Error correcting codes for adiabatic quantum computation

Recently, there has been growing interest in using adiabatic quantum
computation as an architecture for experimentally realizable quantum computers.
One of the reasons for this is the idea that the energy gap should provide some
inherent resistance to noise. It is now known that universal quantum
computation can be achieved adiabatically using 2-local Hamiltonians. The
energy gap in these Hamiltonians scales as an inverse polynomial in the problem
size. Here we present stabilizer codes which can be used to produce a constant
energy gap against 1-local and 2-local noise. The corresponding fault-tolerant
universal Hamiltonians are 4-local and 6-local respectively, which is the
optimal result achievable within this framework.