Abstract |
Quantum computation generalizes the classical model of machine computation
(a la Turing). The computational process which classically is the
sequential action of logical gates on a bit string in {0,1}N is
replaced by a unitary transformation acting on a set of quantum bits
described by a vector in the tensor product of N copies of the
two-dimensional complex Hilbert space. There is good evidence that quantum
computation is significantly more powerful than the classical model.
An important implication, worked out in a sequence of works by several
authors in recent years, is that estimating the extremal eigenvalue of a
Hermitian matrix is a universal problem for all "reasonable"
computational problems, classical or quantum. We will explain this
connection and discuss some related recent work on the ground state problem
of quantum spin systems.
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