Graphene-enabled low-control quantum gates between static and mobile spins

Abstract

We show that the feature of Klein tunneling makes graphene a unique interface for implementing low control quantum gates between static and mobile qubits. A ballistic electron spin is considered as the mobile qubit, while the static qubit is the electronic spin of a quantum dot fixed in a graphene nanoribbon. Scattering is the low control mechanism of the gate, which, in other systems, is really difficult to exploit because of both backscattering and the momentum dependence of scattering. We find that Klein tunneling enables the implementation of quasi-deterministic quantum gates regardless of the momenta or the shape of the wave function of the incident electron. The Dirac equation is used to describe the system in the one particle approximation with the interaction between the static and the mobile spins modelled by a Heisenberg Hamiltonian. Furthermore, we discuss an application of this model to generate entanglement between two well separated static qubits.

SU(2)⊗SU(2) bi-spinor structure entanglement induced by a step potential barrier scattering in two-dimensions

“…For completeness, the chiral profile of the Dirac bi-spinors can be identified through the averaged value of the chiral operator, γ 5 , with γ 5 written in the two qubit SU (2) ⊗ SU (2) representation as γ 5 ≡ σ (1) x ⊗ I…”

“…x ⊗ p · σ (2) + m σ (1) z ⊗ I (2) 2 , from which the free particle solutions of the Dirac equation are given in terms of SU (2) ⊗ SU (2) parity-spin entangled states written as |Ψ s ( p, t) = e i(−1) s Ep t |ψ s ( p) = e i(−1) s Ep t N s (p)…”

“…The growing interest in mapping controllable physical systems onto the bi-spinor structure of the relativistic Dirac equation [1][2][3][4] has been recently translated into a useful theoretical tool for investigating nonrelativistic two-dimensional (2D) systems of utmost scientific appeal [5][6][7]. For instance, the low-energy excitations of a nonrelativistic electrons in the single layer graphene are known for exhibiting a massless Weyl spinor structure often related to 2D Dirac equation solutions.…”

Entanglement of magnetic impurities through electron scattering in an electric field

“…We consider a one-dimensional quantum wire where two 1/2-spin fixed magnetic impurities are located at x 0 distance of each other. The quantum wire can be physically implemented with carbon nanotubes [29,30,31], graphene nanoribbons [20,32], heterostructures [33] or quantum Hall edge states [17,18]. We assume that x 0 is long enough to neglect any direct interaction between the impurities.…”

Inserting Porphyrin Quantum Dots in Bottom‐Up Synthesized Graphene Nanoribbons

“…While bottom-up synthesized GNRs have been touted for their intrinsic exotic electronic, [21][22][23][24][25][26][27][28][29][30][31] magnetic, [25,[29][30][31][32] and optical properties, [16,27,28,[33][34] examples for the deterministic assembly of functional bottom-up synthesized GNRs heterostructures have thus far been limited to uncontrolled copolymerization of molecular precursors on metal surfaces [6,13,18,20] or the study of smallmolecule model systems in solution. [35][36][37] We herein report the solution-based bottom-up synthesis and characterization of a GNR heterostructure comprised of two segments of solubilized cove GNRs (cGNRs) linked by a substituted tetraphenylporphyrin core (1, Scheme 1) acting as a highly tunable molecular quantum dot (QD).…”