Fixing detailed balance in ancilla-based dissipative state engineering

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.