  The valley degree of freedom in the electronic band structure of silicon,
graphene, and other materials is often considered to be an obstacle for quantum
computing (QC) based on electron spins in quantum dots. Here we show that
control over the valley state opens new possibilities for quantum information
processing. Combining qubits encoded in the singlet-triplet subspace of spin
and valley states allows for universal QC using a universal two-qubit gate
directly provided by the exchange interaction. We show how spin and valley
qubits can be separated in order to allow for single-qubit rotations.
