Symmetry-protected non-Abelian braiding of Majorana Kramers' pairs

TL;DR

This paper develops a comprehensive theory for the non-Abelian braiding of Majorana Kramers' pairs in time-reversal invariant topological superconductors, highlighting symmetry protections against noise and decoherence for quantum computing.

Contribution

It introduces an effective Hamiltonian framework and reveals new symmetry protections for MKP braiding, including robustness against certain dynamical noises.

Findings

Braiding is protected by a TR-like symmetry in the effective Hamiltonian.

Dynamical noise does not cause errors unless it breaks a specific TR symmetry.

Error effects from noise are higher order compared to decoherence in non-TR protected Majorana qubits.

Abstract

We develop the complete theory for non-Abelian braiding of Majorana Kramers' pairs (MKPs) in time-reversal (TR) invariant topological superconductors. By introducing an effective Hamiltonian approach to describe the braiding of MKPs, we show that the non-Abelian braiding is protected when the effective Hamiltonian exhibits a new TR like anti-unitary symmetry, which is satisfied if the system is free of dynamical noise. Importantly, even the dynamical noise may not cause error in braiding, unless the noise correlation function breaks a dynamical TR symmetry, which generalizes the TR symmetry protection of MKPs to dynamical regime. Moreover, the resulted error by noise is shown to be a higher order effect, compared with the decoherence of Majorana qubits without TR symmetry protection. These results show that the non-Abelian braiding of MKPs is observable and may have versatile applications to future quantum computation technologies.