Preparation and stabilization of cavity Fock state superpositions with deep reinforcement learning

Photon number superposition states inside a microwave cavity are an essential resource for hardware efficient quantum computing, such as the binomial or cat codes frameworks. Their preparation and stabilization, however, usually require controls relying on second-order interactions to generate the non-classicality of the Wigner function.

Here, we propose instead a protocol based on state-of-the-art off-policy deep distributional reinforcement learning, to obtain heralded state preparation fidelities above 97% on average for a variety of bosonic states. Optimizing with respect to the distribution of returns, rather than their mean, was found to be instrumental in implementing a stable training procedure.

The approach relies on using a coherent displacement as linear control and quantum back action from weak measurements as the only non-linearity implemented with Ramsey type interferometry. Such measurements stabilize subspaces of Fock state superpositions, where by keeping track of the quantum state, our scheme is able to counteract the cavity decoherence rate, recovering from photon loss events in real time. Moreover, the reinforcement learning approach overcomes local minima in the stabilized subspace, reaching higher fidelities than conventional classical feedback protocols.