Quantum Concept Music Score from Quantum Picturalism: Musical Incarnation of a Bell-Pair under Measurements
Rakhat-Bi Abdyssagin, Bob Coecke
TL;DR
The work addresses how to express quantum relational structure within a musical score by introducing Quantum Concept Music (QCM) grounded in $CQM$ and $QPict$. It develops both a colourless classical notation and a colourful quantum notation to represent relational content, and introduces a concrete two-qubit Bell-score framework for live performance. A key contribution is the Bell-like arrangement mapping two qubits to distinct instruments (Quantum Guitar and Grand Piano) under measurement, including an entanglement-driven mapping and non-deterministic outcomes that can be guided or explored by performers or audiences. The approach offers a template for live performance and AI-assisted music generation that generalizes beyond Western notation and supports cross-genre exploration and quantum education.
Abstract
We initiate the development of a new language and theory for quantum music, to which we refer as Quantum Concept Music (QCM). This new music formalism is based on Categorical Quantum Mechanics (CQM), and more specifically, its diagrammatic incarnation Quantum Picturalism (QPict), which is heavily based on ZX-calculus. In fact, it is naturally inherited from CQM/QPict. At its heart is the explicit notational representation of relations that exist within and between the key concepts of music composition, performance, and automation. QCM also enables one to directly translate quantum phenomena into music compositions in a both intuitively obvious, rigorous and mechanical manner. Following this pattern, we propose a score for musicians interacting like a Bell-pair under measurement, and outline examples of how it could be live performed. While most of the Western classical music notation has heavily relied on linear representation of music - which does not always adequately capture the nature of music - our approach is distinct by highlighting the fundamental relational dimension of music. In addition, this quantum-based technique not only influences the music at the profound level of composition, but also has a direct impact on a live performance, and also provides a new template for automating music, e.g.~in the context of AI-generation. All together, we initiate the creation of new music formalism that is powerful and efficient in capturing the interactive nature of music, both in terms of internal and external interactions, and goes beyond the boundaries of Western classical music notation, which allows to use it in many different genres and directions.