Azhar Iqbal

Dr Azhar Iqbal

Senior Lecturer

School of Electrical and Electronic Engineering

Faculty of Sciences, Engineering and Technology

ORCID: 0000-0002-5221-9384.
My research explores a) intriguing and counter-intuitive aspects of quantum superposition and quantum entanglement using mathematical tools and solution-concepts of game theory b) game theoretical and mathematical modelling, and c) topics in applied mathematics and theoretical physics.

My research interests include a) quantum games, b) game theory, c) applications of geometric algebra, and d) mathematical modelling.

a) Quantum games: The research area of quantum games extends game theory towards the quantum domain and studies strategic interaction among rational agents sharing resources of quantum superposition and entanglement. A quantum game can be considered as strategic maneuvering of a quantum system by agents, considered as players, and usually it involves local unitary transformations and quantum measurement. Each player’ payoff, or utility, depends on the strategic choices of all players and is obtained from outcomes of measurements performed on the quantum system. In 1999 Meyer observed (1,2,3) that the quantum algorithm for an oracle problem can be understood as a quantum strategy for a player in a two-player zero-sum game in which the other player plays classically. Eisert, Wilkens, and Lewenstein (4,5) then developed a quantized version of the well-known game of Prisoners' Dilemma. The possibility to view quantum algorithms as games between quantum and classical players added game theory to the set of mathematical tools being used in present efforts to extend the list of quantum algorithms. Our contributions in this research area include:

  • Evolutionary stability in the quantum regime: Introduced in the 1970s by mathematical biologists, the game-theoretical notion of an Evolutionarily Stable Strategy (ESS) (6,7) models an evolving population under evolutionary pressures. It is a refinement notion on the set of symmetric Nash equilibria and is the central stability solution concept of evolutionary game theory. Our work (8,9,10,11,12,13) determined how an ESS becomes susceptible when the interactions among agents (players) of a population, under evolutionary pressures, become quantum-mechanical. This showed that, in a quantized version of a game, the presence of quantum entanglement can result in not only the emergence of new and novel Nash equilibria but quantum entanglement can also decide the fate of a refinement notion of the Nash equilibrium concept. A review of this work appeared in the book chapter 14.
  • Entanglement determining the game-theoretic outcomes: We studied fate of some well-known game-theoretic solution-concepts in a quantum game, including, “Social Optimality” (15), “Value of Coalition” (16), “Backwards-induction outcome” (17) and “Sub-game Perfect Outcome” (18).
  • Introducing Einstein-Podolsky-Rosen (EPR) setting for quantum games: To identify the truly quantum content of quantum games, we developed an EPR setting for enacting quantum games (19,20).
  • Quantum games from non-factorizable joint probabilities: We developed a new approach in constructing quantum games from the concept of non-factorizable joint probabilities (21).
  • Quantum games from Bell’s inequalities: We developed a new approach to constructing quantum games directly from a system of Bell's inequalities (22).
  • Quantum games on networks: We presented a study of quantum games that are played on networks (23).
  • Bayesian quantum games: Bayesian games have more complex underlying probabilities structure and offer a richer environment to study the role of quantum probabilities in quantum games. We presented the first investigation of quantum Bayesian games in 24 and a follow-up paper is 25.
  • Concept combinations using quantum games: Our work in 26 uses quantum games to gain an improved understanding and description of concept combinations in human cognition.
  • Quantum games when strategies are directional choices: In our recent work in 40, we developed an approach to quantum games in which each player's quantum strategy is implemented by using a directional choice.

b) Game theory: Our work in (classical) game theory include:

  • Developing an extension of the well-known Selten's game model of ransom kidnapping (27);
  • Applications of game theory in network/cybersecurity as presented in the review article 40.

c) Applications of geometric algebra: Geometric Algebra (GA) combines the algebraic structure of Clifford’s algebra with an explicit geometric meaning. It is a coherent mathematical language that augments the powerful geometric intuition with the precision of an algebraic system. Our work on the applications of GA include:

  • Study of Meyer’s quantum penny-flip game using GA (28);
  • Developing a GA-based analysis of the two-player (29) and the three-player quantum games in an EPR-type setup (30);
  • Study of special relativity using the mathematical formalism of GA (31);
  • Investigation of N-player quantum games in an EPR setting (32);
  • Development of an improved formalism for quantum computation based on GA and applying it to Grover's search algorithm (33);
  • Exploration of the benefits of the GA formalism for engineers (34);
  • Study of the functions of multivector variables in GA (35); and
  • Study of time as a geometric property of the GA-based conception of space (36).

d) Mathematical modelling: Mathematical modelling uses mathematical concepts and language in the description of a system. Our work in mathematical modelling include:

  • Work on memristive devices and its applications to circuits and systems simulation is reported in 3738, and 39. Memristor, a portmanteau of “memory” and “resistor”, and is a type of passive circuit element that maintains a relationship between the time integrals of current and voltage across a two-terminal element.
  • Work on mathematical modelling of COVID-19 outbreak in Bahrain (41, 42).

For my author IDs and research impact indicators, please refer to these links:



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  • Appointments

    Date Position Institution name
    2022 - ongoing Senior Lecturer University of Adelaide
    2022 - ongoing Founder Quantum Interactive Decisions
    2020 - 2022 Associate Professor University of Bahrain
    2019 - ongoing Senior Associate Game Theory Sage International Australia
    2019 - ongoing Founder Interactive Decisions
    2013 - 2022 Adjunct Senior Lecturer University of Adelaide
    2013 - 2015 Assistant Professor King Fahd University of Petroleum & Minerals
    2012 - 2012 Senior Research Associate (ARC grant-funded, Level B) University of Adelaide
    2007 - 2011 Australian Research Council's (ARC) Postdoctoral Research Fellow (Level A) University of Adelaide
    2006 - 2007 Japan Society for the Promotion of Science (JSPS) Postdoctoral Research Fellow and Visiting Associate Professor Kochi University of Technology
  • Language Competencies

    Language Competency
    English Can read, write, speak, understand spoken and peer review
    Urdu Can read, write, speak, understand spoken and peer review
  • Education

    Date Institution name Country Title
    2002 - 2006 University of Hull United Kingdom PhD in Applied Mathematics
    2002 - 2006 University of Hull United Kingdom Postgraduate Certificate in Research Training
    1992 - 1995 University of Sheffield United Kingdom BSc (Honours)
  • Research Interests

  • Faculty of Engineering, Computer & Mathematical Sciences (ECMS) Interdisciplinary Research Grant Scheme 2016 (jointly with Prof Derek Abbott & Dr Virginie Masson) at the University of Adelaide, AU$ 30,000 (2016-2017)
  • Discovery Research Grant DP0771453 and Fellowship (Principal Investigator) from Australian Research Council (ARC) at University of Adelaide, AU$ 247,092 (2007-2011)
  • Research Grant P06330 and Fellowship (Principal Investigator) from Japan Society for the Promotion of Science (JSPS) at Kochi University of Technology, Japanese Yen 4,958,500 (2006-2007)
  • Fully funded PhD Research Scholarship from the University of Hull, UK, for overseas research students (2002-2005)
  • Fully funded Merit Scholarship from the Government of Pakistan for studying overseas at the University of Sheffield, UK (1992-1995)

Department of Mathematics, College of Science, University of Bahrain (UoB):

2nd Semester 2020-2021:

  • Fluid Mechanics (Level 3)
  • Calculus II (Level 1)
  • Calculus & Analytical Geometry II (Level 1)
  • Calculus & Analytical Geometry III (Level 2)

1st Semester 2020-2021:

  • Analytical Mechanics (Level 3)
  • Methods of Applied Mathematics (Level 3)
  • Calculus II (Level 1)

2nd Semester 2019-2020:

  • Calculus II (Level 1)
  • Maths for Business Management (Level 1)
  • Calculus & Analytic Geometry III (Level 2)

School of Electrical & Electronic Engineering, University of Adelaide:

  • Avionic Sensors & Systems Combined (Level 4), 2014 Semester 2: Guest Lecturer
  • Communications/Principles of Communication Systems (Combined) (Level 4), 2012 Semester 1: Guest Lecturer
  • Communications/Principles of Communication Systems (Combined) (Level 4), 2011 Semester 1: Guest Lecturer

Department of Mathematics & Statistics, King Fahd University of Petroleum & Minerals (KFUPM):

  • Methods of Applied Mathematics (Level 3), Jan 2013 to May 2014, taught this course 4 times
  • Elements of Differential Equations (Level 2), Jan 2013 to May 2014, taught this course twice

School of Natural Sciences, National University of Sciences & Technology (NUST):

  • Mathematical Foundations of Quantum Mechanics (Level 4), July-Nov 2006

Riphah International University (RUI):

  • Engineering Electromagnetics (Level 2), Sep 2000-Sep 2001

Tutoring experience

School of Electrical & Electronic Engineering, University of Adelaide:

  • Electronic Circuits (Level 2), 2022 Semester 1
  • Electronic Circuits (Level 2), 2018 Semester 1
  • Electronic Circuits (Level 2), 2017 Semester 1
  • Electronic Circuits (Level 2), 2016 Semester 1
  • Electronic Systems (Level 1), 2016 Semester 1

Maths Learning Centre (MLC), University of Adelaide:

  • Undergrad Maths courses (Various Levels), 2017 to 2019.
  • Position: Senior Lecturer
  • Phone: 83135589
  • Email:
  • Campus: North Terrace
  • Building: Ingkarni Wardli, floor Level Three
  • Org Unit: School of Electrical and Electronic Engineering

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