In 1994 Peter Shor [65] published a factoring algorithm for a
quantum computer that finds the prime factors of a composite
integer N more efficiently than is possible with the known
algorithms for a classical com puter. Since the difficulty of the
factoring problem is crucial for the se curity of a public key
encryption system, interest (and funding) in quan tum computing and
quantum computation suddenly blossomed. Quan tum computing had
arrived. The study of the role of quantum mechanics in the theory
of computa tion seems to have begun in the early 1980s with the
publications of Paul Benioff [6]' [7] who considered a quantum
mechanical model of computers and the computation process. A
related question was discussed shortly thereafter by Richard
Feynman [35] who began from a different perspec tive by asking what
kind of computer should be used to simulate physics. His analysis
led him to the belief that with a suitable class of "quantum
machines" one could imitate any quantum system.
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