Concept# BQP

Summary

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. 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.
Definition
BQP can be viewed as the languages associated with certain bounded-error uniform families of quantum circuits. A language L is in BQP if and only if there exists a polynomial-time uniform family of quantum circuits {Q_n\colon n \in \mathbb{N}}, such that

- For all n \in \mathbb{N}, Qn takes n qubits as input and output

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