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Class BQP stands for Bounded-Error Quantum Polynomial-Time. They are the class of decision problems solvable in polynomial time by a quantum Turing machine, with at most 1/3 probability of error.
NP is class of decision problems which are solvable on a non-deterministic Turing machine in polynomial time.
Relation between BQP and NP: Of course, unless P vs NP problem gets resolves, we won’t be able to give exact relationship between these two classes. But, it is known that P⊆BQP and it is conjectured that NP-complete problems like Traveling Salesman problem can’t be solved in polynomial time with bounded-error even on quantum computers.
The relationship between NP and BPP is unknown. All we know is that BPP⊆PNP . The exact relationship among these classes remain an open problem for now.
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Answer:
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