How can quantum theory be used to model human performance on complex information processing tasks? Quantum computing and quantum information theory is relatively new, but it is already a highly developed field (Nielsen and Chuang, 2000). The concept of a quantum computer was introduced by Feynman in 1982 (Feynman, 1982). Soon afterwards, a universal quantum computer was formulated by David Deutsch in 1989 using quantum gates, which he demonstrated could perform computations not possible with classic Turing machines, including generating genuine random numbers and performing parallel calculations within a single register. Subsequently, new quantum algorithms were discovered by Peter Schor in 1984 and Lov Grover in 1997 that could solve important computational problems, such as factoring and searching, faster than any known Turing machine. However, all of these accomplishments were designed for actual quantum computers, and only very small versions have been realized so far. Moreover, if we are not working under the assumption that the brain is a quantum computer, then what has all of this to do with information processing by humans?

The answer is that quantum information processing theory provides new and powerful principles for modelling human performance. Currently, there are three general approaches to modelling information processing with humans. One is based on production rule systems such as used in Act-R (Anderson, 1993), EPIC (Meyer & Kieres, 1997), and Soar (Laird et al., 1987); a second is neural network (Grossberg, 1982) and connectionist network (Rumelhart & McClelland, 1986) models; and a third is Bayesian models (Griffiths et al., 2008).