  Temperature determines the relative probability of observing a physical
system in an energy state when that system is energetically in equilibrium with
its environment. In this paper, we present a theory for engineering the
temperature of a quantum system different from its ambient temperature. We
define criteria for an engineered quantum bath that, when coupled to a quantum
system with Hamiltonian $H$, drives the system to the equilibrium state
$\frac{e^{-H/T}}{{{\rm{Tr}}}(e^{-H/T})}$ with a tunable parameter $T$. This is
basically an analog counterpart of the digital quantum metropolis algorithm.
For a system of superconducting qubits, we propose a circuit-QED approximate
realization of such an engineered thermal bath consisting of driven lossy
resonators. Our proposal opens the path to simulate thermodynamical properties
of many-body quantum systems of size not accessible to classical simulations.
Also we discuss how an artificial thermal bath can serve as a temperature knob
for a hybrid quantum-thermal annealer.
