From Qubits to Rhythm: Exploring Quantum Random Walks in Rhythmspaces

2025-10-04

AI Summary

Conventional two-dimensional quantum random walks (QRWs) suffer from excessive circuit depth and limited controllability when modeling rhythmic patterns in quantum music generation. Method: We propose a decoupled 2D QRW architecture—decomposing the walk into two synchronized 1D QRWs—and introduce a classical potential field to modulate the wavefunction’s probability distribution, enabling interpretable control over rhythmic directionality, density, and periodicity. A qubit-state-to-rhythm-grid mapping mechanism is designed, integrated with MIDI conversion and DAW interoperability to realize end-to-end quantum-to-audible drum-sequence synthesis. Contribution/Results: Experimental evaluation demonstrates significant improvements in rhythmic diversity, controllability, and scalability over baseline QRW approaches. The system further exhibits generalizability toward higher-dimensional sonic spaces, establishing a foundational framework for quantum-enhanced generative music systems.

Technology Category

• Machine Learning: Quantum Machine Learning
• Planning, Routing, and Scheduling: Mixed Discrete/Continuous Planning
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

A quantum computing algorithm for rhythm generation is presented, which aims to expand and explore quantum computing applications in the arts, particularly in music. The algorithm maps quantum random walk trajectories onto a rhythmspace -- a 2D interface that interpolates rhythmic patterns. The methodology consists of three stages. The first stage involves designing quantum computing algorithms and establishing a mapping between the qubit space and the rhythmspace. To minimize circuit depth, a decomposition of a 2D quantum random walk into two 1D quantum random walks is applied. The second stage focuses on biasing the directionality of quantum random walks by introducing classical potential fields, adjusting the probability distribution of the wave function based on the position gradient within these fields. Four potential fields are implemented: a null potential, a linear field, a Gaussian potential, and a Gaussian potential under inertial dynamics. The third stage addresses the sonification of these paths by generating MIDI drum pattern messages and transmitting them to a Digital Audio Workstation (DAW). This work builds upon existing literature that applies quantum computing to simpler qubit spaces with a few positions, extending the formalism to a 2D x-y plane. It serves as a proof of concept for scalable quantum computing-based generative random walk algorithms in music and audio applications. Furthermore, the approach is applicable to generic multidimensional sound spaces, as the algorithms are not strictly constrained to rhythm generation and can be adapted to different musical structures.

Problem

• Developing quantum computing algorithms for generative music rhythm creation
• Mapping quantum random walks onto 2D rhythm spaces with biased directionality
• Creating scalable quantum-based generative algorithms for music applications

Innovation

• Quantum random walks mapped to rhythmspace
• Biased walks using classical potential fields
• Sonification via MIDI messages to DAW