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Quantum computing and polynomial equations over the finite field Z_2

Christopher M. Dawson·Henry L. Haselgrove·Andrew P. Hines·Duncan Mortimer·Michael A. Nielsen·Tobias J. Osborne
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Abstract

What is the computational power of a quantum computer? We show that determining the output of a quantum computation is equivalent to counting the number of solutions to an easily computed set of polynomials defined over the finite field Z_2. This connection allows simple proofs to be given for two known relationships between quantum and classical complexity classes.

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Christopher M. Dawson, Henry L. Haselgrove, Andrew P. Hines, Duncan Mortimer, Michael A. Nielsen, Tobias J. Osborne. 2004-08-20. Quantum computing and polynomial equations over the finite field Z_2. https://arxiv.org/abs/quant-ph/0408129

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