  This paper combines quantum computation with classical neural network theory
to produce a quantum computational learning algorithm. Quantum computation uses
microscopic quantum level effects to perform computational tasks and has
produced results that in some cases are exponentially faster than their
classical counterparts. The unique characteristics of quantum theory may also
be used to create a quantum associative memory with a capacity exponential in
the number of neurons. This paper combines two quantum computational algorithms
to produce such a quantum associative memory. The result is an exponential
increase in the capacity of the memory when compared to traditional associative
memories such as the Hopfield network. The paper covers necessary high-level
quantum mechanical and quantum computational ideas and introduces a quantum
associative memory. Theoretical analysis proves the utility of the memory, and
it is noted that a small version should be physically realizable in the near
future.
