Quantum Computer Music. Foundations, Methods and Advanced Concepts

Description

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'être 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 System’s 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 900 Hz Sinewave Using Four Qubits 11.4.1.2 Simulated QFT of Audio with a Single 900 Hz Sinewave Using Eight Qubits 11.4.1.3 Simulated QFT of Audio with a Single 900 Hz Sinewave Using Twelve Qubits 11.4.1.4 Simulated QFT of Bach’s Music Using Four Qubits 11.4.1.5 Simulated QFT of Bach’s Music Using Eight Qubits 11.4.1.6 Simulated QFT of Bach’s Music Using Twelve Qubits 11.4.2 Experiments Using IBM Q’s Hardware Backend 11.4.2.1 QFT of Audio with a Single 900 Hz Sinewave Using a Four-Qubits Hardware 11.4.2.2 QFT of Bach’s Music Using a Four-Qubits Hardware 11.4.2.3 QFT of Bach’s 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