A Limit on the Speed of Quantum Computation in Determining Parity
Quantum Physics
2009-01-23 v2
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.
Cite
@article{arxiv.quant-ph/9802045,
title = {A Limit on the Speed of Quantum Computation in Determining Parity},
author = {E. Farhi and J. Goldstone and S. Gutmann and M. Sipser},
journal= {arXiv preprint arXiv:quant-ph/9802045},
year = {2009}
}
Comments
9 pages, latex