Quantum Entanglement in Physics and Extended Techniques in Music

María Luisa Dalla Chiara, Roberto Giuntini, Eleonora Negri

Eduardo Reck Miranda

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.

Eduardo Reck Miranda

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).

Joonwon Seo, Mariana Montiel

Classical Recurrent Neural Networks (RNNs) summarize musical context into a deterministic hidden state vector, imposing an information bottleneck that fails to capture the inherent ambiguity in music. We propose the Density Matrix RNN (DM-RNN), a novel theoretical architecture utilizing the Density Matrix. This allows the model to maintain a statistical ensemble of musical interpretations (a mixed state), capturing both classical probabilities and quantum coherences. We rigorously define the temporal dynamics using Quantum Channels (CPTP maps). Crucially, we detail a parameterization strategy based on the Choi-Jamiolkowski isomorphism, ensuring the learned dynamics remain physically valid (CPTP) by construction. We introduce an analytical framework using Von Neumann Entropy to quantify musical uncertainty and Quantum Mutual Information (QMI) to measure entanglement between voices. The DM-RNN provides a mathematically rigorous framework for modeling complex, ambiguous musical structures.

Shengjun Wu