BQP computational complexity theory BQP stands for Bounded error, Quantum, Polynomial time. It denotes the class of decision problems solvable by a quantum computer in polynomial time, with an error probability of at most 1/3 for all instances. In other words, there is an algorithm for a quantum computer that solves the decision problem with high probability and is guaranteed to run in polynomial time. On any given run of the algorithm, it has a probability of at most 1/3 that it will give the wrong answer.