Quantum computing and polynomial equations over Z_2
C. Dawson, Henry L. Haselgrove, Andrew P. Hines, Duncan Mortimer, Morten Nielsen, Tobias J. Osborne · Quantum Information and Computation · 2005
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, namely BQP/P/\#P and BQP/PP.