The word “quantum” is from the Latin for “how much” and in this book mathematician David Orrell shows how it applies to the world of economic transactions. Written in clear and accessible language, the book covers the essential mathematics behind topics including quantum cognition, option pricing, and quantum game theory, and delves into the nuts and bolts of quantum mechanics, the principles of quantum economic modelling, and the basics of quantum computer logic. On the way the reader will learn how quantum interference can be used to model cognitive dissonance, how a quantum walk goes further than a random walk, and how financial entanglement explains the rate of mortgage default. It is aimed at anyone who wants to understand the quantum ideas working their way into economics and finance, without getting drowned in wave equations.

As interest in quantum computing grows, many companies from established banks to startups are looking at ways to perform financial simulations using quantum algorithms. But what if we should be using quantum models anyway – because the monetary system has quantum properties of its own, and because they work?

David Orrell is an applied mathematician with extensive experience in mathematical modelling, and the author of a dozen books on science and economics.

**CONTENTS**

**INTRODUCTION 1**

Burn the mathematics 2

Quantum aversion 4

Quantum fog 6

**CHAPTER 1 WHY QUANTUM? 11**

Not so strange 13

A quantum of value 14

Transactions as a measurement process 15

Entanglements 17

Money creation 19

Quantum economic person 21

Dynamics 23

How much 24

Some information 26

Summary 27

Further reading 29

**CHAPTER 2 SOME BASICS 30**

The Hilbert space 30

Quantum measurements 33

Example: a binary decision 34

Entropic force 36

Projection sequences 37

The quarter law 39

Density matrix 40

Quantum coin 42

Summary 43

Further reading 45

**CHAPTER 3 QUANTUM UTILITY 47**

Expected utility theory 47

Behavioural economics 49

The sure thing effect 52

The unsure thing effect 53

Loss aversion 54

Ellsberg paradox 55

Allais effect 56

Summary 57

Further reading 58

**CHAPTER 4 MENTAL INTERFERENCE 59**

Wave splitter 59

The disjunction effect 61

Projection sequence 62

The attraction function 63

The conjunction effect 65

The order effect 65

Clinton and Gore 67

Summary 69

**CHAPTER 5 THE QUANTUM WALK 71**

Background 71

The classical random walk 72

The quantum version 73

Quantum diffusion 77

Decoherence 80

Applications 80

Summary 82

**CHAPTER 6 OPTION PRICING 84**

Walking the line 85

Quantum fluctuations 86

The binomial model 87

Pricing options 89

Quantum anomalies 92

Model with two assets 96

Discussion 98

Summary 99

**CHAPTER 7 QUANTUM GAMES 101**

Background 101

The penny flip 103

The prisoner’s dilemma 106

Entangled prisoners 107

Experiments 112

Summary 113

Further reading 114

**CHAPTER 8 QUANTUM OSCILLATIONS 117**

Background 118

Quantize this 119

The harmonic oscillator 122

Creation and annihilation 124

Coherent state 126

Dynamics 128

Discussion 129

Summary 130

Further reading 131

**CHAPTER 9 PROBABILISTIC SUPPLY AND DEMAND 133**

Background 134

Case with single buyer and seller 135

Market makers 136

Multiple agents 137

Effects on price flexibility 140

Entropic force interpretation 142

The entropic oscillator 143

Discussion 145

Summary 146

**CHAPTER 10 QUANTIZED SUPPLY AND DEMAND 15**0

The quantum financial oscillator 151

Quantum mass 152

Quantum versus classical 154

Information exchange 157

Applications 158

Summary 160

Tables 162

**CHAPTER 11 THE QUANTUM MARKET 16**4

Financial bosons 165

Monetary exchange 166

Cash flow 167

Quantum (in)security 169

Discussion 170

Summary 172

Further reading 173

**CHAPTER 12 ENTANGLEMENTS 174**

Preference reversal 175

Mortgage default 178

Quantum costs 180

Social entanglement 181

Financial entanglement 182

Entanglement versus correlation 184

Derivatives 185

Discussion 186

Summary 188

Further reading 189

**CHAPTER 13 BUILDING QUANTUM MODELS 190**

Principles for modelling 191

Probabilistic transactions 193

Quantum agent-based models 198

Weak foundations 200

Summary 201

Further reading 202

**CHAPTER 14 CONCLUSIONS 204**

The will is our pendulum 204

A new operating system 207

Shut up and calculate 208

Reasons to be quantum 210

The prediction test 212

Quantum by another name 215

Quantum calculation 217

**APPENDIX QUANTUM GATES 220**

Tensor product 220

Basic logic gates 221

Multiple qubits 222

Circuit representation 223

Measurement 224

Example: The quantum walk 224

Quantum programming 225

**BIBLIOGRAPHY 228****INDEX 236**

Errors And Typos – first printing 2020