We show that two electrons confined in a square semiconductor quantum dot have two isolated low-lying energy eigenstates, which have the potential to form the basis of scalable computing elements (qubits). Initialisation,one-qubit and two-qubit universal gates, and readout are performed using electrostatic gates and magnetic fields. Two-qubit transformations are performed via the Coulomb interaction between electrons on adjacent dots. Choice of initial states and subsequent asymmetric tuning of the tunnelling energy parameters on adjacent dots control the effect of this interaction. Notes: J.H. Jefferson, M. Fearn and D.L.J. Tipton, QinetiQ, Sensors and Electronics Division, St. Andrews Road, Malvern, WR14 3PS, UK 29 Pages