CONTROLLED NOT GATE BASED ON A TWO-LAYER SYSTEM OF THE FRACTIONAL QUANTUM HALL EFFECT

After a coordinate transformation, the wavefunction of the ground state of the fractional Quantum Hall Eect is found to be the congregation of free independent particles immune to thermal phonon disturbance. Based on the pseudo-spin states appearing in the two layer system of fractional Quantum Hall Eect, we propose a new controlled NOT gate with very large decoherence time. Recently, quantum computing has been attracting the attention of many researchers. Many quantum computing devices have been proposed. 1 The main difculty in practical operation of most of those devices is the existence of strong decoherence which causes error in the computing procedure. The eect appears as the decrease in the nondiagonal terms of the density matrix of the initial pure state through the interaction between the state and environment, which results in the decrease in interference. In this paper, we point out that (i) the wavefunction representing the quantum state of the fractional Quantum Hall Eect (FQHE) 2;3 is found, after appropriate coordinate transformation, to be the congregation of independent \free particles" with no particle{particle interaction, (ii) the decoherence time D of the \free particle" state is expected eectively to be innity due to ignorable thermal phonon disturbance, and (iii) the macroscopic quantum nature with particle-number deniteness (N t 0) of FQHE has excellent adaptability to the qubit device using particle number change in comparison with the superconductor device where the macroscopic quantum nature has phase deniteness ( t 0). These properties reveal the possibility that FQHE provides ideal quantum computing devices having particle quantum states with D!1.