Advances in Quantum Computer Music

The following sections are included:

• Foreword
• Preface
• About the Editor
• About the Contributors
• Contents

This chapter provides an introduction to the structure of quantum states and outlines a general method for sonifying such states. Quantum systems exist in a superposition of multiple states simultaneously, and sonifications can serve as useful auditory representations of component states in such systems. These sonifications could allow one to “listen” to a simulated quantum system without measuring it and could provide interesting creative resources for composers and musicians. The sonification method has three steps: determine a distinct sound for each basis state, find the measurement probabilities of each basis state, and modulate the sound based on those values. We provide a detailed investigation into each step of the sonification process, examining several approaches as well as technical and creative considerations. We also consider extensions to the base approach, including incorporating stochasticism, accounting for quantum phase, handling time evolution, and sonifying physical systems. Musical examples are heavily sprinkled throughout, including fully-worked-through pieces.

Feedback delay networks are signal-processing structures, extensively used in digital audio effects and artificial reverberation, that can be designed around a unitary matrix that multiplies the vector output of a bunch of delay lines. Replacing matrix-vector multiplication with unitary evolution of a quantum state, a new class of signal-processing structures is created, whose behaviour and sonic properties are being explored. The output of 2ⁿ delay lines is encoded in an n-qubit quantum state that is made to be evolved and temporarily stored in the feedback loop, being subject to quantum as well as to classical operations.

This chapter explores the sonification of three quantum mechanical phenomena: quantum simulators, Rabi oscillations, and the Wigner function. By linking the fields of sound research and quantum mechanics, we aim to represent fundamental quantum phenomena through sound. We examine how quantum randomness can be expressed musically, using examples such as the phase transition between two states of cold atoms in an optical lattice. Additionally, we explore how single-particle phenomena like Rabi oscillations can be conveyed through musical structures. A key feature of our approach is using musical timbres to represent random quantum events, creating a unique auditory experience for interpreting quantum mechanics.

The amount of thematic memory in a musical composition, as a balance between expectation and surprise, greatly influences the perception and appreciation of beauty. Here, we describe a method to quantify the musical memory based on a criterion used in physics to measure memory in quantum states. We present the results of our analysis for compositions of different authors, including Verdi, Wagner, and Mannone. We also discuss further lines of research.

This chapter introduces a way to implement quantum probability amplitude modulation (QPAM) (Itaborai, 2023b) as a semi-stochastic model in the compositional process. QPAM offers a mediating ground between the composer, the algorithm and randomness. It also enables the composer to have a control over the degree of randomness by utilising the inherent stochastic nature of quantum computational algorithms. The chapter demonstrates possible applications of QPAM through a quantum computer simulation in a musical context, to achieve controlled indeterminacy in the composition. At the end, some of the compositions, that use QPAM or a semi-stochastic approach through quantum computation, are introduced.

Though some years remain before quantum computation can outperform conventional computation, it already provides resources that can be used for exploratory purposes in various fields. This includes the algorithmic generation of content for music, computer games and the visual arts. The so-called “Quantum Blur” method represents the first step on this journey, providing a simple proof-of-principle example of how quantum software can be useful in these areas today. Here we analyse the “Quantum Blur” method and compare it to conventional blur effects. We also consider two different methods by which the method can be applied to music.

This chapter and the experiments described within explore how “human entanglement” might be represented and even emulated by physical entanglement. To achieve this, a notion of “tonal centrality” between two musicians is captured via MIDI and passed as a parameter into a quantum simulation taking place on an embedded device (a Raspberry Pi Pico). The results of these simulations are then coded back into MIDI and sent to the players’ instruments. The closer the musicians’ tonality is, the more their instruments will be entangled in a |Φ⁺ ⟩ state, and the further away they are the more their instruments will be entangled in a |Ψ⁺⟩ state. The intention is to create random parameters that are correlative — i.e., the same on both instruments — or anti-correlative — i.e., the bit-wise opposite of each other, influenced by the tonal relationship from the players. These random parameters sharing these particular properties add a new dimension for quantummusical expression. This concept was realised experimentally, and the full code and sample outputs are provided. This work aims to pave the way for musicians to explore and experience quantum emulations of their own musical experiences, adding a new nuance and possibilities for the future of entangled ensembles.

This chapter examines the variational quantum harmoniser, a software tool and musical interface that focuses on the problem of sonification of the minimisation steps of variational quantum algorithms (VQAs), used for simulating properties of quantum systems and optimisation problems assisted by quantum hardware. Particularly, it details the sonification of quadratic unconstrained binary optimisation (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 Hexagonal Chambers (Thomas and Itaboraí, 2023).

Artificial intelligence (AI) has recently gained much interest in inspiring and facilitating artists to expand their creative possibilities. Exploiting the physical properties of a quantum system, this chapter proposes Quantum Reservoir Computing (QRC) to build music AI systems. We developed a QRC-based proof-of-concept system that learns music sequencing rules from examples in a given corpus and uses these rules to generate new music. The QRC approach introduced here has demonstrable advantages over the standard deep-learning approaches normally adopted for music AI, one of which is the considerable reduction in the required number of trainable parameters. A proof-of-concept system is demonstrated.

The following section is included:

• Index