Quantum Computing in the Arts and Humanities: An Introduction to Core Concepts, Theory and Applications

Preface
Contents
From Digital Humanities to Quantum Humanities: Potentials and Applications
	1 Introduction
	2 Towards Quantum Humanities
		2.1 Digital Humanities
		2.2 Potential Benefits of Quantum Humanities
		2.3 Current Challenges of Quantum Humanities
	3 Quantum Humanities Use Case: Project MUSE
		3.1 MUSE Ontology
		3.2 MUSE Film Corpus
		3.3 MUSE Data Set
		3.4 MUSE Data Analysis
		3.5 MUSE Costume Patterns
	4 Analysing Data
		4.1 Data Analysis Pipeline
		4.2 Categorical Data
		4.3 Creating Pattern Languages Based on Data Analysis
	5 Artificial Neural Networks
		5.1 Neurons
		5.2 Neural Networks
		5.3 Perceptrons
		5.4 Restricted Boltzmann Machines
		5.5 Autoencoders
	6 Variational Hybrid Quantum–Classical Algorithms
		6.1 The Main Idea
		6.2 Maximum Cut: A Combinatorial Optimization Problem
		6.3 QAOA
		6.4 Computing Maximum Cuts via Eigenvalues
		6.5 VQE
	7 QHAna: A Quantum Humanities Analysis Tool
		7.1 Support the Identification of (Costume) Patterns
		7.2 Comparing Classical and Quantum Machine Learning Algorithms
		7.3 Improve the Understanding of the Benefits of Quantum Computing
		7.4 Integration of Heterogeneous Tools
		7.5 Provide Easy Access to Quantum Computing
	8 Conclusion and Outlook
	References
Quantum Computing and Cognitive Simulation
	1 Introduction
		1.1 Mathematical Notation
	2 Cognitive Phenomena
		2.1 Asymmetry of Similarity Judgements
		2.2 Diagnosticity
		2.3 Conjunction and Disjunction Fallacies
		2.4 Question Order Models
		2.5 The `Sure Thing' Principle
		2.6 Categorization
		2.7 Negation
	3 Quantum Models
		3.1 Overview of Quantum Models in Psychology
		3.2 Similarity Judgements
		3.3 Diagnosticity
		3.4 Conjunction Fallacy and Over/Underextension
		3.5 Violation of the `Sure Thing' Principle
		3.6 Question Order Models and Contextuality
		3.7 Contextuality
		3.8 Concept Combination and Overextension
		3.9 Modelling of Over- and Underextension in Psychological Data
		3.10 Cognitive and Neuronal Structures
		3.11 Tensor Product Representations
	4 Concluding Remarks
		4.1 Potential for Quantum Computing to Contribute  to Cognitive Science
	References
The Philosophy of Quantum Computing
	1 Introduction
	2 Fundamental Concepts
		2.1 Classical States
		2.2 Classical Computers
		2.3 Physical Perspectives on Computer Science
		2.4 Quantum States and Operations
	3 Quantum Computation and Parallel Universes
	4 Quantum Computation and Entanglement
	5 The Gottesman–Knill Theorem
	6 Computer Simulations and Locally Causal Models of Quantum Phenomena
	7 Computational Perspectives on Physics
	8 Concluding Remarks
	References
Quantum-Like Cognition and Rationality: Biological and Artificial Intelligence Systems
	1 Introduction
	2 Brief Comparison: Classical Versus Quantum Probability
	3 Classical (Bayesian) Versus Quantum (Generally Non-Bayesian) Rationality
	4 Advantages, Disadvantages, and Roots of Quantum Rationality
		4.1 Liberalization of Decision-Making
		4.2 Dysfunctional Disagreement and Information Overload
		4.3 Social Laser
	5 Classical Versus Quantum Approach to the Problem  of Agreement on Disagree
	6 Common Knowledge: Illustrative Examples
	7 Kolmogorov's Model of Classical Probability Theory
	8 Classical Formalization of Common Knowledge and Aumann Theorem
		8.1 States of the World
		8.2 Agents' Information Representations
		8.3 Common Prior
		8.4 CP-Formalization of the Notion of Common Knowledge
		8.5 Aumann Theorem
	9 Basics of Quantum Formalism
		9.1 States
		9.2 Observables, Born Rule for Probability, and Projection Postulate
		9.3 Quantum Logic
	10 Quantum Formalization of Common Knowledge and Aumann Theorem with Interference Term
		10.1 Quantum States of the World
		10.2 Agents' Quantum Information Representations
		10.3 Quantum Way of Common Knowledge Formalization
		10.4 Quantum Version of Aumann's Theorem
	11 Concluding Discussion
	References
Quantum Music, Quantum Arts and Their Perception
	1 Realm of Quantum Expressibility
	2 Quantum Musical Tones
		2.1 Bundling Octaves into Single Tones
		2.2 Coherent Superposition of Tones as a New Form of Musical Parallelism
		2.3 Classical Perception of Quantum Musical Parallelism
	3 Quantum Musical Entanglement
	4 Quantum Musical Complementarity and Contextuality
	5 Bose and Fermi Model of Tones
	6 Quantum Visual Arts
	7 Can Quantum Art Render Cognitions and Perceptions Beyond Classical Art?
	8 Summary
	References
Quanta in Sound, the Sound of Quanta: A Voice-Informed Quantum Theoretical Perspective on Sound
	1 SoundvoiceQuanta
		1.1 Some Postulates to Live by
	2 The Quantum Vocal Theory of Sound
		2.1 Preparation and Measurement Along Axes
		2.2 Measurement Along an Arbitrary Direction
		2.3 Purity and Mixing
		2.4 Not Too Sure? Uncertainty Can Be Measured
		2.5 Time Flies
	3 Quantum Vocal Sound Processing
		3.1 Playing with Pure States
		3.2 Playing with Mixed States
		3.3 From Signal Processing to Quantum Computing,  and Back
	4 Quantum Evolution of the State (of the Art)
		4.1 Concluding Remarks
	References
Quantum Cinema and Quantum Computing
	1 Introduction
	2 Quantum Cinema—A Digital Vision
	3 Lady Lovelace—Poetical Science and the Role of Imagination
		3.1 Art and Science
		3.2 The Role of Imagination
		3.3 How Can We Imagine a Simple Quantum System?
	4 The Heisenberg Uncertainty Principle and the Copenhagen Interpretation
		4.1 Heisenberg’s Movie Frame Analogy
	5 Up, Up to Higher Dimensions
		5.1 Higher-Dimensional “Quantum Stuff” and the Curse of Dimensionality
	6 Schrödinger’s “Entanglement”
		6.1 A Proposal for a Space that Enables Schrödinger’s “Entanglement”
		6.2 Entangled States in Quantum Computing
		6.3 A Space Composed of Cells
	7 Hidden Parameters: Never Neglect a Woman (Grete Hermann)
		7.1 More Ignorance and Paradoxes
	8 The Geometry of Quantum States
		8.1 A New Object in Quantum Geometry
		8.2 Quantum Gates
		8.3 Quantum Lattices—Why Not Use a 5-Dimensional Cubic Grid?
	9 The Hypersphere S3
	10 Quantum Algorithms and Fourier Transform
		10.1 Quantum Algorithms and Fuchsian Groups
		10.2 Factorization of Prime Numbers
		10.3 Bernoulli Numbers and the Riemann Hypothesis
	References
How to Make Qubits Speak
	1 Networks of Words
	2 Language Is Quantum-Native
	3 Our New Attempt
	4 The Actual Experiment
	5 QNLP
	6 Beyond Language
	7 String Diagrams Are Everywhere
	8 Compositionality
	9 Meaning-Aware Relational Wholism
	10 ...Let's Get Playing!
	11 Outlook
	References
A Quantum Computing Approach to Harnessing the Logic of the Mind for Brain–Computer Interfacing
	1 Introduction
	2 Brain–Computer Interfacing
		2.1 The Electroencephalogram (EEG)
		2.2 The Semantics of the EEG
	3 An EEG-Based Logic of the Mind
	4 A Brief Introduction to Quantum Computing and Logic Operations
		4.1 The Basics of Quantum Computing
		4.2 Quantum Logic Operators
	5 Building Logic Expressions from EEG Information
	6 Generating Quantum Circuits for Logic Satisfiability
	7 Technical and Practical Considerations
		7.1 Reducing Outliers
		7.2 Running on Quantum Hardware
		7.3 Quantum Advantage?
	8 A Quantum BCI Musical Instrument
	9 Concluding Remarks
	Appendix 1: Examples from the BCI System
		Example 1
		Example 2
		Example 3
		Example 4
	Appendix 2: Study Using IBM Quantum Computing Resources
	References
The History of Games for (Quantum) Computers
	1 Introduction
	2 The 1950s: What Can Games Do for Computers?
	3 The 1960s: What Can Computers Do for Games?
	4 The 1970s: Commercial Success
	5 The 2010s: What Can Games Do for Quantum Computers?
	6 Quantum Games Without Quantum Computers
	7 The 2020s: What Can Quantum Computers Do for Games?
	8 Battleships with Partial NOT Gates
	9 Single-Qubit Procedural Generation
		9.1 The Basic Properties of Qubits
		9.2 Properties of an Initialized Qubit
		9.3 The X Gate
		9.4 The H and RX Gates
		9.5 The Bloch Sphere
		9.6 Single-Qubit Terrain Generation
	10 Conclusion
	References