Masters Defense: Morten Munk-Nielsen

Dephasing of Majorana box qubits.

The Majorana box qubit is an exciting proposal for realising a qubit using Majorana bound states. Majorana bound states are delocalised over potentially big distances, and for that reason the box qubit is expected to have a long coherence time in the face of local noise. As of yet there has been no concrete study of how long the coherence time is.
After a review of Majorana physics and in particular the box qubit, the main work in this thesis is to provide the study of this. This is done modelling the noisy environment as a capacitative coupling from box qubit to an environment impedance, resulting in a fluctuating potential. It is then demonstrated that these fluctuations lead to decoherence of the box qubit. The main result is an expression for the instantaneous Majorana propagator, the decay of which is shown to be a measure of information loss in the system. For systems where the gap energy in the Majorana system is much larger than the characteristic energy scale in the electric circuit we find an expression for the dephasing rate of the qubit, which suggests long life time for the qubit.