PostBQP = PP
Scott Aaronson showed that the complexity classes PostBQP (postselected bounded error quantum polynomial time) and PP (probabilistic polynomial time) are equal. The result was significant because this quantum computation reformulation of PP gave new insight and simpler proofs of properties of PP.
The usual definition of a PostBQP circuit family is one with two outbit qubits P (postselection) and Q (output) with a single measurement of P and Q at the end such that the probability of measuring P = 1 has nonzero probability, the conditional probability Pr ≥ 2/3 if the input x is in the language, and Pr ≥ 2/3 if the input x is not in the language. For technical reasons we tweak the definition of PostBQP as follows: we require that Pr ≥ 2−nc for some constant c depending on the circuit family. Note this choice does not affect the basic properties of PostBQP, and also it can be shown that any computation consisting of typical gates (e.g. Hadamard, Toffoli) has this property whenever Pr > 0.
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