  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
$\varepsilon$ in the tricritical Ising model. The deconfinement of $\tau$ and
$\varepsilon$ via the interaction between the fermion modes yields the anyon
{collisions} and gives the braiding of either $\tau$ or $\varepsilon$. 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.
