Quantum Algorithm for Joint Melody-Harmony Generation

A proof-of-concept quantum architecture applies the Harrow-Hassidim-Lloyd (HHL) algorithm to music generation, encoding melodic preference via Narmour implication-realisation and Krumhansl-Kessler tonal stability. The system matrix represents these music-cognition principles, and its solution vector yields a note-pair distribution. To overcome HHL's output reading limitation, a coherent Fourier harmonic oracle applies chord-transition weights directly to the amplitude vector, enabling a single measurement to select both melody notes and a two-chord progression. A two-note/two-chord block is used to manage exponential state space growth. The work, published on arXiv (2604.20882), demonstrates a novel intersection of quantum computing and music theory.