Manipulation of Majorana states in X-junction geometries

Abstract

We study quantum manipulation based on four Majorana bound states in X-junction geometry. The parameter space of this setup is bigger than of the previously studied Y-junction and is described by SO(4) symmetry group. In order for quantum computation to be dephasing free, two Majorana states have to stay degenerate at all times. We find a condition necessary for that and compute the Berry's phase, $2\alpha$, accumulated during the manipulation. We construct simple protocols for the variety of values of $\alpha$, including $\pi /8$ needed for the purposes of quantum computation. Although the manipulations in general X-junction geometry are not topologically protected, they may prove to be a feasible compromise for aims of quantum computation.

6 pages, 4 figures

References in corpus (10)

• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
• Evidence of Majorana fermions in an Al - InAs nanowire topological superconductor
• Observation of Majorana Fermions in a Nb-InSb Nanowire-Nb Hybrid Quantum Device
• Superconductor-Nanowire Devices from Tunneling to the Multichannel Regime: Zero-Bias Oscillations and Magnetoconductance Crossover
• Topological Phases of Noncentrosymmetric Superconductors: Edge States, Majorana Fermions, and the Non-Abelian Statistics
• Flux-controlled quantum computation with Majorana fermions
• Exotic and excited-state radiative transitions in charmonium from lattice QCD
• Parity independence of the zero-bias conductance peak in a nanowire based topological superconductor-quantum dot hybrid device

Cited by in corpus (1)

• Detecting coupling of Majorana bound states with an Aharonov-Bohm interferometer