ABSTRACT - DRUM - University of Maryland

Chapter 5
Topological Protection of Majorana-Based Qubits
In this chapter we investigate the effect of finite-temperature thermal fluctuations
on three key aspects of topological quantum computation: quantum coherence
of the topological qubits, topologically-protected quantum gates and the read-out
of qubits. Since the information is encoded in non-local degrees of freedom of the
ground state many-body wavefunction, it is important to keep the system close to
the ground state. However, any systems realized in the laboratory are operated at
a finite temperature T > 0. To prevent uncontrollable thermal excitations, it is
generally accepted that T has to be way below the bulk excitation gap. However,
complications appear when there exist various types of single-particle excitations
with different magnitudes of gaps which can change the occupation of the nonlocal
fermionic modes. Note that throughout the chapter we assume that Majorana
fermions are sufficiently far away from each other and neglect exponentially small
energy splitting due to inter-vortex tunneling. The effect of these processes on topological
quantum computing has been discussed elsewhere [91, 106]. Another trivial
effect not considered in this work is a situation where the fermion parity conservation
is explicitly broken by the Majorana mode being in direct contact with a
bath of fermions (electrons and holes) where obviously the Majorana will decay into
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