Universal topological quantum computation with strongly correlated Majorana edge modes

Abstract

Majorana-based quantum gates are not complete for performing universal topological quantum computation while Fibonacci-based gates are difficult to be realized electronically and hardly coincide with the conventional quantum circuit models. In Ref. \cite{hukane}, it has been shown that a strongly correlated Majorana edge mode in a chiral topological superconductor can be decomposed into a Fibobacci anyon $\tau$ and a thermal operator anyon $\epsilon$ in the tricritical Ising model. The deconfinement of $\tau$ and $\epsilon$ via the interaction between the fermion modes yields the anyon {collisions} and gives the braiding of either $\tau$ or $\epsilon$. With these braidings, the complete members {of} a set of universal gates, the Pauli gates, the Hadamard gate and extra phase gates for 1-qubit as well as controlled-not gate for 2-qubits, are topologically assembled. Encoding quantum information and reading out the computation results can be carried out through electric signals. With the sparse-dense mixed encodings, we set up the quantum circuit {where the controlled-not gate turns out { to be} a probabilistic gate} and design the corresponding devices with thin films of the chiral topological superconductor. As an example of the universal topological quantum computing, we show the application to Shor's integer factorization algorithm.