Universal quantum computation on a semiconductor quantum wire network

Abstract

Universal quantum computation (UQC) using Majorana fermions on a 2D topological superconducting (TS) medium remains an outstanding open problem. This is because the quantum gate set that can be generated by braiding of the Majorana fermions does not include \emph{any} two-qubit gate and also the single-qubit $\pi /8$ phase gate. In principle, it is possible to create these crucial extra gates using quantum interference of Majorana fermion currents. However, it is not clear if the motion of the various order parameter defects (vortices, domain walls, \emph{etc.}), to which the Majorana fermions are bound in a TS medium, can be quantum coherent. We show that these obstacles can be overcome using a semiconductor quantum wire network in the vicinity of an $s$-wave superconductor, by constructing topologically protected two-qubit gates and any arbitrary single-qubit phase gate in a topologically unprotected manner, which can be error corrected using magic state distillation. Thus our strategy, using a judicious combination of topologically protected and unprotected gate operations, realizes UQC on a quantum wire network with a remarkably high error threshold of $0.14$ as compared to $10^{-3}$ to $10^{-4}$ in ordinary unprotected quantum computation.

7 pages, 2 figures

References in corpus (9)

• Non-Abelian Anyons and Topological Quantum Computation
• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
• Classification of topological insulators and superconductors in three spatial dimensions
• Tunable Supercurrent Through Semiconductor Nanowires
• Splitting of Majorana modes due to intervortex tunneling in a p + ip superconductor
• Numerical Analysis of Quasiholes of the Moore-Read Wavefunction
• Anyonic Braiding in Optical Lattices
• Suppression of Tunneling in a Superconducting Persistent-Current Qubit

Cited by in corpus (4)

• Interaction Effects in Topological Superconducting Wires Supporting Majorana Fermions
• Search for Majorana fermions in multiband semiconducting nanowires
• Interface Between Topological and Superconducting Qubits
• Topologically non-trivial superconductivity in spin-orbit coupled systems: Bulk phases and quantum phase transitions