Scalable Quantum Reinforcement Learning on NISQ Devices with Dynamic-Circuit Qubit Reuse and Grover Optimization

A scalable and resource-efficient quantum reinforcement learning framework is presented that eliminates the linear qubit-scaling barrier in multi-step quantum Markov decision processes (QMDPs). The proposed framework integrates a QMDP formulation, dynamic-circuit execution, and Grover-based amplitude amplification into a unified quantum-native architecture. Environment dynamics are encoded entirely within quantum Hilbert space, enabling coherent superposition over state-action sequences and a direct quantum agent-environment interface without intermediate quantum-to-classical conversion. The central contribution is a dynamic execution model for multi-step QMDPs that employs mid-circuit measurement and reset to recycle a fixed physical quantum register across sequential interactions. This approach preserves trajectory fidelity relative to a static unrolled QMDP, generating identical state-action sequences while reducing the physical qubit requirement from 7xT to a constant 7, independent of the interaction horizon T. Thus, the qubit complexity of multi-step QMDPs is transformed from O(T) to O(1) while maintaining functional equivalence at the level of trajectory generation. Trajectory returns are evaluated via quantum arithmetic, and high-return trajectories are marked and amplified using amplitude amplification to increase their sampling probability. Simulations confirm preservation of trajectory fidelity with a 66% qubit reduction compared to a static design. Experimental execution on an IBM Heron-class processor demonstrates feasibility on noisy intermediate-scale quantum hardware, establishing a scalable and resource-efficient foundation for large-scale quantum-native reinforcement learning.