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?

The field is developing rapidly, and this second edition contains many updates including new material on quantum logic and quantum agent-based models, and a guest chapter from Ramy Aboushelbaya and Marko Mayr of Quantum Dice on quantum hardware

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

CONTENTS OF THE SECOND EDITION

Introduction 1

1 Why quantum?            9

1.1 Not so strange                           10

1.2 A quantum of value                         11

1.3 Transactions as a measurement process             12

1.4 Entanglements                           13

1.5 Money creation                           15

1.6 Quantum economic person                     16

1.7 Dynamics                             18

1.8 How much                             18

1.9 Summary                               21

1.10 Further reading                           21

2 Some basics 25

2.1 The Hilbert space                         25

2.2 Quantum measurements                       27

2.3 Example: a binary decision                     28

2.4 Entropic force                           30

2.5 Projection sequences                       31

2.6 The quarter law                           33

2.7 Density matrix                           34

2.8 Quantum coin                           35

2.9 Complications                           37

2.10 Summary                               38

2.11 Further reading                           38

3 Quantum propensity 41

3.1 Expected utility theory                       41

3.2 Behavioural economics                       43

3.3 The sure thing effect                       45

3.4 The unsure thing effect                       46

3.5 Loss aversion                             47

3.6 Ellsberg paradox                           48

3.7 Allais effect                             49

3.8 Summary                               50

3.9 Further reading                           51

4 Mental interference 53

4.1 Framing events                           53

4.2 Wave splitter                             54

4.3 The disjunction effect                       55

4.4 Projection sequence                         57

4.5 The attraction function                       58

4.6 The conjunction effect                       60

4.7 The order effect                           60

4.8 Clinton and Gore                         62

4.9 Summary                               63

5 Computing in colour 65

5.1 Qubits                               66

5.2 Basic logic gates                           67

5.3 Gates on multiple qubits                     68

5.4 Circuit representation                       70

5.5 Example: An entanglement circuit                 72

5.6 Example: The quantum walk                   74

5.7 Example: Quantum learning                   75

5.8 Quantum programming                       76

5.9 Summary                               76

5.10 Further reading                           77

6 The quantum walk 79

6.1 Background                             79

6.2 The classical random walk                     80

6.3 The quantum version                       81

6.4 Quantum diffusion                         85

6.5 Decoherence                             86

6.6 Applications                             87

6.7 Summary                               89

7 Option pricing 91

7.1 Walking the line                           92

7.2 Quantum fluctuations                       93

7.3 The binomial model                         94

7.4 Pricing options                           96

7.5 Quantum anomalies                         96

7.6 Model with two assets                       101

7.7 Discussion                             103

7.8 Summary                               104

8 Quantum games 105

8.1 The penny flip                           106

8.2 The prisoner’s dilemma                       108

8.3 Quantum rules                           109

8.4 Entangled prisoners                         111

8.5 The projection game                         115

8.6 Summary                               117

9 Quantum oscillations 119

9.1 Background                             120

9.2 Quantize this                           121

9.3 The harmonic oscillator                       123

9.4 Creation and annihilation                     126

9.5 Coherent state                           128

9.6 Dynamics                             129

9.7 Discussion                             130

9.8 Summary                               131

9.9 Further reading                           132

10 Probabilistic supply and demand 133

10.1 Background                             133

10.2 Case with single buyer and seller                 134

10.3 Market makers                           136

10.4 Multiple agents                           137

10.5 Effects on price flexibility                     139

10.6 Entropic force interpretation                   140

10.7 The entropic oscillator                       141

10.8 Discussion                             144

10.9 Summary                               144

10.10Further reading                           145

11 Quantized supply and demand 147

11.1 The quantum financial oscillator                 148

11.2 Quantum mass                           149

11.3 Quantum versus classical                     150

11.4 Information exchange                       153

11.5 Applications                             154

11.6 Summary                               155

11.7 Tables                               156

12 The quantum market 159

12.1 Financial bosons                           159

12.2 Monetary exchange                         160

12.3 Cash flow                             162

12.4 Quantum (in)security                       163

12.5 The colour of money                       164

12.6 Discussion                             165

12.7 Summary                               167

12.8 Further reading                           167

13 Entanglements 169

13.1 Preference reversal                         170

13.2 Mortgage default                         172

13.3 A quantum of debt                         174

13.4 Social entanglement                         175

13.5 Financial entanglement                       176

13.6 Entanglement versus correlation                 178

13.7 Derivatives                             179

13.8 Discussion                             180

13.9 Summary                               181

13.10Further reading                           182

14 Building quantum models 183

14.1 Principles for modelling                       184

14.2 Probabilistic transactions                     185

14.3 Production and consumption                   188

14.4 Option pricing with supply and demand             189

14.5 Quantum agent-based models                   193

14.6 New foundations                           196

14.7 Summary                               197

15 Quantum gateway 199

15.1 The will is our pendulum                     199

15.2 A new operating system                       201

15.3 Shut up and calculate                       202

15.4 Reasons to be quantum                       204

15.5 The prediction test                         205

15.6 Quantum by another name                     208

15.7 Quantum calculation                       210

16 The practicalities of quantum hardware 213

16.1 Quantum insecurity                         213

16.2 The current state of quantum hardware             214

16.3 A look into the (near) future                   218

Bibliography 221

Index 233