Quantum computing through electron propagation in edge states of quantum spin Hall systems

Abstract

We propose to implement quantum computing based on electronic spin qubits by controlling the propagation of the electron wave packets through the helical edge states of quantum spin Hall systems (QSHs). Specifically, two non-commutative single-qubit gates, which rotate a qubit around z and y axes, can be realized by utilizing gate voltages either on a single QSH edge channel or on a quantum point contact structure. The more challenging two-qubit controlled phase gate can be implemented through the on-demand capacitive Coulomb interaction between two adjacent edge channels from two parallel QSHs. As a result, a universal set of quantum gates can be achieved in an all-electrical way. The fidelity and purity of the two-qubit gate are calculated with both time delay and finite width of the wave packets taken into consideration, which can reach high values with the existing high-quality single electron source.

Coherent spin transport through helical edge states of topological insulator

“…Similar to the low-temperature case [34][35][36][37][38] , one can suggest twoqubit manipulation schemes taking into account the electron-electron interaction. To this end, one can use interferometers connected in parallel and coupled by interaction (see Fig.…”

“…Such qubits can be controlled by changing the magnetic field and the strength of the SO interaction 17,33 . Taking into account, the electron-electron interaction makes it also possible to construct effective two-qubit computational schemes in two coupled interferometers based on conventional materials 35,36 , on edge states of the integer quantum Hall effect 37,38 and on helical states 34 . Signatures of electron-electron interaction in HES was already observed experimentally 39,40 .…”

Ballistic 3-port interferometric logic gates in the quantum Hall regime

“…Note that throughout the paper we have considered the case of spin-independent scattering at potential barriers, which implies from a practical point of view either smallenough magnetic fields, such that the Zeeman splitting is not important, or that the spin-orbit coupling can be neglected, or that spin-polarized charge carriers are injected. The situation of spin-resolved propagation would complicate the interpretation of the results, not because charge carriers with opposite spins propagate along channels on the opposite sides of the 2DEG but, especially, because spin rotation takes place at quantum point contacts [14,22].…”

“…A different route for implementing logic operations in solid-state systems involves configurations in materials with long mean-free-paths of charge carriers, such as graphene [9][10][11] or 2DEGs [12] based on interference between quantum wavefunctions traversing different paths. This last category includes also logic gates based on quantum interference between edge states in electron interferometers defined by quantum point contacts (QPCs) [13,14]. Such few-or single-channel electron interferometers working in the quantum Hall effect regime have the advantage of high sensitivity and visibility [15], as well as of a well-establish, even analytical [13,16,17], modeling of propagating single-particle wavefunctions or wavepackets.…”

“…Such few-or single-channel electron interferometers working in the quantum Hall effect regime have the advantage of high sensitivity and visibility [15], as well as of a well-establish, even analytical [13,16,17], modeling of propagating single-particle wavefunctions or wavepackets. Moreover, conditional operations involving logic gates implemented by electronic interferometers based on edge states could be envisaged taking into account the Coulomb interaction of different interferometers [14,18,19] or the coupling of different cavities by edge states [20].…”