Prospects for Quantum Computing with an Array of Ultracold Polar Paramagnetic Molecules

Arrays of trapped ultracold molecules represent a promising platform for implementing a universal quantum computer. DeMille has detailed a prototype design based on Stark states of polar $^1Sigma$ molecules as qubits. Herein, we consider an array of polar $^2Sigma$ molecules which are, in addition, inherently paramagnetic and whose Hunds case (b) free-rotor states are Bell states. We show that by subjecting the array to combinations of concurrent homogeneous and inhomogeneous electric and magnetic fields, the entanglement of the arrays Stark and Zeeman states can be tuned and the qubit sites addressed. Two schemes for implementing an optically controlled CNOT gate are proposed and their feasibility discussed in the face of the broadening of spectral lines due to dipole-dipole coupling and the inhomogeneity of the electric and magnetic fields.