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It has been impossible to make a quantum computer with only these unitary ‘single bit’ operations yet ( about 2003 ).
Furthermore, it’s equal to this subject in importance to perform ‘two-bit’ quantum operation ( or to control the unitary e-volution of entangled states ).
Thus, both one & two-qubit gates are needed to build an universal quantum computer.
An example for an universal two-qubit gate is the controlled-NOT operation :
|00〉→ |00〉; |01〉→ |01〉; |10〉→ |11〉; |11〉→ |10〉
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