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Bulletin of the American Physical Society

Decoherence Patterns of Topological Qubits from Majorana Modes

Sung Po Chao, Shih Hao Ho, Chung Hsien Chou, Feng-Li Lin

Published Mar 2, 2015• 0 citations
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Decoherence patterns of topological qubits from Majorana modes

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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.

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In this paper, we consider the decoherence patterns of a topological qubit made of two Majorana zero modes in the generic linear and circular motions in the Minkowski spacetime. We show that the reduced dynamics is exact without Markov approximation. Our results imply that the acceleration will cause thermalization as expected by Unruh effect. However, for the short-time scale, we find the rate of decoherence is anti-correlated with the acceleration, as kind of decoherence impedance. This is in fact related to the “anti-Unruh” phenomenon previously found by studying the transition probability of Unruh-DeWitt detector. We also obtain the information backflow by some time modulations of coupling constant or acceleration, which is a characteristic of the underlying non-Markovian reduced dynamics. Moreover, by exploiting the nonlocal nature of the topological qubit, we find that some incoherent accelerations of the constituent Majorana zero modes can preserve the coherence instead of thermalizing it.

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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.
In this work we study the decoherence of topological qubits in linear motions. The topological qubit is made of two spatially-separated Majorana zero modes which are the edge excitations of Kitaev chain [1]. In a previous work [2], it was shown by one of us and his collaborators that the decoherence of topological qubit is exactly solvable, moreover, topological qubit is robust against decoherence in the super-Ohmic environments. We extend the setup of [2] to consider the effect of motions on the decoherence of the topological qubits. Our results show the thermalization as expected by Unruh effect. Besides, we also find the so-called "anti-Unruh" phenomena which shows the rate of decoherence is anti-correlated with the acceleration in short-time scale. Moreover, we modulate the motion patterns of each Majorana modes and find information backflow and the preservation of coherence even with nonzero accelerations. This is the characteristics of the underlying non-Markovian reduced dynamics. We conclude that he topological qubit is in general more robust against decoherence than the usual qubits, and can be take into serious consideration for realistic implementation to have robust quantum computation and communication. This talk is based on our work in [3].
In this paper, we consider the decoherence patterns of a topological qubit made of two Majorana zero modes in the generic linear and circular motions in the Minkowski spacetime. We show that the reduced dynamics is exact without Markov approximation. Our results imply that the acceleration will cause thermalization as expected by Unruh effect. However, for the short-time scale, we find the rate of decoherence is anti-correlated with the acceleration, as kind of decoherence impedance. This is in fact related to the “anti-Unruh” phenomenon previously found by studying the transition probability of Unruh-DeWitt detector. We also obtain the information backflow by some time modulations of coupling constant or acceleration, which is a characteristic of the underlying non-Markovian reduced dynamics. Moreover, by exploiting the nonlocal nature of the topological qubit, we find that some incoherent accelerations of the constituent Majorana zero modes can preserve the coherence instead of thermalizing it.