  We propose a practical implementation of a universal quantum computer that
uses local fermionic modes (LFM) rather than qubits. The device layout consists
of quantum dots tunnel coupled by a hybrid superconducting island and a tunable
capacitive coupling between the dots. We show that coherent control of Cooper
pair splitting, elastic cotunneling, and Coulomb interactions allows us to
implement the universal set of quantum gates defined by Bravyi and Kitaev. Due
to the similarity with charge qubits, we expect charge noise to be the main
source of decoherence. For this reason, we also consider an alternative design
where the quantum dots have tunable coupling to the superconductor. In this
second device design, we show that there is a sweetspot for which the local
fermionic modes are charge neutral, making the device insensitive to charge
noise effects. Finally, we compare both designs and their experimental
limitations and suggest future efforts to overcome them.
