Enhancing variational quantum state diagonalization using reinforcement learning techniques

Abstract

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.

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“…As the first application of the framework, in the Chapter 3 we consider the reinforcement learning assisted variational quantum state diagonalization (VQSD) which we term as RL-VQSD [85] in a noiseless scenario. The algorithm focuses on identifying the unitary rotation under which a given quantum state becomes diagonal in the computational basis.…”

“…Many factors can be used as a pointer for an efficient ansatz (A eff ) but for the sake of the thesis we primarily focus on the following definition to define an efficient ansatz [85]: Definition 3.1.1: An ansatz is efficient if the depth and the total number of gates are smaller compared to the state-of-the-art ansatz structures, and which returns a lower error in solving the problem.…”

“…In a nutshell, the RL-based algorithm, i.e. RL-VQSD we introduce in [85] utilizes a state-of-the-art encoding method for RL-state space, representing the variational circuit, along with a dense reward function to show that our approach can be successfully used for diagonalizing arbitrary mixed quantum states. Moreover, we also demonstrate that compared to LHEA, the ansatz proposed by the RL-agent is more efficient (Def.…”

“…In this thesis, we introduce a simple yet effective infrastructure for a reinforcement learning-based quantum architecture search algorithm. To show the performance of the thesis, we propose an RL-VQSD [85] and CRL-VQE [7] algorithm that is built upon the framework introduced in this thesis. We solve these problems in the absence and the presence of noise and gather valuable insights.…”