Abstract:Motivated by recent proposals of Majorana qubits and the read-out of their quantum state we investigate a qubit setup formed by two parallel topological wires shunted by a superconducting bridge. The wires are further coupled to two quantum dots, which are also linked directly, thus creating an interference loop. The transport current through this system shows an interference pattern which distinguishes two basis states of the qubit in a QND measurement. We analyze various properties of the interference curren… Show more
“…As we are particularly interested in decoherence, i.e., the decay of off-diagonal elements of ρ(t ), this approximation is particularly well suited here. In contrast to previous works [18,19,[66][67][68][69], our approach is able to capture quantum backaction effects on the MBQ state since the quantum dynamics of the dot fermion is taken into account.…”
Section: Introductionmentioning
confidence: 96%
“…This means that (i) the readout device itself should not exchange particles with the dot-MBQ system and (ii) the decoherence due to the readout should be fast compared to decoherence caused by external noise sources which do affect the total parity. Previous theoretical studies of measurement-induced decoherence in Majorana qubits [18,19,[66][67][68][69] have analyzed related questions but without taking into account the detailed quantum dynamics of the dot and thereby, in particular, neglecting quantum backaction effects [70]. In this paper, we propose and study a flexible and powerful theoretical approach which can ultimately provide a unified and quite realistic description of the parity-to-charge conversion process and the corresponding readout dynamics in such a topologically protected system.…”
We study the time-dependent effect of Markovian readout processes on Majorana qubits whose parity degrees of freedom are converted into the charge of a tunnel-coupled quantum dot. By applying a recently established effective Lindbladian approximation [
“…As we are particularly interested in decoherence, i.e., the decay of off-diagonal elements of ρ(t ), this approximation is particularly well suited here. In contrast to previous works [18,19,[66][67][68][69], our approach is able to capture quantum backaction effects on the MBQ state since the quantum dynamics of the dot fermion is taken into account.…”
Section: Introductionmentioning
confidence: 96%
“…This means that (i) the readout device itself should not exchange particles with the dot-MBQ system and (ii) the decoherence due to the readout should be fast compared to decoherence caused by external noise sources which do affect the total parity. Previous theoretical studies of measurement-induced decoherence in Majorana qubits [18,19,[66][67][68][69] have analyzed related questions but without taking into account the detailed quantum dynamics of the dot and thereby, in particular, neglecting quantum backaction effects [70]. In this paper, we propose and study a flexible and powerful theoretical approach which can ultimately provide a unified and quite realistic description of the parity-to-charge conversion process and the corresponding readout dynamics in such a topologically protected system.…”
We study the time-dependent effect of Markovian readout processes on Majorana qubits whose parity degrees of freedom are converted into the charge of a tunnel-coupled quantum dot. By applying a recently established effective Lindbladian approximation [
“…The most fundamental one, that of observing a quantized zero bias peak in conductance [4,11,12], can be mimicked by trivial Andreev bound states [10,[13][14][15][16] or level repulsion in multiband systems [17,18], thus several detection schemes also exploiting Majorana nonlocality have been proposed [19][20][21]. From the point of view of the applications, one of the schemes for the readout of Majorana qubits is based on transport interferometry [22,23], providing further motivation to explore the transport properties of Majorana devices.…”
We present exact analytical results for the differential conductance of a finite Kitaev chain in an N-S-N configuration, where the topological superconductor is contacted on both sides with normal leads. Our results are obtained with the Keldysh nonequilibrium Green's function technique, using the full spectrum of the Kitaev chain without resorting to minimal models. A closed formula for the linear conductance is given, and the analytical procedure to obtain the differential conductance for the transport mediated by higher excitations is described. The linear conductance attains the maximum value of e 2 /h only for the exact zero-energy states. Also, the differential conductance exhibits a complex pattern created by numerous crossings and anticrossings in the excitation spectrum. We reveal the crossings to be protected by inversion symmetry, while the anticrossings result from a pairing-induced hybridization of particlelike and holelike solutions with the same inversion character. Our comprehensive treatment of the Kitaev chain allows us also to identify the contributions of both local and nonlocal transmission processes to transport at arbitrary bias voltage. Local Andreev reflection processes dominate the transport within the bulk gap and diminish for higher excited states but reemerge when the bias voltage probes the avoided crossings. The nonlocal direct transmission is enhanced above the bulk gap but contributes also to the transport mediated by the topological states.
“…Yet, these studies neglect thermal excitations while focussing on dephasing and relaxation in a minimal model of four Majorana zero-modes. Decoherence of Majorana zero-modes in presence of a bath, in particular in the context of Majorana qubits, has been studied using a similar theoretical framework as the present work based on a quantum master equation [41][42][43][44]. These studies have demonstrated the general susceptibility of Majorana zero-modes to environment-induced potential fluctuations in finite systems.…”
Braiding Majorana zero-modes around each other is a promising route towards topological quantum computing. Yet, two competing maxims emerge when implementing Majorana braiding in real systems: On the one hand, perfect braiding should be conducted adiabatically slowly to avoid non-topological errors. On the other hand, braiding must be conducted fast such that decoherence effects introduced by the environment are negligible, which are generally unavoidable in finite-size systems. This competition results in an intermediate time scale for Majorana braiding that is optimal, but generally not error-free. Here, we calculate this intermediate time scale for a T-junction of short one-dimensional topological superconductors coupled to a bosonic bath that generates fluctuations in the local electric potential, which stem from, e.g., environmental photons or phonons of the substrate. We thereby obtain boundaries for the speed of Majorana braiding with a predetermined gate fidelity. Our results emphasize the general susceptibility of Majorana-based information storage in finite-size systems and can serve as a guide for determining the optimal braiding times in future experiments.
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