  Is the notion of a quantum computer resilient to thermal noise unphysical? We
address this question from a constructive perspective and show that local
quantum Hamiltonian models provide self-correcting quantum computers. To this
end, we first give a sufficient condition on the connect- edness of excitations
for a stabilizer code model to be a self-correcting quantum memory. We then
study the two main examples of topological stabilizer codes in arbitrary
dimensions and establish their self-correcting capabilities. Also, we address
the transversality properties of topological color codes, showing that 6D color
codes provide a self-correcting model that allows the transversal and local
implementation of a universal set of operations in seven spatial dimensions.
Finally, we give a procedure to initialize such quantum memories at finite
temperature.
