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6 results

Quantum Models of Cognition and Decision
  • Principles and Applications
  • 2nd edition
  • Jerome R. Busemeyer, Peter D. Bruza
  • Published online:
    14 November 2024
    Print publication:
    21 November 2024
  • Quantum Models of Cognition and Decision, Second Edition presents a fully updated and expanded version of this innovative and path-breaking text. It offers an accessible introduction to the intersection of quantum theory and cognitive science, covering new insights, modelling techniques, and applications for understanding human cognition and decision making. In it, Busemeyer and Bruza delve into such topics as the non-commutative nature of judgments, quantum interference as a general principle governing human decision making, contextuality in modelling human cognition, and thought-provoking speculation about what a quantum approach to cognition might reveal about the ultimate nature of the human mind. Additions include new material on measurement, open systems, and applications to computer science. Requiring no prior background in quantum physics, this book comes complete with a tutorial and fully worked-out applications in important areas of cognition and decision.

  • 2 - Review of Quantum Mechanics for Quantum Computing

  • Shayan Majidy, Harvard University, Massachusetts, Christopher Wilson, University of Waterloo, Ontario, Raymond Laflamme, University of Waterloo, Ontario
  • Book:
    Building Quantum Computers
    Published online:
    29 November 2024
    Print publication:
    11 July 2024, pp 12-46

  • Summary

    Chapter 2 serves as a primer on quantum mechanics tailored for quantum computing. It reviews essential concepts such as quantum states, operators, superposition, entanglement, and the probabilistic nature of quantum measurements. This chapter focuses on two-level quantum systems (i.e. qubits). Mathematical formulations that are specific to quantum mechanics are introduced, such as Dirac (bra–ket) notation, the Bloch sphere, density matrices, and Kraus operators. This provides the reader with the necessary tools to understand quantum algorithms and the behaviour of quantum systems. The chapter concludes with a review of the quantum harmonic oscillator, a model to describe quantum systems that are complementary to qubits and used in some quantum computer implementations.

  • 14 - Transition Rules

  • from Part III - A Short Course in Quantum Field Theory
  • David W. Snoke, University of Pittsburgh
  • Book:
    Interpreting Quantum Mechanics
    Published online:
    09 May 2024
    Print publication:
    16 May 2024, pp 201-218

  • Summary

    This chapter surveys several different mathematical methods for time-dependent change of quantum states using quantum field theory. The Bloch sphere method is introduced, which can be used to show the physics discussed in Chapter 3, that electronic transitions, or “jumps,” are not instantaneous.