Xion-Jun Liu (Peking University): Symmetry-Protected Non-Abelian Braiding of Majorana Kramers' Pairs
Topological superconductors, which host Majorana zero modes, are a most attractive research topic in condensed matter physics. Due to the Kramers theorem, in a time-reversal invariant topological superconductor the Majorana modes come in pairs, called Majorana Kramer pairs (MKPs). The recent study showed that, due to the time-reversal symmetry protection, the MKPs may obey non-Abelian braiding statistics, while it was later suggested that local rotation among a single MKP may cause errors in MKP-based qubits. In the work presented in this talk, I shall show the complete symmetry condition for non-Abelian braiding of MKPs. By introducing an effective Hamiltonian approach to describe the braiding of MKPs, we show that the ideal non Abelian braiding is protected when the effective Hamiltonian exhibits a new time-reversal like anti-unitary symmetry, which is satisfied if the system is free of dynamical noise. On the other hand, the presence of dynamical noise may bring about decoherence only when the correlation function of such noise breaks the time-reversal like symmetry in the time domain. Interestingly, the resulted error is found to be a higher order effect, compared with the decoherence of Majorana qubits without time-reversal symmetry protection, caused by the dynamical perturbations. These results show that the non-Abelian braiding of MKPs is observable and may have versatile applications to future quantum computation technologies.