Quantum Technology for Economists (Contributions to Economics)

Foreword
Declarations
Contents
Acronyms
1 Introduction
	1.1 Background
	References
2 Preliminaries
	2.1 Quantum States
		2.1.1 Quantum Bits
		2.1.2 Vector Representation
		2.1.3 Dirac Notation
		2.1.4 Superposition
		2.1.5 Entanglement
			2.1.5.1 Entanglement Misconceptions
	2.2 Quantum Dynamics
	2.3 Quantum Measurement
		2.3.1 Partial Measurement
		2.3.2 Mid-circuit Measurement
	2.4 Quantum Circuits
	2.5 Phase Kickback
	2.6 Phase Estimation
	2.7 Quantum Fourier Transform
	2.8 Oracles
	2.9 No-Cloning Theorem
	2.10 Tensor Networks
	2.11 Computational Complexity
	References
3 Quantum Algorithms
	3.1 Theoretical Progress and Applications
		3.1.1 Numerical Differentiation
		3.1.2 Interpolation
		3.1.3 Linear Systems
			3.1.3.1 Quantum Linear System Problems
			3.1.3.2 Linear Regression
			3.1.3.3 Matrix Inversion
			3.1.3.4 Finite Element Methods
			3.1.3.5 Computational Finance
			3.1.3.6 Machine Learning
			3.1.3.7 Principal Component Analysis
		3.1.4 Statistical Distance
		3.1.5 Monte Carlo Methods
			3.1.5.1 Asset Pricing
			3.1.5.2 Financial Stress Testing
			3.1.5.3 Foreign Exchange Reserve Management
			3.1.5.4 Risk Modeling
			3.1.5.5 Macroeconomic Modeling
		3.1.6 Matrix Powers
		3.1.7 Bayesian Networks
		3.1.8 Clustering Algorithms
		3.1.9 Combinatorial Optimization
			3.1.9.1 Financial Crash Prediction
			3.1.9.2 Portfolio Optimization
			3.1.9.3 Foreign Exchange Reserve Management
			3.1.9.4 High-Value Payment Settlement
			3.1.9.5 Dynamic Programming
			3.1.9.6 Macroeconomic Models
			3.1.9.7 Unit Commitment Problem
		3.1.10 Maximum Independent Set Problems
			3.1.10.1 Solution on a Quantum Annealer
			3.1.10.2 Solution on a Neural Atom Quantum Computer
		3.1.11 Quantum Walk
		3.1.12 Random Number Generation
		3.1.13 Unstructured Search
	3.2 Theoretical Limitations
	3.3 Experimental Progress on Quantum Hardware
	References
4 Quantum Financial Technology
	4.1 Background
	4.2 The First Quantum Money Scheme
		4.2.1 Wiesner\'s Scheme
		4.2.2 Attacks on Wiesner\'s Scheme
	4.3 Properties of Modern Schemes
		4.3.1 Public Quantum Money
		4.3.2 Quantum Lightning
			4.3.2.1 Example: Knot-Based Quantum Lightning
		4.3.3 Bills, Coins, and Anonymity
		4.3.4 Security
		4.3.5 Oracles
			4.3.5.1 Complexity-Theoretic No-Cloning Theorem
		4.3.6 Efficiency
		4.3.7 Classical Verification and Mintability
		4.3.8 Noise Tolerance
	4.4 Experimental Implementation
		4.4.1 Remaining Challenges for Quantum Money
	4.5 Defense Against Quantum Attacks
		4.5.1 Post-quantum Cryptography
			4.5.1.1 Implementation at Central Banks
		4.5.2 Quantum Key Distribution
			4.5.2.1 A Minimal QKD Scheme
			4.5.2.2 Modern QKD Schemes
			4.5.2.3 Limitations
	References