The promise of quantum computing to open new unexplored possibilities in several scientific fields has been long discussed, but until recently the lack of a functional quantum computer has confined this discussion mostly to theoretical algorithmic papers. It was only in the last few years that small but functional quantum computers have become available to the broader research community. One paradigm in particular, quantum annealing, can be used to sample optimal solutions for a number of NP-hard optimization problems represented with classical operations research tools, providing an easy access to the potential of this emerging technology. One of the tasks that most naturally fits in this mathematical formulation is feature selection. In this paper, we investigate how to design a hybrid feature selection algorithm for recommender systems that leverages the domain knowledge and behavior hidden in the user interactions data. We represent the feature selection as an optimization problem and solve it on a real quantum computer, provided by D-Wave. The results indicate that the proposed approach is effective in selecting a limited set of important features and that quantum computers are becoming powerful enough to enter the wider realm of applied science.

Quantum Annealing (QA) is a quantum computing paradigm for solving combinatorial optimization problems formulated as Quadratic Unconstrained Binary Optimization (QUBO) problems. An essential step in QA is minor embedding, which maps the problem graph onto the sparse topology of the quantum processor and then adjusts the problem weights. The process of mapping the problem variables to the hardware is computationally expensive and scales poorly with increasing problem size and hardware complexity. Existing heuristics are often developed for specific problem graphs or hardware topologies and are difficult to generalize. To address this limitation, we explore the use of machine learning methods, which would allow a much greater degree of flexibility, in particular of Reinforcement Learning (RL). RL offers a promising alternative by treating minor embedding as a sequential decision-making problem, where an agent learns to construct minor embeddings by iteratively mapping the problem variables to the hardware qubits. We propose a RL-based approach to minor embedding using a Proximal Policy Optimization agent, testing its ability to embed both fully connected and randomly generated problem graphs on two hardware topologies, Chimera and Zephyr. The results show that our agent consistently produces valid minor embeddings even when they span over more than a thousand qubits, in particular on the more modern Zephyr topology. Our proposed approach is also able to scale to moderate problem sizes and adapts well to different graph structures, highlighting RL’s potential as a flexible and general-purpose framework for minor embedding in QA but also pointing to limitations that will need to be addressed, for example in reducing the number of qubits required.

Quantum Annealing (QA) is a quantum computing paradigm for solving combinatorial optimization problems formulated as Quadratic Unconstrained Binary Optimization (QUBO) problems. An essential step in QA is minor embedding, which maps the problem graph onto the sparse topology of the quantum processor. This process is computationally expensive and scales poorly with increasing problem size and hardware complexity. Existing heuristics are often developed for specific problem graphs or hardware topologies and are difficult to generalize. Reinforcement Learning (RL) offers a promising alternative by treating minor embedding as a sequential decision-making problem, where an agent learns to construct minor embeddings by iteratively mapping the problem variables to the hardware qubits. We propose a RL-based approach to minor embedding using a Proximal Policy Optimization agent, testing its ability to embed both fully connected and randomly generated problem graphs on two hardware topologies, Chimera and Zephyr. The results show that our agent consistently produces valid minor embeddings, with reasonably efficient number of qubits, in particular on the more modern Zephyr topology. Our proposed approach is also able to scale to moderate problem sizes and adapts well to different graph structures, highlighting RL's potential as a flexible and general-purpose framework for minor embedding in QA.

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.