Decoherence patterns of topological qubits from Majorana modes

Abstract

We investigate the decoherence patterns of topological qubits in contact with the environment using a novel way of deriving the open system dynamics, rather than using the Feynman-Vernon approach. Each topological qubit is made up of two Majorana modes of a 1D Kitaev chain. These two Majorana modes interact with the environment in an incoherent way which yields peculiar decoherence patterns of the topological qubit. More specifically, we consider the open system dynamics of topological qubits which are weakly coupled to fermionic/bosonic Ohmic-like environments. We find atypical patterns of quantum decoherence. In contrast to the case for non-topological qubits-which always decohere completely in all Ohmic-like environments-topological qubits decohere completely in Ohmic and sub-Ohmic environments but not in super-Ohmic ones. Moreover, we find that the fermion parities of the topological qubits, though they cannot prevent the qubit states from exhibiting decoherence in sub-Ohmic environments, can prevent thermalization turning the state into a Gibbs state. We also study the cases in which each Majorana mode can couple to different Ohmic-like environments, and the time dependence of concurrence for two topological qubits.

Error generation and propagation in Majorana-based topological qubits

“…There is a range of problematic processes that potentially limit the effectiveness of topological quantum memories. The majority of these [30][31][32][33][34][35][36][37][38][39][40] concern the inevitable interaction with an external environment. However research in this area has also focused on errors due to changes of the internal system parameters over a finite time, e.g., due to fluctuations in the underlying gate potentials 41 , thermal noise 42 , or the deliberate shuttling of Majorana-Bound-States (MBS) around a network [43][44][45][46][47][48][49][50][51] .…”

Decoherence of topological qubit in linear and circular motions: decoherence impedance, anti-Unruh and information backflow

“…In [32] the topological qubits made of pairs of Majorana modes have been introduced and their decoherence dynamics were then studied. A novel feature for these peculiar qubits is their robustness against quantum decoherence in the super-Ohmic environments.…”

“…The derivation of (2.5) and (2.6) has been sketched in [32], which involves the evaluation of the cosh/sinh correlators cosh O i (t) cosh O i (t) and sinh O i (t) sinh O i (t) . However, a not so rigorous procedure of re-exponentiation of O i (t)O i (t) is invoked to obtain the cosh/sinh correlators.…”

“…The exact reduced dynamics for such (static) topological qubits has been obtained without solving the master equation in [31,32]. The solvability of the reduced dynamics for the topological qubit is due to the spatial separation of the constituent Majorana zero modes so that the influence functional is further restricted by the additional locality constraint which is absent for the usual qubit.…”

“…This paper is organized as follows: in the next section we will briefly review the formulation of the topological qubit and its the reduced dynamics developed in [32]. In the section 3 we develop the formalism to study the reduced dynamics for a moving topological qubit by generalizing the one given in [23] for the usual UDW detector.…”