From Qubits to Rhythm: Exploring Quantum Random Walks in Rhythmspaces

TL;DR

The paper addresses translating quantum random walk dynamics into rhythmic generation within a 2D rhythmspace. It proposes a three-stage pipeline that maps qubit-space trajectories to rhythmspace, biases walks with classical potential fields via quantum feedback, and sonifies paths into MIDI patterns for a DAW using Python and Qiskit. Key contributions include a low-depth circuit by decomposing 2D walks into two 1D walks, a set of potential-field biasing schemes (null, linear, Gaussian, inertial Gaussian), and a complete sonification workflow tied to rhythmspace visuals, representing a scalable proof-of-concept for quantum-based music generation. The work demonstrates how quantum-inspired generative processes can expand creative workflows in music and provides a framework adaptable to higher-dimensional sound spaces as quantum hardware advances.

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.

Figures (11)

• Figure 1: Pipeline of the mappings and information exchange between the components of the code.
• Figure 2: Quantum circuit for quantum random walk generation.
• Figure 3: Illustration of the 49 positions of the quantum walk within the qubit space. An example of a 3-step walk is shown. The variable $n$ represents the pixels within a square of this qubit grid, and in this work, $n$ is set to 10.
• Figure 4: Qubits' window updating as the path in the rhythmspace progresses.
• Figure 5: A simple diagram illustrating how the quantum feedback induced by a potential field tunes the probability distribution of the states of a given wave function. In this example, the tuning favors states 3 and 4, indicating that the potential is enhancing their corresponding positions in the rhythmspace.