  This paper serves as a bridge between quantum computing and analogical
modeling (a general theory for predicting categories of behavior in varying
contexts). Since its formulation in the early 1980s, analogical modeling has
been successfully applied to a variety of problems in language. Several
striking similarities between quantum mechanics and analogical modeling have
recently been noted: (1) traditional statistics can be derived from a
non-statistical basis by assuming data occurrences are accessed through a
spin-up state (given two equally probable quantum states, spin-up and
spin-down); (2) the probability of predicting a particular outcome is
determined by the squaring of an underlying linear measure and is the result of
decoherence (which occurs when a quantum system is observed); and (3) a natural
measure of certainty (called the agreement) is based on one chance of guessing
the right outcome and corresponds to the integrated squaring of Schroedinger's
wave equation.
  Analogical modeling considers all possible combiantions of a given context of
n variables, which is classical terms leads to an exponential explosion on the
order of 2**n. This paper proposes a quantum computational solution to this
exponentiality by applying a cycle of reversible quantum operators to all 2**n
possibilities, thus reducing the time and space of analogical modeling to a
polynomial order.

Quantum Physics