低维参数空间下的量子优化控制

QUANTUM OPTIMAL CONTROL IN LOW DIMENSIONAL PARAMETER SPACE

宋垚

11930061

硕士

材料工程

邓修豪

2021-05-21

2021-06-15

南方科技大学

深圳

近年来,由于超导练字比特良好的扩展性和退相干时间，使其有望成为最早实现量子计算的固态量子计算体系之一。然而，由于超导量子计算系统本身的不确定性和硬件约束，使得量子控制变得愈发困难。它要求控制波形具有足够的解析性并且带宽可控，以便在实验中进一步做参数整定，抑制泄漏误差。基于此，本文提出了一种新的脉冲工程方法GRAB（Gradient-based and bandwidth-limited），它是一种基于梯度并且带宽可控的方法，通过将滤波过程引入到优化过程中，使得优化后的波形具有足够的平滑性和解析性。GRAB中最强大的两个工具是DFT滤波技术和自动微分技术，它们在工程上已经是非常成熟的工具。前者保证了控制脉冲的带宽可控、幅度可控以及端点置零，后者保证了算法的收敛性，即使在处理复杂的计算过程和模型时也具有同等能力。为了证明GRAB的兼容性和优越性，我们将在制备PI门上与两类最流行的量子控制方法：GRAPE-LIKE和CRAB-LIKE 进行比较，GRAB算法获得了和GRAPE-LIKE同数量级的门保真度：>99.99%，比CRAB-LIKE算法高出一个量级，同时获得了平滑并且具备有限带宽的优化控制脉冲，使得GRAB算法获得的优化波形的实用性要远高于其他两类算法。同时我们探究了谐波数Nc对算法精度和收敛性的影响，Nc越大则波形越复杂，算法收敛的速度和精度就会越高，结合我们调参的经验，我们建议取Nc=5。进一步，我们从SWIFT理论给出的CNOT波形出发，在两个transmon通过腔耦合的系统上实现了26ns的CNOT门，门操作时间减少了8ns，同时门保真度也从>99%提高到>99.9%，并且优化后的波形具备更加明确的解析表达式。基于此，我们可以说GRAB算法是一种半数值、半解析的量子优化控制算法。

In recent years, due to its good scalability and decoherence time, superconducting qubit have developed rapidly, expected to be one of the earliest solid-state quantum computing systems. However, due to the uncertainty and hardware constraints of superconducting qubit system, quantum control meets a significant challenge. It requires that the control pulse has enough analyticity and controllable bandwidth, so that the parameters can be further adjusted in the experiment and the leakage error can be suppressed. Based on this, this paper proposes a new pulse engineering method GRAB which is a \textbf{gra}dient-based and \textbf{b}andwidth-limited method. By introducing the filtering process into the optimization process, the optimized pulse has enough smoothness and analyticity. The two most powerful tools in GRAB are DFT filtering technology and auto-differentiation technology, which are very mature tools in engineering. The former ensures that the bandwidth and amplitude of the control pulse can be controlled and the endpoint can be set to zero, while the latter ensures the convergence of the algorithm, which has the same ability even when dealing with complex calculation process and model. To demonstrate GRAB's compatibility and superiority, we will compare our method with the two most popular quantum control methods: GRAPE-LIKE and CRAB-LIKE, on driving a quantum gate $I\otimes\sigma_x$.We also explore the influence of $N_c$ on the accuracy and convergence. Furthermore, based on SWIFT theory, we start from the initial CNOT pulse with gate fidelity $> 99.9\% $, gate time $T=35.44$ns. After GRAB, we obtain a 26ns CNOT gate with fidelity $> 99.9\% $. From this point of view, GRAB method is actually a semi-analytical and semi-numerical quantum optimization control method.

超导量子比特 自动微分 DFT滤波 GRAPE-LIKE

superconducting qubit auto-differentiation DFT filter GRAPE-LIKE

中文

独立培养

南方科技大学

宋垚. 低维参数空间下的量子优化控制[D]. 深圳. 南方科技大学,2021.