Generalized commutative gates and applications
Qin Liu · Journal of Northwest University · 2010
Aim To establish the relationship between generalized controlled-NOT gates U(k,l)CN and U(l,k)CN.Methods Using some methods of operator theory.Results Generalized commutative gates C(k,l)n are introduced so as to exchange the kth quantum bit and lth quantum bit,a calculation formula is given.Conclusion A relationship between generalized controlled-NOT gates U(k,l)CN and U(l,k)CN is established,and the matrix representations of related gates are obtained.