This article is about the computational complexity class. For other uses, see BQP (disambiguation).
BQP in relation to other probabilistic complexity classes (ZPP, RP, co-RP, BPP, PP), which generalise P within PSPACE. It is unknown if any of these containments are strict.
In computational complexity theory, bounded-error quantum polynomial time (BQP) is 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.[1] It is the quantum analogue to the complexity class BPP.
A decision problem is a member of BQP if there exists a quantum algorithm (an algorithm that runs on a quantum computer) that solves the decision problem with high probability and is guaranteed to run in polynomial time. A run of the algorithm will correctly solve the decision problem with a probability of at least 2/3.
BQP algorithm (1 run)
Answer
produced
Correct answer
Yes
No
Yes
≥ 2/3
≤ 1/3
No
≤ 1/3
≥ 2/3
BQP algorithm (k runs)
Answer
produced
Correct answer
Yes
No
Yes
> 1 − 2−ck
< 2−ck
No
< 2−ck
> 1 − 2−ck
for some constant c > 0
^Michael Nielsen and Isaac Chuang (2000). Quantum Computation and Quantum Information. Cambridge: Cambridge University Press. ISBN 0-521-63503-9.
computational complexity theory, bounded-error quantum polynomial time (BQP) is the class of decision problems solvable by a quantum computer in polynomial...
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classes are defined using quantum Turing machines, including the classes BQP and QMA These are explained in greater detail below. A number of important...
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