Coulomb-assisted braiding of Majorana fermions in a Josephson junction array

Abstract

We show how to exchange (braid) Majorana fermions in a network of superconducting nanowires by control over Coulomb interactions rather than tunneling. Even though Majorana fermions are charge-neutral quasiparticles (equal to their own antiparticle), they have an effective long-range interaction through the even-odd electron number dependence of the superconducting ground state. The flux through a split Josephson junction controls this interaction via the ratio of Josephson and charging energies, with exponential sensitivity. By switching the interaction on and off in neighboring segments of a Josephson junction array, the non-Abelian braiding statistics can be realized without the need to control tunnel couplings by gate electrodes.

Majorana and condensed matter physics

“…(Related algebraic structures are implicit in [27]. See also [28][29][30][31] for additional constructions. )…”

Kitaev spin models from topological nanowire networks

“…Finally, let us conclude by summarizing the implications of our results for the quantum computing with nanowire arrays [8,[17][18][19][20] that we used initially to motivate our work. As the formation of the ν = ±1 collective states constitutes a significant source of decoherence, the most obvious impact is the understanding of how to avoid such scenario.…”

“…While this may be possible (see for example Ref. [18]) as the experiments become more sophisticated, for simplicity we assume that the induced superconducting gap | E | and the Fermi momentum k F are equal in all wires. Furthermore, we assume that all wires are of equal length L = L nm and that all the junctions are of equal width W = W nm .…”

“…[6,7] the effective p-wave phase depends on (i) the direction of the spin-orbit coupling, which in turn depends on the orientation of the wire relative to the underlying substrate (see for example [19]), (ii) the direction of the applied Zeeman field, and (iii) the phase of the s-wave superconductor, which is related to the surrounding vector potential (see for example Ref. [18]). …”

“…This near-degenerate manifold serves as the computational space, which can be manipulated ideally only through operations that correspond to the braiding of the localized Majorana modes. These braidings can in principle be performed through controlling locally the relative amplitudes of the couplings J and J on the wires meeting at the N -junctions [8,17,18,20,21].…”