A significant hurdle in the noisy intermediate-scale quantum (NISQ) era is identifying functional quantum circuits. These circuits must also adhere to the constraints imposed by current quantum hardware limitations. Variational quantum algorithms (VQAs), a class of quantum-classical optimization algorithms, were developed to address these challenges in the currently available quantum devices. However, the overall performance of VQAs depends on the initialization strategy of the variational circuit, the structure of the circuit (also known as ansatz), and the configuration of the cost function. Focusing on the structure of the circuit, in this thesis, we improve the performance of VQAs by automating the search for an optimal structure for the variational circuits using reinforcement learning (RL). Within the thesis, the optimality of a circuit is determined by evaluating its depth, the overall count of gates and parameters, and its accuracy in solving the given problem. The task of automating the search for optimal quantum circuits is known as quantum architecture search (QAS). The majority of research in QAS is primarily focused on a noiseless scenario. Yet, the impact of noise on the QAS remains inadequately explored. In this thesis, we tackle the issue by introducing a tensor-based quantum circuit encoding, restrictions on environment dynamics to explore the search space of possible circuits efficiently, an episode halting scheme to steer the agent to find shorter circuits, a double deep Q-network (DDQN) with an $\epsilon$-greedy policy for better stability. The numerical experiments on noiseless and noisy quantum hardware show that in dealing with various VQAs, our RL-based QAS outperforms existing QAS. Meanwhile, the methods we propose in the thesis can be readily adapted to address a wide range of other VQAs.

翻译：在含噪声中等规模量子（NISQ）时代，一个关键障碍是识别功能性量子电路。这些电路还必须满足当前量子硬件限制施加的约束。变分量子算法（VQA）作为一类量子-经典优化算法，是为应对当前可用量子设备中的这些挑战而开发的。然而，VQA的整体性能取决于变分电路的初始化策略、电路结构（即ansatz）以及成本函数的配置。本文聚焦于电路结构，通过使用强化学习（RL）自动化搜索变分电路的最优结构，提升VQA性能。文中，电路的最优性通过评估其深度、门电路和参数的总体数量，以及解决给定问题的准确性来确定。自动化搜索最优量子电路的任务称为量子架构搜索（QAS）。目前QAS的大部分研究主要集中于无噪声场景，而噪声对QAS的影响尚未得到充分探索。本文通过引入基于张量的量子电路编码、限制环境动力学以高效探索可能电路的搜索空间、用于引导智能体寻找更短电路的情节终止方案，以及采用ε-贪婪策略的双深度Q网络（DDQN）来提升稳定性，从而解决该问题。在无噪声和含噪声量子硬件上的数值实验表明，在处理各类VQA时，基于RL的QAS优于现有QAS。同时，本文提出的方法可轻松适配以解决其他广泛的VQA问题。