Complexity Classes:
P: polynomial with no random classical computer
NP: polynomial verification, or, equivalently, there exists a randomized algorithm can try to find the answer with non-zero probability
NP-complete: hardest in NP
BPP: polynomial with random classical computer (BPP = P)
BQP: polynomial with random quantum computer
PP: quantum computer can get 0.5 + \gamma probability, but classical can get 0.5 + \gamma / 2^n probability.
Reduced QC: H, NOT, CNOT, 1QubitRot(pi/8)
is quantum-complete
If no H
: classic
If only NOT, CNOT, H
: classic
Classical Simulation: if there is a quantum decision problem
if QC: Pr\{1\} = \frac{1}{2} + q with -\frac{1}{2} \leq q \leq \frac{1}{2}
then classic: Pr\{1\} = \frac{1}{2} + \frac{q}{2^h} with h = \text{ number of H gates}
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