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.
Dr. Hoffman completed his undergraduate studies at University of Illinois, Urbana-Champaign (2004). After that, he moved to UCLA for his PhD where he worked together with Prof. Yaroslav Tserkovnyak. Since 2014 he is a postdoc in the Department of Physics at University of Basel, under the supervision of Prof. Daniel Loss. Dr. Hoffman interests lie broadly in the theory of quantum transport and nonequilibrium phenomena in nanostructures, with various applications in classical and quantum information.