Two-Qubit Gate Matrices
Just as the columns of a single-qubit gate matrix
correspond to the idealized states, the columns
of a matrix representing a two-qubit gate,
such as the Controlled NOT (CNOT) Gate,
correspond to the four idealized states—
,
, 
, and
— for two qubits:
The letters are complex numbers with the usual conjugates .
Each column ...
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