Prof. Belal Ehsan Baaquie holds a B.S. in Physics from Caltech and a Ph.D. in Theoretical Physics from Cornell University, USA. His main research interest is in the study and application of the mathematical methods of quantum field theory. He has applied the mathematical formalism of field theory to finance and been a major contributor to the emerging field of quantum finance. His current focus is on developing the formalism of quantum finance and applying it to option pricing, corporate coupon bonds, and the theory of interest rates, as well as the study of equity, foreign exchange, and commodities; he has developed forecasting models for commodity prices. He is also applying methodologies from statistical mechanics and quantum field theory to the study of microeconomics and macroeconomics.

Leong-Chuan Kwek is a principal investigator at the Center for Quantum Technologies, NUS, the Co-Director of the Quantum Science and Engineering Center at NTU and a faculty of the National Institute of Education, Singapore. He is the Immediate Past President of the Institute of Physics, Singapore and a Council Member of the Association of Asia Pacific Physical Socieites. He is also an elected Fellow of the American Associaiton for the Advancement of Science (AAAS) and the Institute of Physics, UK (IOP).

Highlights the advantages of a quantum over a classical computer

Reviews the concepts of the classical and quantum computers along with circuits and gates

Uses the Deutsch, Grover, and Shor algorithms for highlighting key features of quantum computing

1 Introduction

2 Classical Computer

2.1 Binary Representation

3 Quantum Computer

3.1 Qubit

4 Classical Gates and Circuits

5 Quantum Gates and Circuits

5.1 Hilbert space

5.2 Measurement

6 Deutsch Algorithm

7 Grover Algorithm

7.1 Grover algorithm: two-qubit

7.3 Grover diffusion and rotation gate G

7.4 Single Recursion: Two qubit

8 Deutsch-Josza Algorithm

9 Simon's Algorithm

9.2 An Illustrative Example

10 Quantum Fourier Transform (QFT) 51

10.1 Quantum circuit of QFT

11 Shor

11.1 Introduction

11.2 Understanding the classical algorithm

11.3 Quantum algorithm

12.1 Quantum Algorithm for Option Pricing

12.2 Quadratic Improvement

12.3 Estimation of Phase

12.4 Call Option

13 Solving Linear Equations

13.2 Harrow-Hassidim-Lloyd Algorithm

13.3 Specific Example

13.4 Other applications

14 Quantum-Classical Hybrid Algorithms

14.1 Why bother?

14.3 Variational Quantum Eigensolvers

15 Quantum Error Correction

15.1 Introduction

15.2 Simple quantum errors

15.3 Kraus Operators

15.5 General properties of quantum error-correcting codes

15.6 Classical Linear Codes

15.7 CSS Codes

16 Efficiency of a Quantum Computer

16.1 So where does quantum computation take place?

16.3 Acknowledgements