Quantum Reinforcement Learning with Dynamic-Circuit Qubit Reuse and Grover-Based Trajectory Optimization

A fully quantum reinforcement learning framework is developed that integrates a quantum Markov decision process, dynamic circuit-based qubit reuse, and Grover's algorithm for trajectory optimization. The framework encodes states, actions, rewards, and transitions entirely within the quantum domain, enabling parallel exploration of state-action sequences through superposition and eliminating classical subroutines. Dynamic circuit operations, including mid-circuit measurement and reset, allow reuse of the same physical qubits across multiple agent-environment interactions, reducing qubit requirements from 7*T to 7 for T time steps while preserving logical continuity. Quantum arithmetic computes trajectory returns, and Grover's search is applied to the superposition of these evaluated trajectories to amplify the probability of measuring those with the highest return, thereby accelerating the identification of the optimal policy. Simulations demonstrate that the dynamic-circuit-based implementation preserves trajectory fidelity while reducing qubit usage by 66 percent relative to the static design. Experimental deployment on IBM Heron-class quantum hardware confirms that the framework operates within the constraints of current quantum processors and validates the feasibility of fully quantum multi-step reinforcement learning under noisy intermediate-scale quantum conditions. This framework advances the scalability and practical application of quantum reinforcement learning for large-scale sequential decision-making tasks.