  Dissipative state engineering is a general term for a protocol which prepares
the ground state of a complex many-body Hamiltonian using engineered
dissipation or engineered environments. Recently, it was shown that a version
of this protocol, where the engineered environment consists of one or more
dissipative qubit ancillas tuned to be resonant with the low-energy transitions
of a many-body system, resulted in the combined system evolving to reasonable
approximation to the ground state. This potentially broadens the applicability
of the method beyond non-frustrated systems, to which it was previously
restricted. Here we argue that this approach has an intrinsic limitation
because the ancillas, seen as an effective bath by the system in the
weak-coupling limit, do not give the detailed balance expected for a true
zero-temperature environment. Our argument is based on the study of a similar
approach employing linear coupling to bosonic ancillas. We explore overcoming
this limitation using a recently developed technique from open-quantum-systems
called pseudomodes. With a simple example model of a 1D quantum Ising chain, we
show that detailed balance can be fixed, and a more accurate estimation of the
ground state obtained, at the cost of two additional unphysical dissipative
modes and the extrapolation error of implementing those modes in physical
systems.
