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Consider a function f which is defined on the integers from 1 to N and takesthe values -1 and +1. The parity of f is the product over all x from 1 to N off(x). With no further information about f, to classically determine the parityof f requires N calls of the function f. We show that any quantum algorithmcapable of determining the parity of f contains at least N/2 applications ofthe unitary operator which evaluates f. Thus for this problem, quantumcomputers cannot outperform classical computers.Comment: 9 pages, late

Limit on the Speed of Quantum Computation in Determining Parity