ON-LINE PhD Defense: Morten Ib Kjærgaard Munk

Majorana bound states: Readout, decoherence and generalizations

The study of topological phases has become one of the most active areas of the field of condensed matter physics. In the last decade, there has been immense experimental progress, owing to quantum leaps in materials science and the theoretical understanding of these systems. A remarkable example of topological phases is topological superconductors. These unusual superconductors are believed to host exotic Majorana quasiparticles whose underlying physics epitomizes the concept of ''spooky action at a distance'' in quantum mechanics: Moving them around one another can change the occupation of fermionic modes. In fact, by braiding them in a complicated fashion, most of the gates necessary for building a quantum computer may be implemented. Furthermore, since quantum information is stored in non-local degrees of freedom, qubits based on Majoranas are believed to be inherently resilient to noise. Along with other promising future applications, this motivates the need for a better understanding of Majorana quasiparticles, which is the overarching theme of this PhD dissertation. The original contributions in the thesis are contained in four projects.

Project A tackles the problem of reading out the state of a Majorana box qubit, a minimal qubit where quantum information is stored in Majorana bound states. By using a novel Lindbladian approximation, we develop a Markovian theory of the dynamics of the reduced density matrix of a Majorana box qubit whose parity degrees of freedom has been converted to charge through the coupling of a quantum dot. 

In Project B, we calculate the dephasing dynamics of an isolated Majorana box qubit subjected to electromagnetic fluctuations in a capacitively coupled electric circuit. These fluctuations are treated as classically oscillating fields, allowing for an intuitive picture of the dephasing as accrued non-adiabatic corrections to the time evolution due to the shifting of the Majorana zero-energy mode.

The problem of dephasing of Majorana qubits due to electromagnetic noise is refined in Project C, where we develop a model using a Bloch-Redfield approach, thus keeping the quantum mechanical nature of the environment modes. This allows us to go to low temperatures, and we find a potential source of fidelity loss in Majorana parity readouts persisting at low temperatures, stemming from the fact that the zero-energy modes are dressed by the bosons, while the readout apparatus measures the bare Majorana modes.

Finally, in project D we propose a model which generalizes Majorana zero-energy modes. It is constructed by starting from a bosonic model analogous to the Ising model, except where the local degrees of freedom and the global gauge symmetry are related to an arbitrary finite non-abelian group. By constructing a generalized Jordan-Wigner transformation, we map the model onto a local model with dyonic degrees of freedom, meaning that they carry both a ''magnetic charge'' in the form of a group element index, as well as an ''electric charge'' corresponding to an irreducible representation of the group. We find that the model generically has a topological phase with zero-energy dyonic edge modes.