Autonomous Floquet Engineering of Bosonic Codes via Reinforcement Learning

TL;DR

This work introduces a reinforcement-learning-assisted Floquet-engineering strategy to autonomously prepare bosonic codes in continuous-variable systems. By combining NcFT-based Floquet synthesis with a TD3-based RL agent, the approach achieves high-fidelity creation of 4-fold rotational cat codes in tens of driving periods, dramatically faster than adiabatic ramps, and remains robust under photon loss and dephasing. The results highlight a general paradigm for integrating machine learning with Floquet control to overcome decoherence in next-generation quantum technologies, with potential applicability across superconducting cavities, optomechanics, and other CV platforms. This framework paves the way toward scalable, fault-tolerant bosonic quantum computation by enabling rapid, noise-resilient state preparation and stabilization.

Abstract

Bosonic codes represent a promising route toward quantum error correction in continuous-variable systems, with direct relevance to experimental platforms such as circuit QED and optomechanics. However, their preparation and stabilization remain highly challenging, requiring ultra-precise control of nonlinear interactions to create entangled superpositions, suppress decoherence, and mitigate dynamic errors. Here, we introduce a reinforcement-learning-assisted Floquet engineering approach for the autonomous preparation of bosonic codes that is general, efficient, and noise-resilient. By leveraging machine learning to optimize Floquet driving parameters, our method achieves over two orders of magnitude reduction in evolution time-requiring only about one percent of that in conventional adiabatic schemes-while maintaining high-fidelity state generation even under strong dissipative and dephasing noise. This approach not only demonstrates the power of artificial intelligence in quantum control but also establishes a scalable and experimentally feasible route toward fault-tolerant bosonic quantum computation. Beyond the specific application to bosonic code preparation, our results suggest a general paradigm for integrating machine learning and Floquet engineering to overcome decoherence challenges in next-generation quantum technologies.

Figures (6)

• Figure 1: A sketch of our reinforcement learning process for the preparation of the bosonic cat states, where the external driving field is dynamically updated by the agent based on the instantaneous fidelity of the evolution state.
• Figure 2: Preparation of 4-fold rotational bosonic cat state with reinforcement learning. (a) Snapshots of Husmi Q-functions of prepared states $\bra{\alpha}\rho_t\ket{\alpha}$ at four different time moments. (b) Stroboscopic time evolution of the prepared state fidelity $\mathcal{F}[\rho_0, \rho(t)]$, cf. Eq. (\ref{['eq:fidelity']}), with respect to the 4-fold rotational target bosonic state $\rho_0=\ket{0_{q,\Theta}}\bra{0_{q,\Theta}}$ given by Eq. (\ref{['eq:q-flod-cat0']}). The red dots indicate the corresponding time moments of the snapshots in (a). Inset: reproduced stroboscopic time evolution of fidelity of the prepared state using the adiabatic ramp method in Ref. guo-PhysRevLett.132.023602. (c) The machine learned driving amplitude $\beta(t)$ (black curve) and the driving frequency $\omega(t)$ (red curve) with the preparation time $160×\times 2\pi/\omega_0$. Inset: reproduced ramp for the driving amplitude $\beta(t)$ (black curve) and the driving frequency $\omega(t)$ (red curve) with the preparation time $5000×\times 2\pi/\omega_0$ in Ref. guo-PhysRevLett.132.023602.
• Figure 3: Fidelity of the prepared state with various levels of photon loss rate $\kappa$ and dephasing rate $\eta$ using the network trained with the lowest noise model, i.e. the case with ${\kappa = 10^{-7}\omega_0}$, ${\eta=10^{-7}\omega_0}$.
• Figure 4: Stroboscopic time evolution of fidelity of the prepared state under various environment noise levels with our reinforcement learning method. The black solid line shows the fidelity evolution at a relatively high noise rate with our original trained policy, i.e. $\kappa=10^{-4}\omega_0, \eta=10^{-4}\omega_0$, where two stages are defined with various background colors. The blue dashed line shows the fidelity evolution at a extremely high noise rate with our original trained policy, i.e. $\kappa=10^{-3}\omega_0, \eta=0$, where the fidelity of the generated state in stage II drops vastly. The red dashed-dotted line shows the fidelity evolution with our retrained model at the same noise level of the blue dashed line case.
• Figure 5: The reinforcement learned control sequences of $\beta(t)$ and $\omega(t)$ obtained with our (a) original trained network and (b) the retrained network, corresponding to the blue dashed line and the red dashed-dotted line in Fig. \ref{['fig:noise-study']} respectively.