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Sonification of Quantum Algorithms with Spline Models of Timbre, Melody, and Rhythm

Matthew Klassen

Published Oct 28, 2025• 1 citation
Publisher

Abstract

In this paper we describe methods for mapping the information contained in a spline model of one cycle of an audio signal to the quantum information setting. We use this mapping to describe methods of sonification of quantum algorithms which use spline models to describe and generate timbre, melody, and rhythm. We show how a musical state vector given by n B-spline coefficients, which represent one cycle of a waveform, can produce these three musical elements simultaneously. We present two modes of correspondence between quantum and musical states. The first mode is derived from proposed signal processing of quantum audio, such as QPAM (Quantum Probability Amplitude Modulation), and the second mode is more abstract, modeling the evolution of musical states through unitary evolution of intermediate states in quantum algorithms. Musical states are initialized using approximate timbres derived from instrument sam- ples or synthesized timbres. Melodic contours are derived from spline models of these timbres, using continuous pitch and duration spaces. Musical examples are discussed, and larger compositional works are currently under development.

DOI
10.5281/zenodo.20650605

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In this paper we describe methods for mapping the information contained in a spline model of one cycle of an audio signal to the quantum information setting. We use this mapping to describe methods of sonification of quantum algorithms which use spline models to describe and generate timbre, melody, and rhythm. We show how a musical state vector given by n B-spline coefficients, which represent one cycle of a waveform, can produce these three musical elements simultaneously. We present two modes of correspondence between quantum and musical states. The first mode is derived from proposed signal processing of quantum audio, such as QPAM (Quantum Probability Amplitude Modulation), and the second mode is more abstract, modeling the evolution of musical states through unitary evolution of intermediate states in quantum algorithms. Musical states are initialized using approximate timbres derived from instrument sam- ples or synthesized timbres. Melodic contours are derived from spline models of these timbres, using continuous pitch and duration spaces. Musical examples are discussed, and larger compositional works are currently under development.
In this paper we describe methods for mapping the information contained in a spline model of one cycle of an audio signal to the quantum information setting. We use this mapping to describe methods of sonification of quantum algorithms which use spline models to describe and generate timbre, melody, and rhythm. We show how a musical state vector given by n B-spline coefficients, which represent one cycle of a waveform, can produce these three musical elements simultaneously. We present two modes of correspondence between quantum and musical states. The first mode is derived from proposed signal processing of quantum audio, such as QPAM (Quantum Probability Amplitude Modulation), and the second mode works with superposition states achievable through quantum algorithms. Musical states are initialized using approximate timbres derived from instrument samples or synthesized timbres. Melodic contours are derived from spline models of these timbres, using continuous pitch and duration spaces. Musical examples are discussed, and larger compositional works are currently in production.
Quantum computing can be employed in computer-aided music composition to control various attributes of the music at different structural levels. This article describes the application of quantum simulation to model compositional decision making, the simulation of quantum particle tracking to produce noise-based timbres, the use of basis state vector rotation to cause changing probabilistic behaviors in granular harmonic textures, and the exploitation of quantum measurement error to cause noisy perturbations of spatial soundpaths. We describe the concepts fundamental to these techniques, we provide algorithms and software enacting them, and we provide examples demonstrating their implementation in computer-generated music
Music is a multifaceted art form that requires a nuanced and comprehensive framework for analysis. This framework should encompass correlations among diverse musical attributes, including melody, harmony, rhythm, timbre, and dynamics. However, modeling the interaction between these attributes is anticipated to require substantial computational resources. In this study, we propose a Bayesian model to represent various musical attributes and explore its implementation and inference on a quantum computer. We show how to translate the Bayesian model to a quantum circuit and perform inference using the quantum rejection sampling algorithm on a quantum simulator. Through empirical evaluation utilizing a real-world dataset, we compare the performance of the quantum algorithm against classical rejection sampling. Our results reveal that the quantum method improves the acceptance rate of generated samples, thereby enhancing posterior probability estimates.
Quantum computing technology is developing at a fast pace. The impact of quantum computing on the music industry is inevitable. This paper maps the emerging field of quantum computer music. Quantum computer music investigates, and develops applications and methods to process music using quantum computing technology. The paper begins by contextualising the field. Then, it discusses significant examples of various approaches developed to date to leverage quantum computing to learn, process and generate music. The methods discussed range from rendering music using data from physical quantum mechanical systems and quantum mechanical simulations to computational quantum algorithms to generate music, including quantum AI. The ambition to develop techniques to encode audio quantumly for making sound synthesisers and audio signal processing systems is also discussed.
This chapter examines the Variational Quantum Harmonizer, a software tool and musical interface that focuses on the problem of sonification of the minimization steps of Variational Quantum Algorithms (VQA), used for simulating properties of quantum systems and optimization problems assisted by quantum hardware. Particularly, it details the sonification of Quadratic Unconstrained Binary Optimization (QUBO) problems using VQA. A flexible design enables its future applications both as a sonification tool for auditory displays in scientific investigation, and as a hybrid quantum-digital musical instrument for artistic endeavours. In turn, sonification can help researchers understand complex systems better and can serve for the training of quantum physics and quantum computing. The VQH structure, including its software implementation, control mechanisms, and sonification mappings are detailed. Moreover, it guides the design of QUBO cost functions in VQH as a music compositional object. The discussion is extended to the implications of applying quantum-assisted simulation in quantum-computer aided composition and live-coding performances. An artistic output is showcased by the piece \textit{Hexagonal Chambers} (Thomas and Itaboraí, 2023).