Engineering the stabilization of rotation and reflection invariant bosonic states

Bosonic states have emerged as a powerful tool for quantum error correction, thanks to their efficient use of the Hilbert space. Notably, cat, GKP, and binomial codes have achieved break-even in recent years. The preparation of such states has recently been explored through the use of measurement-based feedback, where controllers optimized via reinforcement learning (RL) are used. However, the large control space required to achieve high fidelities poses a challenge for efficient learning in a deep RL framework. In this talk, we address this challenge by introducing a parameterized circuit based on the Trotter expansion of an underlying dynamical equation, designed so that the target state is its sole steady state. To guarantee that the target state is an asymptotically stable point, the Trotter expansion combines unitary evolution with a non-unitary component. Specifically, we derive a parameterized sequence comprising a SNAP gate interleaved with two displacement gates, which stabilizes bosonic states with rotational and reflection symmetries. Through numerical simulations, we show how RL can then further enhance the protocol’s performance, improving the rate of convergence and minimizing leakage.