  Hamiltonian quantum computing, such as the adiabatic and holonomic models,
can be protected against decoherence using an encoding into stabilizer subspace
codes for error detection and the addition of energy penalty terms. This method
has been widely studied since it was first introduced by Jordan, Farhi, and
Shor (JFS) in the context of adiabatic quantum computing. Here we extend the
original result to general Markovian environments, not necessarily in Lindblad
form. We show that the main conclusion of the original JFS study holds under
these general circumstances: assuming a physically reasonable bath model, it is
possible to suppress the initial decay out of the encoded ground state with an
energy penalty strength that grows only logarithmically in the system size, at
a fixed temperature.
