Use of quantum encoders and quantum decoding for implementing the CNOT gate

摘要

A now method based on quantum encoders is developed for implementing quantum computational gates, especially the CNOT gate. Photonic qubits are used where vertical bar 0 > and vertical bar 1 > represent horizontal vertical bar H > and vertical vertical bar 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 x 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. (C) 2008 Optical Society of America