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Recent progress in nanoscale quantum optics and superconducting qubits hasmade the creation of strongly correlated, and even topologically ordered,states of photons a real possibility. Many of these states are gapped andexhibit anyon excitations, which could be used for a robust form of quantuminformation processing. However, while numerous qubit array proposals exist toengineer the Hamiltonian for these systems, the question of how to stabilizethe many-body ground state of these photonic quantum simulators against photonlosses remains largely unanswered. We here propose a simple mechanism whichachieves this goal for abelian and non-abelian fractional quantum Hall statesof light. Our construction uses a uniform two-photon drive field to couple thequbits of the primary lattice with an auxiliary ``shadow" lattice, composed ofqubits with a much faster loss rate than the qubits of the primary quantumsimulator itself. This coupling causes hole states created by photon losses tobe rapidly refilled, and the system's many-body gap prevents further photonsfrom being added once the strongly correlated ground state is reached. Thefractional quantum Hall state (with a small, transient population of quasiholeexcitations) is thus the most stable state of the system, and all otherconfigurations will relax toward it over time. The physics described here couldbe implemented in a circuit QED architecture, and the device parameters neededfor our scheme to succeed are in reach of current technology. We also propose asimple 6 qubit device, which could easily be built in the near future, that canact as a proof of principle for our scheme.

Induced self-stabilization in fractional quantum Hall states of light