Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Effects of decoherence on diabatic errors in Majorana braiding   The braiding of two non-Abelian Majorana modes is important for realizing
topological quantum computation. It can be achieved through tuning the coupling
between the two Majorana modes to be exchanged and two ancillary Majorana
modes. However, this coupling also makes the braiding subject to
environment-induced decoherence. Here, we study the effects of decoherence on
the diabatic errors in the braiding process for a set of time-dependent
Hamiltonians with finite smoothness. To this end, we employ the master equation
to calculate the diabatic excitation population for three kinds of decoherence
processes. (1) Only pure dehasing: the scaling of the excitation population
changed from $T^{-2k-2}$ to $T^{-1}$ ($k$ is the number of the Hamiltonian's
time derivatives vanishing at the initial and final times) as the braiding
duration $T$ exceeds a certain value. (2) Only relaxation: the scaling
transforms from $T^{-2k-2}$ to $T^{-2}$ for $k=0$ and to $T^{-a}$ ($a>3$) for
$k>0$. (3) Pure dephasing and relaxation: the original scaling switches to
$T^{-1}$ firstly and then evolves to $T^{-2}$ in the adiabatic limit.
Interestingly, the third scaling-varying style holds even when the expectation
of pure dephasing rate is much smaller than that of the relaxation rate, which
is attributed to the vanishing relaxation at the turning points of the
braiding.

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The categories of this paper are: bayes-an
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The categories of this paper are: solv-int
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The categories of this paper are: nlin
2
The categories of this paper are: math
7
The categories of this paper are: hep-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: chem-ph
1
The categories of this paper are: cs
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The categories of this paper are: ao-sci
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The categories of this paper are: eess
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The categories of this paper are: cmp-lg
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The categories of this paper are: econ
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The categories of this paper are: stat
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The categories of this paper are: q-alg
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The categories of this paper are: dg-ga
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The categories of this paper are: astro-ph