New universal gates for topological quantum computation with Fibonacci-$\boldsymbol{\varepsilon}$ composite Majorana edge modes on topological superconductor multilayers

Abstract

We propose a new design of universal topological quantum computer device through a hybrid of the 1-, 2- and 7-layers of chiral topological superconductor ($\chi$TSC) thin films. Based on the $SO(7)_1/(G_2)_1$ coset construction, strongly correlated Majorana fermion edge modes on the 7-layers of $\chi$TSC are factorized into the composite of the Fibonacci $\tau$-anyon and $\varepsilon$-anyon modes in the tricritical Ising model. Furthermore, the deconfinement of $\tau$ and $\varepsilon$ via the interacting potential gives the braiding of either $\tau$ or $\varepsilon$. Topological phase gates are assembled by the braidings. With these topological phase gates, we find a set of fully topological universal gates for the $(\tau,\varepsilon)$ composite Majorana-Ising-type quantum computation. Because the Hilbert space still possesses a tensor product structure of quibts and is characterized by the fermion parities, encoding quantum information in this machine is more efficient and substantial than that with Fibonacci anyons. The computation results is easier to be read out by electric signals, so are the initial data inputted.Comment: 6 pages, 3 figues, revised versio