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Precise relationship between BQP and NP

Ascertain the exact inclusion relationship between the complexity classes BQP and NP, determining whether NP is contained in BQP, BQP is contained in NP, or neither inclusion holds.

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Background

After reviewing classical and quantum complexity classes (BPP and BQP), the authors highlight uncertainty about how BQP relates to NP. They note indications for possible inclusions in either direction but emphasize that the question remains unresolved.

Resolving the relationship between BQP and NP is foundational for understanding the power of quantum computation relative to classical complexity theory.

References

The question of BQP and its relation to NP is a matter that is more difficult. There are indications that perhaps NP is contained in BQP, as there are results for the opposite being true--this then still represents a question that is an issue in science and is considered unresolved.

— On the Theory of Quantum and Towards Practical Computation (2403.09682 - Kudelić, 7 Feb 2024) in Section Questions that Puzzle the Mind