  We theoretically propose a set of universal quantum gates acting on a hybrid
qubit formed by coupling a quantum dot spin qubit and Majorana fermion qubit.
First, we consider a quantum dot tunnel-coupled to two topological
superconductors. The effective spin-Majorana exchange facilitates a hybrid CNOT
gate for which either qubit can be the control or target. The second setup is a
modular scalable network of topological superconductors and quantum dots. As a
result of the exchange interaction between adjacent spin qubits, a CNOT gate is
implemented that acts on neighboring Majorana qubits, and eliminates the
necessity of inter-qubit braiding. In both setups the spin-Majorana exchange
interaction allows for a phase gate, acting on either the spin or the Majorana
qubit, and for a SWAP or hybrid SWAP gate which is sufficient for universal
quantum computation without projective measurements.
