ABSTRACT - DRUM - University of Maryland

a a †
1 2
Figure 5.2: Schematic illustration of the topological qubit coupled to thermal bath,
modeled by a collection of harmonic oscillators.
Then the polarization of the qubit 〈σ z 〉 = Tr[σ z ˆρ r ] satisfies d t 〈σ z 〉 = −2λ〈σ z 〉.
Therefore the lifetime of the topological qubit is given by T 1 ∼ λ −1 . Physically,
this is reasonable since we introduce tunneling term between the Majorana fermion
and the gapped fermionic environment so the fermion parity of the qubit is no
longer conserved.
It is expected that λ is determined by the exponential factor
e −∆/T when T ≪ ∆. Therefore, this provides a quantitative calibration of the
protection of the topological qubit at finite temperature. In the high-temperature
limit T ≫ ∆, the distribution function scales linearly with T so the decay rate is
proportional to T .
This is quite expected since T ≫ ∆, the gap does not play
a role. We note that a recent work by Goldstein and Chamon [110] studying the
decay rate of Majorana zero modes coupled to classical noise essentially corresponds
to the high-temperature limit of our calculation T ≫ ∆ and, as such, does not
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