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：在噪声中等规模量子（NISQ）时代，一个重大挑战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所施加的约束条件。变分量子算法（VQA）作为一类量子-经典优化算法，旨在解决现有量子设备中的这些挑战。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（也称为ansatz）、以及代价函数的配置。本文聚焦于电路结构，通过使用强化学习（RL）自动搜索变分电路的最优结构，从而提升VQA的性能。本文中，电路的最优性通过评估其深度、门和参数的总数、以及解决给定问题的准确性来确定。自动搜索最优量子电路的任务被称为量子架构搜索（QAS）。目前QAS的大多数研究主要聚焦于无噪声场景，然而噪声对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、用于引导智能体发现更短电路的情节终止方案、以及采用ε-贪心策略的双深度Q网络（DDQN）来提升稳定性，从而解决该问题。在无噪声和有噪声量子硬件上的数值实验表明，在处理各类VQA时，我们基于RL的QAS优于现有QAS方法。同时，本文提出的方法可易于推广至其他广泛的VQA问题。