Braiding properties of Majorana Kramers pairs
نویسندگان
چکیده
We consider the braiding of Kramers pairs of Majorana bound states. We derive the most general transformation on the many-body ground state that is applied as the result of such a braiding process. The result is derived in the context of a toy model, but we will show that it has the most general form that is compatible with local and global conservation of electron parity. In accordance with earlier work, the resulting transformation turns out to be path dependent, which shows that Kramers pairs of Majorana bound states cannot be used for topological quantum computation. We also discuss under which conditions the result is path independent and corresponds to two independent exchanges of pairs of Majorana bound states.
منابع مشابه
Local adiabatic mixing of Kramers pairs of Majorana bound states.
We consider Kramers pairs of Majorana bound states under adiabatic time evolution. This is important for the prospects of using such bound states as parity qubits. We show that local adiabatic perturbations can cause a rotation in the space spanned by the Kramers pair. Hence, the quantum information is unprotected against local perturbations, in contrast to the case of single localized Majorana...
متن کاملMonte Carlo studies of the self-correcting properties of the Majorana quantum error correction code under braiding
The Majorana code is an example of a stabilizer code where the quantum information is stored in a system supporting well-separated Majorana bound states (MBSs). We focus on one-dimensional realizations of the Majorana code, as well as networks of such structures, and investigate their lifetime when coupled to a paritypreserving thermal environment. We apply the Davies prescription, a standard m...
متن کاملDetection of Majorana Kramers Pairs Using a Quantum Point Contact.
We propose a setup that integrates a quantum point contact (QPC) and a Josephson junction on a quantum spin Hall sample, experimentally realizable in InAs/GaSb quantum wells. The confinement due to both the QPC and the superconductor results in a Kramers pair of Majorana zero-energy bound states when the superconducting phases in the two arms differ by an odd multiple of π across the Josephson ...
متن کاملKramers pairs of Majorana fermions and parafermions in fractional topological insulators
We propose a scheme based on topological insulators to generate Kramers pairs of Majorana fermions or parafermions in the complete absence of magnetic fields. Our setup consists of two topological insulators whose edge states are brought close to an s-wave superconductor. The resulting proximity effect leads to an interplay between a nonlocal crossed Andreev pairing, which is dominant in the st...
متن کاملMajorana Braiding with Thermal Noise.
We investigate the self-correcting properties of a network of Majorana wires, in the form of a trijunction, in contact with a parity-preserving thermal environment. As opposed to the case where Majorana bound states are immobile, braiding Majorana bound states within a trijunction introduces dangerous error processes that we identify. Such errors prevent the lifetime of the memory from increasi...
متن کامل