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
        }
}
  • Barenco, Bennett, Weinfurter
  • Published 23 March 1995
  • Mathematics
  • Physical review. A, Atomic, molecular, and optical physics
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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