The development of variational quantum algorithms is 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 the variational diagonalization method, which constitutes an important algorithmic subroutine, and it can be used directly for working 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. To achieve this, we utilize a novel encoding method that can be used to tackle the problem of circuit depth optimization using a reinforcement learning approach. We demonstrate that our approach provides a solid approximation to the diagonalization task while using a small number of gates. 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 the depth of quantum circuits is limited by the hardware capabilities.

翻译：变分量子算法的发展对于NISQ计算机的应用至关重要。这类算法需要短量子电路，从而更易于在近期硬件上实现，目前已有许多此类方法被开发出来。其中特别值得关注的是变分对角化方法，它构成了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，该方法可用于识别量子态的特征，例如系统的纠缠性质，或在量子机器学习算法中发挥作用。在本工作中，我们通过利用强化学习来设计量子态对角化任务所需的超浅量子电路。为此，我们采用了一种新颖的编码方法，该方法可用于通过强化学习途径解决电路深度优化问题。我们证明，该方法在使用少量量子门的情况下，能够为对角化任务提供可靠的近似。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，因此可用于量子电路深度受硬件能力限制的场景。