Entangling Spins in Double Quantum Dots and Majorana Bound States

We theoretically investigate the coupling between a singlet-triplet (ST) spin qubit realized in a double quantum dot and a topological qubit composed of Majorana bound states. First, we derive an effective Hamiltonian which facilitates an entangling gate between the two individual qubits, thereby enabling a CNOT gate and, subsequently, a SWAP gate. Using standard readout and single qubit operations of the ST qubit, we show how the former gate can be used to readout the state of Majorana qubit while the latter gate enables universal quantum computation of the topological qubit. We estimate the fidelity of the entangling and SWAP gate operations to be 0.9997 and 0.993, respectively, using parameters that are consistent with realizing both of the qubits within a nanowire. Furthermore, we find that the coupling between the ST qubit and a single Majorana bound state induces an oscillation between the two singlet-triplet levels which has the utility to (1) perform single qubit operations on the singlet-triplet around the x axis without a need for a gradient of Zeeman fields and (2) provide a signature for the presence of zero energy bound states. Lastly, we propose a scheme to extend our setup to a scalable network using the ST-Marjorana bound state qubit as the atomic unit.