Hybrid Topological Quantum Computation with Majorana Fermions: A Cold Atom Setup

Abstract

In this paper we present a hybrid scheme for topological quantum computation in a system of cold atoms trapped in an atomic lattice. A topological qubit subspace is defined using Majorana fermions which emerge in a network of atomic Kitaev one-dimensional wires. We show how braiding can be efficiently implemented in this setup and propose a direct way to demonstrate the non-Abelian nature of Majorana fermions via a single parity measurement. We then introduce a proposal for the efficient, robust and reversible mapping of the topological qubits to a conventional qubit stored in a single atom. There, well-controlled standard techniques can be used to implement the missing gates required for universal computation. Our setup is complemented with an efficient non-destructive protocol to check for errors in the mapping.

16 pages, 18 figures

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Cited by in corpus (17)

• Topological quantum matter with cold atoms
• Localized Majorana-like modes in a number conserving setting: An exactly solvable model
• Braiding errors in interacting Majorana quantum wires
• Cavity-mediated unconventional pairing in ultracold fermionic atoms
• Majoranas in Noisy Kitaev Wires
• Multiple signatures of topological transitions for interacting fermions in chain lattices
• Photoinduced $\frac{1}{2}\frac{e^2}{h}$ and $\frac{3}{2}\frac{e^2}{h}$ conductance plateaus in topological insulator-superconductor heterostructures
• Holographic optical traps for atom-based topological Kondo devices
• Andreev and Majorana bound states in single and double quantum dot structures
• Fano-Majorana effect and bound states in the continuum on a crossbar-shaped quantum dot hybrid structure
• Teleporting quantum information encoded in fermionic modes
• Effects of Gapless Bosonic Fluctuations on Majorana Fermions in Atomic Wire Coupled to a Molecular Reservoir
• Bound states in the continuum poisoned by Majorana fermions
• Quantum gates by periodic driving
• Bulk-boundary correspondence in topological systems with the momentum dependent energy shift
• Dirac topological insulator in the d${}_{z^2}$ manifold of a honeycomb oxide
• Extended edge modes and disorder preservation of a symmetry-protected topological phase out of equilibrium