The variational quantum algorithms are crucial for the application of NISQ computers. Such algorithms require short quantum circuits, which are more amenable to implementation on near-term hardware, and many such methods have been developed. One of particular interest is the so-called variational quantum state diagonalization method, which constitutes an important algorithmic subroutine and can be used directly to work with data encoded in quantum states. In particular, it can be applied to discern the features of quantum states, such as entanglement properties of a system, or in quantum machine learning algorithms. In this work, we tackle the problem of designing a very shallow quantum circuit, required in the quantum state diagonalization task, by utilizing reinforcement learning (RL). We use a novel encoding method for the RL-state, a dense reward function, and an $\epsilon$-greedy policy to achieve this. We demonstrate that the circuits proposed by the reinforcement learning methods are shallower than the standard variational quantum state diagonalization algorithm and thus can be used in situations where hardware capabilities limit the depth of quantum circuits. The methods we propose in the paper can be readily adapted to address a wide range of variational quantum algorithms.

翻译：变分量子算法是NISQ计算机应用的关键。此类算法需要较短的量子电路，更易于在近期待硬件上实现，目前已有多种相关方法被开发出来。其中特别引人注目的是所谓的变分量子态对角化方法，这是一种重要的算法子程序，可直接用于处理编码在量子态中的数据。具体而言，它可用于辨别量子态的特征（例如系统的纠缠特性），或在量子机器学习算法中发挥作用。在本研究中，我们通过利用强化学习技术解决了量子态对角化任务中设计极浅量子电路的问题。我们采用了一种新颖的强化学习状态编码方法、密集奖励函数以及ε-贪婪策略来实现这一目标。我们证明，强化学习方法提出的电路比标准变分量子态对角化算法更浅，因此可在硬件能力限制量子电路深度的场景中使用。本文提出的方法可轻松适配以解决各类变分量子算法问题。