A QUBO-QAOA Framework for Rhythmic Generation in Hindustani Music

Abstract This study presents a quantum-inspired optimization framework for generating rhythmic cycles (taals) in Hindustani classical music via Quadratic Unconstrained Binary Optimization (QUBO) formulations solved via the Quantum Approximate Optimization Algorithm (QAOA). By mapping tabla bols to binary decision variables, musical grammar – including rhythmic anchors like the Sam and Khali – is encoded as penalty terms with a cost Hamiltonian. Comparative benchmarking against classical autoregressive architectures, such as WaveNet and LSTM-RNN, reveals a significant efficiency gap. The proposed framework achieves a 97.8% constraint satisfaction rate using only 12 variational parameters, representing a reduction of 4-6 orders of magnitude in model complexity compared to deep learning baselines. Furthermore, the quantum approach facilitates zero-shot generation, deriving its power from rule-encoding rather than data-intensive training. Energy landscape analysis demonstrates that quantum tunnelling through the mixing operator allows the system to navigate sparse rhythmic manifolds more effectively than classical gradient-descent methods. These results establish a rigorous foundation for quantum-enhanced computational musicology, offering a scalable, interpretable, and parameter-efficient paradigm for the digital preservation and creative evolution of structured oral traditions.