  An interesting problem in the field of quantum error correction involves
finding a physical system that hosts a ``passively protected quantum memory,''
defined as an encoded qubit coupled to an environment that naturally wants to
correct errors. To date, a quantum memory stable against finite-temperature
effects is only known in four spatial dimensions or higher. Here, we take a
different approach to realize a stable quantum memory by relying on a
driven-dissipative environment. We propose a new model, the photonic-Ising
model, which appears to passively correct against both bit-flip and phase-flip
errors in two dimensions: A square lattice composed of photonic ``cat qubits''
coupled via dissipative terms which tend to fix errors locally. Inspired by the
presence of two distinct $\mathbb{Z}_2$-symmetry-broken phases, our scheme
relies on Ising-like dissipators to protect against bit flips and on a
driven-dissipative photonic environment to protect against phase flips. We also
discuss possible ways to realize the photonic-Ising model.
