Sara Giordano

Sara Giordano, Miguel A. Martin-Delgado

We have devised an artificial intelligence algorithm with machine reinforcement learning (Q-learning) to construct remarkable entangled states with 4 qubits. This way, the algorithm is able to generate representative states for some of the 49 true SLOCC classes of the four-qubit entanglement states. In particular, it is possible to reach at least one true SLOCC class for each of the nine entanglement families. The quantum circuits synthesized by the algorithm may be useful for the experimental realization of these important classes of entangled states and to draw conclusions about the intrinsic properties of our universe. We introduce a graphical tool called the state-link graph (SLG) to represent the construction of the Quality matrix (Q-matrix) used by the algorithm to build a given objective state belonging to the corresponding entanglement class. This allows us to discover the necessary connections between specific entanglement features and the role of certain quantum gates that the algorithm needs to include in the quantum gate set of actions. The quantum circuits found are optimal by construction with respect to the quantum gate-set chosen. These SLGs make the algorithm simple, intuitive and a useful resource for the automated construction of entangled states with a low number of qubits.

Sara Giordano, Kornikar Sen, Miguel A. Martin-Delgado

A reinforcement learning (RL) framework is introduced for the efficient synthesis of quantum circuits that generate specified target quantum states from a fixed initial state, addressing a central challenge in both the NISQ era and future fault-tolerant quantum computing. The approach utilizes tabular Q-learning, based on action sequences, within a discretized quantum state space, to effectively manage the exponential growth of the space dimension. The framework introduces a hybrid reward mechanism, combining a static, domain-informed reward that guides the agent toward the target state with customizable dynamic penalties that discourage inefficient circuit structures such as gate congestion and redundant state revisits. By leveraging sparse matrix representations and state-space discretization, the method enables scalable navigation of high-dimensional environments while minimizing computational overhead. Benchmarking on graph-state preparation tasks for up to seven qubits, we demonstrate that the algorithm consistently discovers minimal-depth circuits with optimized gate counts. Moreover, extending the framework to a universal gate set for arbitrary quantum states, it still produces minimal depth circuits, highlighting the algorithm's robustness and adaptability. The results confirm that this RL-driven approach efficiently explores the complex quantum state space and synthesizes near-optimal quantum circuits, providing a resource-efficient foundation for quantum circuit optimization.