For quantum annealing, as opposed to circuit based quantum computing, the solution to a computational problem is encoded in the ground state of a quantum system. Therefore its susceptibility to environmental effects is a different but not less important open question essential to a scalable implementation. In this work we use renormalization group techniques to study the effect of Ohmic baths in a regime typical for practical adiabatic quantum computation. We show qualitative change to the effective Hamiltonian as well as the reduced qubit density matrix encoding entanglement between system and bath. An effective dephasing of the reduced density matrix limits the extractable information from many qubit entangled groundstates. We find that the annealing process is no longer restricted to the qubits and discuss possible drawbacks or benefits of annealing in the combined system–bath states.