  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 $^1\Sigma$ molecules as qubits. Herein,
we consider an array of polar $^2\Sigma$ molecules which are, in addition,
inherently paramagnetic and whose Hund's 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 array's 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.
