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The Representation of Numbers by States in Quantum Mechanics

  • Paul Benioff

Abstract

The representation of numbers by tensor product states of composite quantum systems is examined. Consideration is limitedto k — ary representations of length L and arithmetic mod K L An abstract representation on an L fold tensor product Hilbert space H arith of number states and operators for the basic arithmetic operation is described. Unitary maps onto a physical parameter based tensor product space H phy are defined and the relations between these two spaces and the dependence of algorithm dynamics on the unitary maps is discussed. The important condition of efficient implementation by physically realizable Hamiltonians of the basic arithmetic operations is also discussed.

Keywords:

Number representation quantum states quantum computers 

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Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • Paul Benioff
    • 1
  1. 1.Physics DivisionArgonne National LaboratoryArgonne

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