Quantum Measurement Of Majorana Qubit And Zero Modes

Majorana fermions satisfy non-Abelian statistics and have non-local topological protection.As a consequence,majorana feimions have important application value in fault-tolerant topological quantum computing.In recent years,Majorana zero mode(MZM)could realizied by the field of condensed matter.Therefore the detection of the existence of Majorana zero mode and the research on Majorana qubits have attracted wide attention.This thesis focus on the study of quantum measurement of Majorana qubit and zero modes by a quantum point contact(QPC).For the quantum measurement of Majorana qubits,in terms of the coupled quantum dot(QD),the information of Majorana qubits can be converted into QD-MZM combined parity.The information of the parity can be obtained by the dot occupation number,steady-state current and noise spectrum.The results show that both the dot occupation number only and current can distinguish parity at small voltage.The noise spectrum including the shot noise can distinguish parity both at large voltage and small voltage.The signal characteristics of the noise spectrum are more sensitive to parity than those of the dot occupation number and the steady-state current.We investigate the quantum transport in a ring system composed of a quantum dot coupled to the Majorana zero modes.There is a phase tuned by the applied magnetic flux inside the ring.By measuring the conductance and noise spectrum,we find that the conductance is insensitive to the phase regardless of the QD-MZMs coupling strength.However,the noise spectrum is strong dependent on the phase with both weak and strong couplings.The location and height of the peaks in the noise spectrum are sensitive to the phase,especially for weak coupling.The underlying physical mechanism is also discussed.