Dephasing of Majorana-based qubits

Knapp, Christina; Karzig, Torsten; Lutchyn, Roman M.; Nayak, Chetan

doi:10.1103/physrevb.97.125404

Cited by 79 publications

(96 citation statements)

References 59 publications

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“…This, however, strongly depends on the location of the charge density. If, as pointed out in [40], it happens to be close to the SC shell, the screening effect is larger and the pinning is suppressed. Nevertheless, as we analyze below in Fig.…”

Section: Model and Theoretical Approachmentioning

confidence: 98%

Interaction-induced zero-energy pinning and quantum dot formation in Majorana nanowires

Escribano¹,

Yeyati²,

Prada³

2018

Beilstein J. Nanotechnol.

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Majorana modes emerge in non-trivial topological phases at the edges of specific materials such as proximitized semiconducting nanowires under an external magnetic field. Ideally, they are non-local states that are charge-neutral superpositions of electrons and holes. However, in nanowires of realistic length their wave functions overlap and acquire a finite charge that makes them susceptible to interactions, specifically with the image charges that arise in the electrostatic environment. Considering a realistic three-dimensional model of the dielectric surroundings, here we show that, under certain circumstances, these interactions lead to a suppression of the Majorana oscillations predicted by simpler theoretical models, and to the formation of low-energy quantum-dot states that interact with the Majorana modes. Both features are observed in recent experiments on the detection of Majoranas and could thus help to properly characterize them.

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Section: Model and Theoretical Approachmentioning

confidence: 98%

Interaction-induced zero-energy pinning and quantum dot formation in Majorana nanowires

Escribano¹,

Yeyati²,

Prada³

2018

Beilstein J. Nanotechnol.

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“…In comparison, we ignore other mechanisms, such as, e.g. quasiparticle poisoning involving excitations above the superconducting gap [15], or those which arise when the MBSs have a non-zero overlap [16]. When switched on for the read-out the tunneling leads to a rapid initial decay on the scale of the inverse tunneling rate.…”

Section: Introductionmentioning

confidence: 99%

Transport signatures of a Majorana qubit and read-out-induced dephasing

Qin

Shnirman

et al. 2019

New J. Phys.

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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 current and the read-out process, including the resulting dephasing and relaxation. We also analyze the effects of varying control parameters such as gate voltages on the current. The characteristic dependencies may serve as a signature of Majorana bound states.

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“…We therefore assume that these quasiparticles have low mobility so that the excitation stays in the vicinity of the nanowire. We will discuss two distinct types of qubit errors: flip error in which the parity of a single qubit changes, and phase error in which the two parity states of a qubit incur a relative phase.It has been argued that the main source of quasiparticle poisoning is mediated by the electron-phonon interaction [52,58,59]. Theoretically, the rate that phonons split apart Cooper pairs and one of the electrons from the pair changes the occupation of the Majorana mode goes as Γ ∆ = τ −1 0 exp[−∆β] where τ 0 is the characteristic timescale describing electron-phonon coupling, ∆ is the superconducting gap and β is the inverse temperature.…”

mentioning

confidence: 99%

“…Theoretically, the rate that phonons split apart Cooper pairs and one of the electrons from the pair changes the occupation of the Majorana mode goes as Γ ∆ = τ −1 0 exp[−∆β] where τ 0 is the characteristic timescale describing electron-phonon coupling, ∆ is the superconducting gap and β is the inverse temperature. For bulk InAs the electron-phonon coupling timescale is on the order of tens of nanoseconds (τ 0 ≈ 10 ns) [52].The exponentially decaying characteristic of the Cooper pair breaking rate saturates at low temperature where relatively large non-thermal quasiparticle densities have been observed experimentally [42][43][44][45][46][47]. In this case the exponential is replaced by the quasi-particle density in the following way [52]:where n qp is the quasi-particle density and V is the volume of the superconductor in the vicinity of the edge modes.…”

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confidence: 99%

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One-dimensional error-correcting code for Majorana qubits

Stenger

Mong

2020

Phys. Rev. A

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Although Majorana platforms are promising avenues to realizing topological quantum computing, they are still susceptible to errors from thermal noise and other sources. We show that the error rate of Majorana qubits can be drastically reduced using a 1D repetition code. The success of the code is due the imbalance between the phase error rate and the flip error rate. We demonstrate how a repetition code can be naturally constructed from segments of Majorana nanowires. We find the optimal lifetime may be extended from a millisecond to over one second.The main road block in achieving quantum computation [1] is dealing with quantum error. Isolating a bit of quantum information from its environment is challenging enough, however, in order to realize a useful quantum computation machine it is necessary to maintain coherence for thousands of entangled qubits. Topological qubits are useful in that they have built-in fault tolerance due to the spatial separations between the anyons and the boundary modes [2]. Majorana zero modes [3][4][5], which appear as end modes of p-wave superconducting nanowires, are one the most promising directions in topological quantum computing [4,[6][7][8][9][10][11][12][13][14]. These Majorana end modes can store information non-locally and can be braided to perform topologically protected logic gates [15][16][17][18][19][20][21][22].Although topological qubits have some level of protection from error they will still require error correction in order to be fully implemented as computational qubits. A perfect Majorana qubit would be infinitely long and held at zero temperature. Nonzero temperatures lead to a finite quasiparticle density, which will cause errors in the qubit. There exist error correction codes such as the toric code [2], surface codes [23][24][25][26], and color codes [27][28][29], which can be implemented on Majorana qubits [30][31][32][33][34][35][36][37] or in other schemes such as planar codes [38,39]. However, these error correction schemes require a great deal of overhead, having a large number of redundant qubits in order to catch and correct error. As Kitaev pointed out [2], any topological phase of matter can be identified as an error correcting code. In this vain, we ask if the 1D fermionic topological phase [40,41] built from a chain of Majorana nanowires can be identified with a "fermion-parity protected error correcting code". Such a chain would require only a line of physical qubits instead of a surface.In this paper, we show how a chain of Majorana nanowires can be used to significantly improve the qubit lifetime, because of a hierarchy of different error types in Majorana qubits. Due to an unexpectedly high observed density of quasiparticles [42][43][44][45][46][47], we argue that phase errors in Majorana qubits are orders of magnitude greater than bit flip errors. This phase error can be corrected at the expense of the much smaller bit flip error using the repetition code [48][49][50]. We describe the repetition code in the language of Majorana qubits. The code...

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Dephasing of Majorana-based qubits

Cited by 79 publications

References 59 publications

Interaction-induced zero-energy pinning and quantum dot formation in Majorana nanowires

Interaction-induced zero-energy pinning and quantum dot formation in Majorana nanowires

Transport signatures of a Majorana qubit and read-out-induced dephasing

One-dimensional error-correcting code for Majorana qubits

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