Quantum Cognition and Decision Notes


Life is complex, it has both real and imaginary parts. (Anonymous)



                     Research is based upon work supported by NSF SES-1560554 and AFOSR FA9550-15-1-0343

Stanislaw Ulam, Richard Feynman, John Von Neumann


Introduction Chapters

Published Papers





Computer Programs





Cognitive scientists face some of the same types of problems that forced physicists to abandon classical dynamics. Their measurements are often incompatible, and the first measurement may disturb a second measurement. Thus only partial information about a complex system can be obtained at any point in time.  Combining partial information about a system into a coherent understanding of the entire system is the hallmark of quantum theory. Quantum theory provides a fundamentally different approach to logic, reasoning, and probabilistic inference. For example, quantum logic does not always follow the distributive axiom of Boolean logic; quantum probabilities do not always obey the Kolmogorov law of total probability; quantum reasoning does not always obey the principle of monotonic reasoning.  The tutorial papers listed below present the basic assumptions of classic versus quantum information processing theories. These basic assumptions are examined, side by side, in a parallel and elementary manner. Classic theory emerges as a possibly overly restrictive case of the more general quantum theory. The fundamental implications of these contrasting assumptions for modeling cognition are examined.


Acknowledgments: This program of research was only possible with the help of great collaborators who have made major contributions to the theory of quantum cognition. This includes (in alphabetical order) S.N. Balakrishnan, Jan Broekaert, Peter Bruza, Riccardo Franco, Peter Kvam, Rob Nosofsky, Tim Pleskac, Emmanuel Pothos, Rich Shiffrin, Jennifer Trueblood, James Yearsley, and students Pegah Fakhari, Gunnar Epping, Adam Huang, K. Rajagopal, Rong Zheng, and Qizi Zhang. 





Busemeyer, J. R. & Bruza, P. D. (2012) Quantum Models of Cognition and Decision. Cambridge University Press


Introductory Chapters and Articles:

Yearsley, J. , & Busemeyer, J. R. (2016) Quantum Cognition and Decision Theories: A Tutorial

Journal of Mathematical Psychology, 74, 99-116.


Bruza, P. D., Busemeyer, J. R. (2015) Quantum cognition: A new theoretical approach to psychology. Trends in Cognitive Science, 19 (7), 383-393


Pothos, E. M., & Busemeyer, J. R. (2013). Can quantum probability provide a new direction for cognitive modeling?  Behavioral and Brain Sciences, 36, 255-274. (Target Article).


Busemeyer, J. R. (2012). Introduction to quantum probability for social and behavioral scientists. In Rudolph, L. (Ed.), Qualitative mathematics for the social sciences: Mathematical models for research on cultural dynamics. New York, NY: Routledge. (pp.  


Busemeyer, J. R., Kvam, P. D., & Pleskac, T. J. (2020) Comparison of Markov versus quantum dynamical

models of human decision making. Wiley Interdisciplinary Reviews: Cognitive Science.


Pothos,E.M., Busemeyer, J. R. (2022) Quantum Cognition. Annual Review of Psychology, 73, 749-778





Articles published recently in Busemeyer Lab:



Pothos, E. M., & Busemeyer, J. R. (2009). A quantum probability model explanation for violations of rational decision theory. Proceedings of the Royal Society, B, 276 (1665), 2171-2178)



Busemeyer, J. R., Pothos, E., Franco, R., & Trueblood, J. S. (2011). A quantum theoretical explanation for probability judgment errors.  Psychological Review, 118, 193-218.  


Trueblood, J. S., & Busemeyer, J. R. (2011). A quantum probability account for order effects on inference. Cognitive Science, 35, 1518-1552 


Pothos, E. M., Busemeyer, J. R., & Trueblood, J. S. (2013). A quantum geometric model of similarity. Psychological Review, 120 (3), 679-696


Kvam, P. D., Pleskac, T. J., Yu, S., & Busemeyer, J. R. (2015) Interference Effects of Choice on Confidence. Proceedings of the National Academy of Science.



Pothos, E. M., Yearsley, J., Shiffrin, R. M. & Busemeyer, J. R. (2017). The rational status of quantum cognition. Journal of Experimental Psychology, 146(7), pp. 968-987. doi: 10.1037/xge0000312



Busemeyer, J. R., Kvam, P. D., & Pleskac, T. J. (2019) Markov versus quantum dynamic models of belief change 

           during evidence monitoring. Scientific Reports, 9, 18025


Broekaert, J. B., Busemeyer, J. R., and Pothos, E. M. (2020) The Disjunction Effect in two-stage

            simulated gambles. An experimental study and comparison of a heuristic logistic, Markov and

            quantum-like model.  Cognitive Psychology. 117,  


Kvam, P, Busemeyer, J. R., & Pleskac, T. (2021) Temporal oscillations in preference strength provide evidence

             for an open system model of constructed preference. Scientific Reports, 11, 8169


Rajagopal, K., Zhang, Q., Balakrishnan, S. N., Fakhari, P., & Busemeyer, J. R. (2021). Quantum amplitude amplification for reinforcement learning. In K. G. Vamvoudakis (Ed) Handbook on Reinforcement Learning and Control.  Springer Studies in Systems, Decision and Control


Busemeyer, J., Zhang, Q., Balakrishnan, S. N. (2020). Application of quantum—Markov open system models to human cognition and decision. Entropy, 22(9), 990.


Epping, G. P., & Busemeyer, J. R. (2023). Using diverging predictions from classical and quantum models to dissociate between categorization systems. Journal of Mathematical Psychology, 112, 102738. 


Zheng, R., Busemeyer, J. R., & Nosofsky, R. M. (2023). Integrating Categorization and Decision‐Making. Cognitive Science, 47(1), e13235.


Huang, J., Busemeyer, J., Ebelt, Z., & Pothos, E. (2024). Bridging the gap between subjective probability and probability judgments: the Quantum Sequential Sampler. Psychological Review


Busemeyer, J. R., Asano, M., and Lu, M. (2024). Explaining Interference Effects in Prisoner Dilemma Games. Experimental Economics, in press



For Other Publications in Quantum Cognition, see these links


Diederick Aerts


Harald Atmanspacher


Reinhard Blutner


Peter Bruza


Andrei Khrennikov


Lian Gabora


Catarina Moriera


Tim Pleskac


Emmanuel Pothos


Jennifer Trueblood


Andreas Wichert


James Yearsley


V. I. Yukalov


Computer Code for HSM Model


Hilbert Space Model Programs




Busemeyer, J. R. & Bruza, P. D. (2012) Quantum models of cognition and decision. Cambridge.

Feynman, R. P., Leighton, R. B., & Sands, M. (1966) The Feynman Lectures on

 Physics: Volume III.  Reading MA: Addison Wesley.

Griffiths, R. B. (2003) Consistent quantum Theory. Cambridge.

Gudder, S. (1998) Quantum probability theory. Academic Press.

Hughes, R. I. G. (1989) The structure and interpretation of Quantum mechanics.

      Cambridge, MA: Harvard University Press.

Khrennikov, A. (2010) Ubiquitous quantum structure. Springer

Nielsen, M. A. & Chuang, I. L. (2000) Quantum computation and Quantum

      information. Cambridge, UK: Cambridge University Press.

Sakurai, J. J. (1994) Modern quantum mechanics. Pearson Education Inc.

Peres, A. (1995) Quantum theory: Concepts and methods. (Fundamental theories of

physics, Vol. 72).  DordRecht: Kluwer.

Susskind, L. and Friedman, A. (2015) Quantum mechanics: The theoretical minimum.  Basic Books

Isham, C. J. (1989) Lectures on quantum theory. World Scientific.

















Cognition and Decision


Quantum Decision Theory:



Quantum cognition



Brain and Cognition




Hammeroff's web site on consciousness




Quantum Workshop Filzbach Switzerland, 2012.  From left to right, Peter beim Graben, Jerome Busemeyer, Sandro Sozzo, Reinhard Blutner, Harald Atmanspacher (Organizer), Emmanuel Pothos.



See Quantum Interaction web site