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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 Z₂. 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.
Dawson et al. (Sun,) studied this question.