# Elementary gates for quantum computation.

@article{Barenco1995ElementaryGF, title={Elementary gates for quantum computation.}, author={Barenco and Bennett and Cleve and DiVincenzo and Margolus and Shor and Sleator and Smolin and Weinfurter}, journal={Physical review. A, Atomic, molecular, and optical physics}, year={1995}, volume={52 5}, pages={ 3457-3467 } }

We show that a set of gates that consists of all one-bit quantum gates (U(2)) and the two-bit exclusive-or gate (that maps Boolean values (x,y) to (x,x ⊕y)) is universal in the sense that all unitary operations on arbitrarily many bits n (U(2 n )) can be expressed as compositions of these gates. We investigate the number of the above gates required to implement other gates, such as generalized Deutsch-Toffoli gates, that apply a specific U(2) transformation to one input bit if and only if the…

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