Reinforcement Learning for Variational Quantum Circuits Design

Variational Quantum Algorithms have emerged as promising tools for solving optimization problems on quantum computers. These algorithms leverage a parametric quantum circuit called ansatz, where its parameters are adjusted by a classical optimizer with the goal of optimizing a certain cost function. However, a significant challenge lies in designing effective circuits for addressing specific problems. In this study, we leverage the powerful and flexible Reinforcement Learning paradigm to train an agent capable of autonomously generating quantum circuits that can be used as ansatzes in variational algorithms to solve optimization problems. The agent is trained on diverse problem instances, including Maximum Cut, Maximum Clique and Minimum Vertex Cover, built from different graph topologies and sizes. Our analysis of the circuits generated by the agent and the corresponding solutions shows that the proposed method is able to generate effective ansatzes. While our goal is not to propose any new specific ansatz, we observe how the agent has discovered a novel family of ansatzes effective for Maximum Cut problems, which we call $R_{yz}$-connected. We study the characteristics of one of these ansatzes by comparing it against state-of-the-art quantum algorithms across instances of varying graph topologies, sizes, and problem types. Our results indicate that the $R_{yz}$-connected circuit achieves high approximation ratios for Maximum Cut problems, further validating our proposed agent. In conclusion, our study highlights the potential of Reinforcement Learning techniques in assisting researchers to design effective quantum circuits which could have applications in a wide number of tasks.

Benchmarking Adaptative Variational Quantum Algorithms on QUBO Instances

In recent years, Variational Quantum Algorithms (VQAs) have emerged as a promising approach for solving optimization problems on quantum computers in the NISQ era. However, one limitation of VQAs is their reliance on fixed-structure circuits, which may not be taylored for specific problems or hardware configurations. A leading strategy to address this issue are Adaptative VQAs, which dynamically modify the circuit structure by adding and removing gates, and optimize their parameters during the training. Several Adaptative VQAs, based on heuristics such as circuit shallowness, entanglement capability and hardware compatibility, have already been proposed in the literature, but there is still lack of a systematic comparison between the different methods. In this paper, we aim to fill this gap by analyzing three Adaptative VQAs: Evolutionary Variational Quantum Eigensolver (EVQE), Variable Ansatz (VAns), already proposed in the literature, and Random Adapt-VQE (RA-VQE), a random approach we introduce as a baseline. In order to compare these algorithms to traditional VQAs, we also include the Quantum Approximate Optimization Algorithm (QAOA) in our analysis. We apply these algorithms to QUBO problems and study their performance by examining the quality of the solutions found and the computational times required. Additionally, we investigate how the choice of the hyperparameters can impact the overall performance of the algorithms, highlighting the importance of selecting an appropriate methodology for hyperparameter tuning. Our analysis sets benchmarks for Adaptative VQAs designed for near-term quantum devices and provides valuable insights to guide future research in this area.

Feature Selection for Classification with QAOA

Feature selection is of great importance in Machine Learning, where it can be used to reduce the dimensionality of classification, ranking and prediction problems. The removal of redundant and noisy features can improve both the accuracy and scalability of the trained models. However, feature selection is a computationally expensive task with a solution space that grows combinatorically. In this work, we consider in particular a quadratic feature selection problem that can be tackled with the Quantum Approximate Optimization Algorithm (QAOA), already employed in combinatorial optimization. First we represent the feature selection problem with the QUBO formulation, which is then mapped to an Ising spin Hamiltonian. Then we apply QAOA with the goal of finding the ground state of this Hamiltonian, which corresponds to the optimal selection of features. In our experiments, we consider seven different real-world datasets with dimensionality up to 21 and run QAOA on both a quantum simulator and, for small datasets, the 7-qubit IBM (ibm-perth) quantum computer. We use the set of selected features to train a classification model and evaluate its accuracy. Our analysis shows that it is possible to tackle the feature selection problem with QAOA and that currently available quantum devices can be used effectively. Future studies could test a wider range of classification models as well as improve the effectiveness of QAOA by exploring better performing optimizers for its classical step.