Journal of Physics Conference Series

Decoherence of Topological Qubit in Linear Motions: Decoherence Impedance, Anti-Unruh and Information Backflow

Pei-Hua Liu, Feng-Li Lin

Published Aug 1, 2017• 0 citations

Abstract

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].

DOI: 10.1088/1742-6596/883/1/012012

Related papers

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

Pei-Hua Liu, Feng-Li Lin

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.

arXiv:1603.05136Journal of High Energy PhysicsJul 1, 201610 citations

Decoherence patterns of topological qubits from Majorana modes

Shih-Hao Ho, Sung-Po Chao, Chung-Hsien Chou +1 more

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.

arXiv:1406.6249New Journal of PhysicsNov 24, 201425 citations

Four-Majorana qubit with charge readout: Dynamics and decoherence

Tommy Li, W. A. Coish, Michael Hell +2 more

We present a theoretical analysis of a Majorana-based qubit consisting of two topological superconducting islands connected via a Josephson junction. The qubit is operated by electrostatic gates which control the coupling of two of the four Majorana zero modes. At the end of the operation, readout is performed in the charge basis. Even though the operations are not topologically protected, the proposed experiment can potentially shed light on the coherence of the parity degree of freedom in Majorana devices and serve as a first step towards topological Majorana qubits. We discuss in detail the charge-stability diagram and its use for characterizing the parameters of the devices, including the overlap of the Majorana edge states. We describe the multilevel spectral properties of the system and present a detailed study of its controlled coherent oscillations, as well as decoherence resulting from coupling to a non-Markovian environment. In particular, we study a gate-controlled protocol where conversion between Coulomb-blockade and transmon regimes generates coherent oscillations of the qubit state due to the overlap of Majorana modes. We show that, in addition to fluctuations of the Majorana coupling, considerable measurement errors may be accumulated during the conversion intervals when electrostatic fluctuations in the superconducting islands are present. These results are also relevant for several proposed implementations of topological qubits which rely on readout based on charge detection.

arXiv:1807.05839Physical review. B./Physical review. BNov 5, 201825 citations

Decoherence dynamics of Majorana qubits under braiding operations

Hon-Lam Lai, Wei-Min Zhang

We study the decoherence dynamics of Majorana qubit braiding operations in a T-junction topological superconducting chain (TSC) system, in which the braiding is performed by controlling the electron-chemical potentials of the TSCs and the couplings between them. By solving rigorously the Majorana qubit dynamics, we show how the Majorana qubit coherence is generated through Bogoliubon correlations formed by exchanging Majorana zero modes (MZMs) between two TSCs in braiding operations. We also demonstrate with the exact master equation how MZMs and also the Bogoliubon correlations dissipate due to charge fluctuations of the controlling gates at both the zero and finite temperatures. As a result, Majorana qubit coherence and also the fermion parity conservation cannot be immune from local perturbations during braiding operations.

arXiv:1909.13056Physical review. B./Physical review. BMay 18, 202012 citations

Topological Protection and Control of Quantum Markovianity

Gian Luca Giorgi, Salvatore Lorenzo, Stefano Longhi

Under the Born–Markov approximation, a qubit system, such as a two-level atom, is known to undergo a memoryless decay of quantum coherence or excitation when weakly coupled to a featureless environment. Recently, it has been shown that unavoidable disorder in the environment is responsible for non-Markovian effects and information backflow from the environment into the system owing to Anderson localization. This turns disorder into a resource for enhancing non-Markovianity in the system–environment dynamics, which could be of relevance in cavity quantum electrodynamics. Here we consider the decoherence dynamics of a qubit weakly coupled to a two-dimensional bath with a nontrivial topological phase, such as a two-level atom embedded in a two-dimensional coupled-cavity array with a synthetic gauge field realizing a quantum-Hall bath, and show that Markovianity is protected against moderate disorder owing to the robustness of chiral edge modes in the quantum-Hall bath. Interestingly, switching off the gauge field, i.e., flipping the bath into a topological trivial phase, allows one to re-introduce non-Markovian effects. Such a result indicates that changing the topological phase of a bath by a tunable synthetic gauge field can be harnessed to control non-Markovian effects and quantum information backflow in a qubit-environment system.

arXiv:2002.04234PhotonicsFeb 8, 202011 citations

Decoherence in open Majorana systems

Earl T. Campbell

Coupling to a thermal bath leads to decoherence of stored quantum information. For a system of Gaussian fermions, the fermionic analog of linear or Gaussian optics, these dynamics can be elegantly and efficiently described by evolution of the system's covariance matrix. Taking both system and bath to be Gaussian fermionic, we observe that decoherence occurs at a rate that is independent of the bath temperature. Furthermore, we also consider a weak coupling regime where the dynamics are Markovian. We present a microscopic derivation of Markovian master equations entirely in the language of covariance matrices, where temperature independence remains manifest. This is radically different from behaviour seen in other scenarios, such as when fermions interact with a bosonic bath. Our analysis applies to many Majorana fermion systems that have been heralded as very robust, topologically protected, qubits. In these systems, it has been claimed that thermal decoherence can be exponentially suppressed by reducing temperature, but we find Gaussian decoherence cannot be cooled away.

arXiv:1502.05626Feb 19, 20155 citations