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Variational Quantum Harmonizer: Generating Chord Progressions and Other Sonification Methods with the VQE Algorithm

Paulo Vitor Itaboraí, Tim Schwägerl, María Aguado Yáñez, Arianna Crippa, Karl Jansen, Eduardo Reck Miranda, Peter Thomas

TL;DR

The paper introduces the Variational Quantum Harmonizer (VQH), a hybrid quantum-classical musical instrument that encodes Quadratic Unconstrained Binary Optimization (QUBO) problems solved via the Variational Quantum Eigensolver (VQE) into sound. It maps intermediate statevectors and marginal qubit distributions to chords, arpeggios, and timbres, enabling both data visualization and artistic composition. The authors present both a QUBO-to-Ising mapping and multiple sonification strategies (additive, subtractive, inharmonic, arpeggios), and demonstrate live-code capable workflows and MIDI interfaces for dynamic performance. They also explore adiabatic VQE approaches, state-superposition chords, and a range of examples illustrating how quantum optimization trajectories can be sonified into musically meaningful progressions. The work highlights the potential of quantum-inspired sonification to provide intuition about optimization processes and to enrich musical practice with quantum computational motifs.

Abstract

This work investigates a case study of using physical-based sonification of Quadratic Unconstrained Binary Optimization (QUBO) problems, optimized by the Variational Quantum Eigensolver (VQE) algorithm. The VQE approximates the solution of the problem by using an iterative loop between the quantum computer and a classical optimization routine. This work explores the intermediary statevectors found in each VQE iteration as the means of sonifying the optimization process itself. The implementation was realised in the form of a musical interface prototype named Variational Quantum Harmonizer (VQH), providing potential design strategies for musical applications, focusing on chords, chord progressions, and arpeggios. The VQH can be used both to enhance data visualization or to create artistic pieces. The methodology is also relevant in terms of how an artist would gain intuition towards achieving a desired musical sound by carefully designing QUBO cost functions. Flexible mapping strategies could supply a broad portfolio of sounds for QUBO and quantum-inspired musical compositions, as demonstrated in a case study composition, "Dependent Origination" by Peter Thomas and Paulo Itaborai.

Variational Quantum Harmonizer: Generating Chord Progressions and Other Sonification Methods with the VQE Algorithm

TL;DR

The paper introduces the Variational Quantum Harmonizer (VQH), a hybrid quantum-classical musical instrument that encodes Quadratic Unconstrained Binary Optimization (QUBO) problems solved via the Variational Quantum Eigensolver (VQE) into sound. It maps intermediate statevectors and marginal qubit distributions to chords, arpeggios, and timbres, enabling both data visualization and artistic composition. The authors present both a QUBO-to-Ising mapping and multiple sonification strategies (additive, subtractive, inharmonic, arpeggios), and demonstrate live-code capable workflows and MIDI interfaces for dynamic performance. They also explore adiabatic VQE approaches, state-superposition chords, and a range of examples illustrating how quantum optimization trajectories can be sonified into musically meaningful progressions. The work highlights the potential of quantum-inspired sonification to provide intuition about optimization processes and to enrich musical practice with quantum computational motifs.

Abstract

This work investigates a case study of using physical-based sonification of Quadratic Unconstrained Binary Optimization (QUBO) problems, optimized by the Variational Quantum Eigensolver (VQE) algorithm. The VQE approximates the solution of the problem by using an iterative loop between the quantum computer and a classical optimization routine. This work explores the intermediary statevectors found in each VQE iteration as the means of sonifying the optimization process itself. The implementation was realised in the form of a musical interface prototype named Variational Quantum Harmonizer (VQH), providing potential design strategies for musical applications, focusing on chords, chord progressions, and arpeggios. The VQH can be used both to enhance data visualization or to create artistic pieces. The methodology is also relevant in terms of how an artist would gain intuition towards achieving a desired musical sound by carefully designing QUBO cost functions. Flexible mapping strategies could supply a broad portfolio of sounds for QUBO and quantum-inspired musical compositions, as demonstrated in a case study composition, "Dependent Origination" by Peter Thomas and Paulo Itaborai.
Paper Structure (32 sections, 19 equations, 20 figures)

This paper contains 32 sections, 19 equations, 20 figures.

Table of Contents

  1. Introduction
  2. The Variational Quantum Harmonizer algorithm
  3. Quadratic Unconstrained Binary Optimization
  4. The Variational Quantum Eigensolver
  5. Parameterized Quantum Circuits
  6. Classical Optimizers
  7. Sonifying the VQE algorithm: Chords and Chord progressions
  8. Qubit words as chords: the QUBO Harp
  9. Using the VQE to minimize (and sonify) the QUBO Problem
  10. The Statevector sonification
  11. Example 1: Linear Cmajor Chord
  12. Example 2: I-IV-V-I Linear Chord Progression
  13. QUBOs and Ising Hamiltonians
  14. The Ising Harp
  15. Example 3: Coupled-Spin Cmajor Chord
  16. ...and 17 more sections

Figures (20)

  • Figure 1: Constituting elements of a digital musical instrument miranda2006new
  • Figure 2: An EfficientSU2 circuit for 5 qubits. The initial $R_y$ rotations are referred to as the 0-thy layer. The 1st layer here indroduces linear entanglement using $CNOT$ gates and additional rotations.
  • Figure 3: A C Major Chord represented in binary
  • Figure 4: Marginal Distribution Evolution for Example 1
  • Figure 5: Visualization of Example 1 sonified with additive synthesis.
  • ...and 15 more figures