Critical states preparation in light-matter systems with deep reinforcement learning

The fast and efficient preparation of quantum critical states is a challenging yet crucial task for various quantum technologies. This difficulty is most particularly for systems near a quantum phase transition, where the closure of the energy gap fundamentally limits the timescale of adiabatic processes and thus precludes rapid state preparation. We propose a framework using deep reinforcement learning (DRL) to rapidly prepare quantum critical states, with broad extendibility to light-matter interaction systems. Specifically, a DRL agent optimizes a set of time-dependent control Hamiltonians to drive the system from an initial noncritical state to a target critical state within a finite time and over experimentally accessible parameter ranges. As a concrete application, we focus on the quantum Rabi model. The DRL-optimized time-dependent control Hamiltonian yields a final state with high fidelity (>0.999) to the target critical state. The protocol can be readily extended to other quantum critical systems described by light-matter interaction models, such as quantum Dicke model. This investigation provides a powerful framework for preparing and manipulating quantum critical states.