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A Limit on the Speed of Quantum Computation in Determining Parity

E. Farhi·J. Goldstone·S. Gutmann·M. Sipser
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Abstract

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

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E. Farhi, J. Goldstone, S. Gutmann, M. Sipser. 1998-10-08. A Limit on the Speed of Quantum Computation in Determining Parity. https://doi.org/10.1103/physrevlett.81.5442

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