Tunable fermionic error correction

Majorana-based qubits are promising candidates for realizing topological quantum computers. Developing experimentally feasible schemes for quantum error correction for such qubits is necessary for achieving scalability. In this work, we show that the ground states of the Kitaev chain Hamiltonian, for any parameter values in the topological phase, form an approximate error-correcting code that corrects local fermionic parity-preserving errors. We also show, numerically, that this code has storage time exponentially large in the system size if the errors are caused only due to weak disorder in the system. The stabilizers for our code are constructed using Wannier functions of the modes of the clean system. We analytically prove the exponential localization of such Wannier functions under semi-open boundary conditions. Our work shows that the adverse effects of disorder on the lifetime of Majorana qubits can be alleviated by tuning the stabilizers with respect to the parameters of the clean system.