  We implement a Szilard engine that uses a 2-bit logical unit consisting of
coupled quantum flux parametrons -- Josephson-junction superconducting circuits
originally designed for quantum computing. Detailed simulations show that it is
highly thermodynamically efficient while functioning as a Maxwell demon. The
physically-calibrated design is targeted to direct experimental exploration.
However, variations in Josephson junction fabrication introduce asymmetries
that result in energy inefficiency and low operational fidelity. We provide a
design solution that mitigates these practical challenges. The resulting
platform is ideally suited to probe the thermodynamic foundations of
information processing devices far from equilibrium.
