Foreword
Preface: Music with quantum computing, a natural progression, but a potentially revolutionary one
References
Contents
1 Introduction to Quantum Computing for Musicians
1.1 Introduction
1.1.1 History Repeating Itself
1.1.2 Raison d'Γͺtre
1.2 Computing Quantum-Mechanically
1.3 Leveraging Quantum Computing for Making Music
1.4 Final Remarks
2 Music Fundamentals for Computer Programmers: Representation, Parametrization and Automation
2.1 Introduction
2.2 Representation
2.2.1 Abstraction Boundaries
2.2.2 Time-Domain Hierarchies
2.3 Thinking Composition: Top-Down Versus Bottom-Up
2.4 Cognitive Archetypes
2.4.1 Metaphorical Associations
2.4.2 Elementary Schemes
2.5 Parametrization and Automation
2.5.1 The Legacy of Arnold Schoenberg
2.5.2 The Legacy of Iannis Xenakis
2.6 Final Remarks
3 Quantum Computer Music: Foundations and Initial Experiments
3.1 Introduction
3.2 Algorithmic Computer Music
3.3 Musical Quantum Walks
3.3.1 One-Dimensional Musical Quantum Walk
3.3.2 Three-Dimensional Musical Quantum Walk
3.4 Basak-Miranda Algorithm
3.4.1 Constructive and Destructive Interference
3.4.2 An Example
3.5 Concluding Discussion
4 Making Music Using Two Quantum Algorithms
4.1 Introduction
4.2 Random Melodies from Quantum Walks
4.2.1 Quantum Random Walks
4.2.2 The Walker's Journey
4.3 Grover's Algorithm
4.3.1 An Unstructured Search
4.3.2 Structure of the Algorithm
4.3.3 Simulating Grover's Algorithm
4.4 Making Music Using Quantum Algorithms
4.4.1 Raw Data and Processing into MIDI
4.4.2 Musicality of the Data
4.4.3 Composition Process
4.5 Conclusion
5 Exploring the Application of Gate-Type Quantum Computational Algorithm for Music Creation and Performance
5.1 Introduction
5.2 Wavefunction-Based Approaches and Quantum Live Coding
5.2.1 Basic Principles of Music Generation Based on the Wavefunction-Based Approach
5.2.2 Example of Music Generation Based on the Wavefunction-Based Approach
5.3 Measurement-Based Approach
5.3.1 Stochastic Note Generation Model
5.3.2 Note-Expression Model
5.4 Closing Summary and Acknowledgements
6 Cellular Automata Music Composition: From Classical to Quantum
6.1 Introduction
6.2 Classical Cellular Automata
6.2.1 One-Dimensional Cellular Automata
6.2.2 The Game of Life: A Two-Dimensional Cellular Automaton
6.3 A Classical Cellular Automata Music System: CAMUS
6.4 Towards Quantum Cellular Automata
6.5 Partitioned Quantum Cellular Automata: PQCA
6.5.1 One-Dimensional PQCA
6.5.2 Two-Dimensional PQCA
6.6 Rendering Music from PQCA
6.6.1 Music from One-Dimensional PQCA
6.6.2 Music from Two-Dimensional PQCA
6.7 Concluding Discussion
7 QuiKo: A Quantum Beat Generation Application
7.1 Introduction
7.2 System Overview
7.3 Algorithm Building Blocks
7.3.1 Quantum Fourier Transform (QFT)
7.3.2 Quantum Phase Estimation
7.4 Pre-processing and Mapping Audio Signals to Qubits
7.4.1 Drum Sample Database Preparation
7.4.2 Sample Database, Quantum Circuit and States
7.5 The Quantum Circuit (QuiKo Circuit)
7.5.1 Static Encoding
7.5.2 Phase Kickback Sequencing
7.6 Results
7.6.1 Decoding and Beat Construction
7.6.2 Analysis
7.6.3 Phase Kick Back Results and Analysis
7.7 Initial Steps to A Complete Quantum Application
7.8 Future Work
8 QAC: Quantum-Computing Aided Composition
Abstract
8.1 Computer Music and Quantum Computing Tools
8.2 Previous Attempts for an Integration
8.3 A New Quantum-Computing Aided Composition
8.4 Early Attempts for QAC
8.5 Introducing The QAC Toolkit
8.5.1 och.microqiskit
8.5.2 och.qisjob
8.6 Implementing BMA with the QAC Toolkit
8.7 QAC in Disklavier Prelude #3
8.8 Closing Remarks
References
9 Quantum Music Playground Tutorial
Abstract
9.1 Introduction
9.1.1 A Bit About Basis States
9.2 Choosing Instruments and Pitches
9.2.1 Shifting the Phase Angles of Basis States
9.3 Playing with Rhythm
9.3.1 Leveraging the CNOT Gate for More Syncopation
9.3.2 Manipulating Rhythms with Controlled-H Gates
9.3.3 Dropping Notes Out of a Pattern
9.3.4 Dropping Out a Note by Putting It in Pitch 15
9.4 Understanding Control Gate Modifiers
9.5 Exploring Additional Musical Functionality
9.5.1 Selecting Musical Octaves
9.5.2 Changing Musical Scales
9.5.3 Transposing Musical Pitches
9.5.4 Folding a Musical Scale
9.5.5 Inverting a Musical Scale
9.5.6 Playing Notes Legato
9.5.7 Playing Harmonic Intervals and Chords
9.5.8 Implementing Time Cycles
9.5.9 Generating Stochastic Pitches
9.6 Indian Classical Music Related Functionality
9.6.1 Selecting Ragas
9.6.2 Controlling Lengths of Time Cycles
9.7 Miscellaneous Functionalities
9.7.1 Loading MIDI Clips
9.7.1.1 QMP Metadata in MIDI Clips
9.7.2 Selecting a MIDI Clip
9.7.3 Moving All Operations on the Quantum Circuit
9.8 Conclusion
10 Quantum Representations of Sound: From Mechanical Waves to Quantum Circuits
10.1 Introduction
10.2 From Mechanical to Quantum
10.2.1 From Mechanical to Analog
10.2.2 From Analogue to Digital
10.2.3 From Digital to Quantum
10.3 Preparation and Retrieval of Quantum Audio
10.3.1 Encoding Time Information
10.3.2 Note on Nomenclature
10.4 Coefficient-Based Representations
10.4.1 Quantum Probability Amplitude Modulation: QPAM
10.4.2 Single Qubit Probability Amplitude Modulations: SQPAM
10.5 State-Oriented Representations
10.5.1 QSM and uQSM
10.5.2 QSM
10.5.3 Fixed Point QSM
10.5.4 Multichannel Audio
10.6 Summary
10.6.1 Running on Real Hardware
10.7 Processing Audio Signals in Quantum Computers
10.7.1 Signal Addition
10.7.2 Concatenation
10.7.3 A Simple Similarity Metric for Making Parallel Comparisons with Multiple SQPAM
10.7.4 Other Proposed Signal Processing Algorithms
10.8 Potential Applications
10.8.1 A Brief Note About Quantum Audio and the Quantum Fourier Transform
10.8.2 Quantum ``Dithering''
10.8.3 Noise Transient Attack
10.8.4 The Geiger Counter Effect Using Wavetable Synthesis
10.9 Final Remarks
11 Experiments in Quantum Frequency Detection Using Quantum Fourier Transform
Abstract
11.1 Introduction
11.1.1 Fourier Analysis
11.1.2 Fourier Transforms
11.1.3 Mathematical Concepts
11.1.3.1 Fourier Transform
11.1.3.2 Fourier Series
11.1.3.3 Discrete-Time Fourier Transform (DTFT)
11.2 Discrete Fourier Transform and Beyond
11.2.1 Discrete Fourier Transform (DFT)
11.2.2 Quantum Gates
11.2.3 Quantum Fourier Transform (QFT)
11.3 Experimental Framework
11.3.1 The Qubit
11.3.2 OpenQASM
11.3.3 Qiskit Aer Provider and Visualization
11.3.4 Systemβs Flowchart
11.3.5 Experimental Design
11.4 Results
11.4.1 Experiments with the Aer Simulation Backend
11.4.1.1 Simulated QFT of Audio with a Single 900Β Hz Sinewave Using Four Qubits
11.4.1.2 Simulated QFT of Audio with a Single 900Β Hz Sinewave Using Eight Qubits
11.4.1.3 Simulated QFT of Audio with a Single 900Β Hz Sinewave Using Twelve Qubits
11.4.1.4 Simulated QFT of Bachβs Music Using Four Qubits
11.4.1.5 Simulated QFT of Bachβs Music Using Eight Qubits
11.4.1.6 Simulated QFT of Bachβs Music Using Twelve Qubits
11.4.2 Experiments Using IBM Qβs Hardware Backend
11.4.2.1 QFT of Audio with a Single 900Β Hz Sinewave Using a Four-Qubits Hardware
11.4.2.2 QFT of Bachβs Music Using a Four-Qubits Hardware
11.4.2.3 QFT of Bachβs Music Using an Eight-Qubits on Real Hardware
11.5 Discussion
11.5.1 Application for Final Mixdown in the Recording Studio
11.5.2 Application for Active Acoustics in Auditoriums
11.5.3 Application for Cardiac Anomaly Detection and Waveform Analysis
11.6 Conclusion
References
12 Sing and Measure: Sound as Voice as Quanta
12.1 Sound of The Quantum Sphere
12.2 The Quantum Vocal Theory of Sound
12.2.1 Phon and Measurement in the Computational Basis
12.2.2 Phon and Measurement in the Hadamard Basis
12.2.3 Phon and Measurement in the Complex Basis
12.2.4 Non-commutativity
12.2.5 The Density Operator
12.2.6 Time Evolution
12.3 Evolutions of a Vocal Improvisation
12.3.1 Hamiltonian Evolution from Pitch-Down
12.3.2 Evolution of a Mixed State
12.4 Conclusion and Perspective
13 A Quantum Natural Language Processing Approach to Musical Intelligence
13.1 Introduction
13.2 Music and Meaning
13.2.1 Brain Resources Overlap
13.2.2 Meaning is Context
13.3 Computational Modelling and Algorithmic Composition
13.4 Brief Introduction to Quantum Computing
13.5 DisCoCat Modelling
13.5.1 A Musical DisCoCat Model
13.6 Machine Learning of Music
13.6.1 Generating a Training Corpus with a Context-Free Grammar
13.6.2 Pregroup Converter: From Context-Free Grammars to Pregroup Grammars
13.6.3 Optimiser: Diagrammatic Rewriting
13.6.4 Circuit Converter: Translating Musical Compositions into Quantum Circuits
13.6.5 Training the System to Classify
13.7 Quanthoven: Leveraging the Quantum Classifier to Compose
13.8 Final Remarks
14 Adiabatic Quantum Computing and Applications to Music
Abstract
14.1 Introduction
14.2 Adiabatic Computation
14.2.1 Example: Simple Harmonic Oscillator
14.2.2 Example: Two Hamiltonians
14.3 Runtime
14.4 The D-Wave Computer
14.5 Algorhythms
14.5.1 Definition of the Task
14.5.2 Music of Algorhythms
14.6 Expandability and Applications
14.7 Concluding Discussion
References
15 Applications of Quantum Annealing to Music Theory
15.1 Introduction
15.2 Music Composition as an Optimization Problem
15.3 Technical Background
15.3.1 Combinatorial Optimization
15.3.2 Quantum Annealing
15.3.3 Markov Random Fields
15.4 Music Composition Using Quantum Annealing
15.4.1 Melody Generation
15.4.2 Rhythm Generation
15.4.3 Harmony Generation
15.5 Conclusion and Future Work
16 Making Sound with Light: Sound Synthesis with a Photonic Quantum Computer
16.1 Introduction
16.2 Photonic Quantum Computing
16.2.1 Qumodes
16.2.2 CV States
16.2.3 CV Gates
16.2.4 CV Measurements
16.3 Gaussian Boson Sampling
16.3.1 GBS Distribution
16.3.2 Programming a GBS Device
16.3.3 GBS Implementation for the PhotonSynths
16.4 The PhotonSynths
16.4.1 PhotonSynth 1: Photon-Driven Additive Sound Spectrum
16.4.2 PhotonSynth 2: Furnishing Dynamics to the Spectrum
16.4.3 PhotonSynth 3: Granular Sound Sampling
16.5 Final Remarks
17 New Directions in Quantum Music: Concepts for a Quantum Keyboard and the Sound of the Ising Model
17.1 Introduction
17.2 Qeyboard: Some Concepts for a Real-Time Quantum Keyboard
17.2.1 Real-Time Interface for Evolving a Dynamical Parameterized Quantum Circuit
17.2.2 Measurements
17.2.3 Synthesis
17.3 The Sound of the Ising Model
17.3.1 Variational Quantum Algorithms
17.3.2 How to Play a Quantum System
17.4 Summary and Outlook
18 Superconducting Qubits as Musical Synthesizers for Live Performance
Abstract
18.1 Introduction
18.2 Quantum Experiments Used to Generate Sounds
18.2.1 Nonequilibrium Quasiparticles in Superconducting Qubits
18.2.2 Error-Detected Networking for 3D Circuit Quantum Electrodynamics
18.2.3 Experimental Data as Control Voltages
18.3 A Simple Quantum Synthesizer
18.3.1 Two-State
18.3.2 Four-State
18.3.3 Bad Follower
18.4 Quantum Sound: Superconducting Qubits as Music Synthesizers
18.4.1 From Noise to Meaning
18.5 Conclusions
Acknowledgements
References