Master Equations for Error-Suppressed Hamiltonian Quantum Computing

Error suppression and coherent diabatic evolution have emerged as important features of Hamiltonian quantum computation that are likely to be necessary for quantum speedup. We derive Markovian master equations for systems encoded with an error detecting code protecting the code space against interactions with the environment. This protection is enforced with a penalty Hamiltonian consisting of the generators of the stabilizer group of the error detecting code, splitting the Hilbert space into stabilizer subspaces. When the gap of the penalty Hamiltonian is larger than the frequencies of the encoded system Hamiltonian as well as the inverse of the bath correlation time, transitions out of the code space can be expressed in Davies-Lindblad form, while logical errors that occur in transitions across degenerate stabilizer subspaces can be treated with coarse graining for diabatic quantum annealing.