Use of quantum encoders and quantum decoding for implementing the CNOT gate
Y. Ben-Aryeh · Journal of the Optical Society of America B · 2008
A new method based on quantum encoders is developed for implementing quantum computational gates, especially the CNOT gate. Photonic qubits are used where ∣0> and ∣1> represent horizontal ∣H> and vertical ∣V> polarized photons, respectively. By the use of polarizing beam splitters (PBSs) and entangled two-photon states in a certain experimental scheme, each input qubit state is copied, with a certain probability of success, into four equivalent input qubit states. The present method concentrates on the special case where the initial two-qubit state is separable. The CNOT gate (multiplied by 2) is decomposed into a summation of four unitary matrices each of dimension 4×4 and where each of these unitary matrices operates on a corresponding copy of the input two-qubit state. By adding the amplitudes of the four two-qubit states, which is obtained in a decoding interference experiment, the CNOT gate is implemented.