Decomposing the SWAP quantum gate
Yorick Hardy, W.‐H. Steeb · Journal of Physics A Mathematical and General · 2006
Quantum gates are represented by unitary operators on a Hilbert space. We consider the unitary operators on and describe the component operators on each Hilbert space in the product space. From these criteria we derive a decomposition for a specific class of unitary operators such that each operator in the product has Schmidt rank bounded by 2. This decomposition directly yields the XOR (controlled NOT) implementation of the SWAP operation.