control technology to further improve the pulse of traditional geometric gates in the framework of non-adiabatic geometric quantum computation, so that realizes high-fidelity and robust geometric quantum computing.The main research contents are as follows:(1) Based on non-adiabatic geometric quantum computation, a new scheme of non-cyclic non-adiabatic geometric quantum computation is researched. The new scheme uses non-cyclic and non-adiabatic geometric phases to construct quantum gates. Compared with the conventional non-adiabatic geometric quantum computation, this scheme is not restricted by the cyclic conditions, so the operation time of constructing the non-adiabatic geometric gate can be reduced. Therefore, our scheme is more robust in resisting environmental decoherence. In addition, the large detuning process caused by the strong dipole interaction between Rydberg atoms can be used to construct a non-trivial two-qubit geometric entanglement gate. (2) Based on non-adiabatic holonomic (non-commutative geometric phase) quantum computation, a new optimizable geometric quantum computation scheme (NHQC+) is researched that can maintain flexibility and robustness against certain noise at the same time. NHQC+ breaks the strict limitations of the previous schemes on coupled pulses of different energy levels, so it can combine non-adiabatic geometric gates with most of the existing best optimal control methods such as dynamic decoupling, composite pulses and shortcut to adiabaticity. Therefore, we can further improve the robustness of the geometric quantum gates to different control errors. This scheme can be applied to various physical platforms, such as superconducting qubit, NV center in diamond, trapped ions, and Rydberg atoms. In order to verify the feasibility and the stability against noise of the NHQC+, we have successfully demonstrated it in the superconducting quantum system through the joint experimental group. Through the control of the superconducting energy level, we can achieve precise control of the geometric quantum phase generated by the evolution of the system and realize any specified geometric quantum gate.(3) Based on the weakly nonlinear superconducting qubit system, a new method of non-adiabatic holonomic quantum computation is researched to suppress the state leakage. The scheme is to design experimental microwave control parameters through quantum optimal control technology, which can further reduce the leakage of qubit states to the non-computational bases. Compared with the conventional non-adiabatic holonomic quantum computation, the numerical results show that our scheme can suppress the error of the geometric quantum gate to 0.001 under the same conditions. In addition, we have further verified the suppressed effect of the scheme on leakage errors in experiment.(4) Based on non-adiabatic holonomic quantum computation, an unconventional geometric quantum computation with time optimal control (B-NHQC) is researched. B-NHQC uses time optimal control technology to optimize the time for all non-adiabatic holonomic quantum gates, and thus minimizing the impact of decoherence caused by environmental noise. Simutaneously, it also solves the limitations of traditional non-adiabatic holonomic quantum computation: even for small angle rotations, all operations are exactly performed at the same time. In addition, the new scheme can also combine with composite pulses to further enhance the robustness of geometric quantum gates to pulse errors. Our joint experimental group also successfully demonstrate the B-NHQC scheme in the superconducting quantum system, and verifie the stability of the scheme to control noise and environmental noise.(5) To solve the problem that non-adiabatic geometric quantum computation lacks robustness against global control error, the condition of super-robust geometric control is researched. On this basis, a non-adiabatic holonomic (geometric) quantum computation based on the condition of super-robust geometric control is also researched. The scheme can significantly improve the stability of non-adiabatic geometric gate against experimental control errors and does not require complex pulse sequences. In addition, to verify the experimental feasibility of the superconducting non-adiabatic holonomic quantum computation and its robustness to the global control error, the scheme is successfully demonstrated experimentally in a superconducting quantum circuit system. The experimental results show that the non-adiabatic holonomic quantum gate based on the condition of super-robust geometric control can suppress the global experimental control error to the fourth order.

量子计算 几何相位 非绝热和乐量子计算 量子优化控制 超导量子比特

quantum computation geometric phase non-adiabatic holonomic quantum computation quantum optimal control superconducting qubit.

中文

联合培养

南方科技大学

刘宝杰. 几何量子门的脉冲优化问题[D]. 深圳. 哈尔滨工业大学,2021.