When is a product of finite order qubit gates of infinite order?
Katarzyna Karnas, Adam Sawicki · Journal of Physics A Mathematical and Theoretical · 2017
Abstract We consider a product of two finite order quantum S U ( 2 ) -gates U 1 , U 2 and ask when U 1 ⋅ U 2 has an infinite order. Using the fact that S U ( 2 ) is a double cover of S O ( 3 ) we actually study the product O ( γ , k → 12 ) of two rotations O ( ϕ , k → 1 ) ∈ S O ( 3 ) and O ( ϕ , k → 2 ) ∈ S O ( 3 ) about axes k → 1 , k → 2 ∈ R 3 . In particular, we focus on the case when k