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In computer science, the controlled NOT gate is a quantum logic gate that is an essential component in the construction of a gate-based quantum computer. It can be used to entangle and disentangle Bell states. Any quantum circuit can be simulated to an arbitrary degree of accuracy using a combination of CNOT gates and single qubit rotations.
The CNOT can be expressed in the Pauli basis as:
Being both unitary and Hermitian, CNOT has the property e i θ U = I + U {\displaystyle e^{i\theta U}=I+U} and U = e i π 2 = e − i π 2 {\displaystyle U=e^{i{\frac {\pi }{2}}}=e^{-i{\frac {\pi }{2}}}} , and is involutory.
The CNOT gate can be further decomposed as products of rotation operator gates and exactly one Ising coupling gate , for example