Swapping Quantum Annealing Errors into a Cavity

Quantum annealing is a promising form of quantum computation, but it slows down at a small energy gap $\mathrm{\Delta }$ during the anneal, and the errors it makes there remain undetected. We introduce cavity quantum annealing, in which a cavity mode of frequency $O(1)\gg \mathrm{\Delta }$, coupled mid-schedule, swaps these errors into photons. In the $p$-spin model, this reduces the annealing time to nearly the square root of that required without the cavity. Moreover, counting the photons certifies the result: high-photon runs, with an $O(1)$ yield, reach a ground-state fidelity above $99.99\mathrm{\%}$ orders of magnitude sooner, a gain that grows exponentially with system size. A pre-loaded photon instead runs the swap in reverse, preparing an excited state. More broadly, our work shows that cavities can enhance computations performed with qubits, paving the way toward high-fidelity quantum state preparation by quantum annealing.