problems BQP quantum Turing machine BPP probabilistic Turing machines time complexity Turing machine polynomial time computer
The class of problems that can be efficiently solved by a quantum computer with bounded error is called BQP, for "bounded error, quantum, polynomial time". More formally, BQP is the class of problems that can be solved by a polynomial-time quantum Turing machine with an error probability of at most 1/3. As a class of probabilistic problems, BQP is the quantum counterpart to BPP ("bounded error, probabilistic, polynomial time"), the class of problems that can be solved by polynomial-time probabilistic Turing machines with bounded error. It is known that 





B
P
P
⊆
B
Q
P




{\displaystyle {\mathsf {BPP\subseteq BQP}}}

 and is widely suspected that 





B
Q
P
⊊
B
P
P




{\displaystyle {\mathsf {BQP\subsetneq BPP}}}

, which intuitively would mean that quantum computers are more powerful than classical computers in terms of time complexity.
