Deep Reinforcement Learning for Quantum State Preparation with Weak Nonlinear Measurements

Riccardo Porotti1,2, Antoine Essig3, Benjamin Huard3, and Florian Marquardt1,2

1Max Planck Institute for the Science of Light, Erlangen, Germany
2Department of Physics, Friedrich-Alexander Universität Erlangen-Nürnberg, Germany
3Univ Lyon, ENS de Lyon, CNRS, Laboratoire de Physique,F-69342 Lyon, France

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Quantum control has been of increasing interest in recent years, e.g. for tasks like state initialization and stabilization. Feedback-based strategies are particularly powerful, but also hard to find, due to the exponentially increased search space. Deep reinforcement learning holds great promise in this regard. It may provide new answers to difficult questions, such as whether nonlinear measurements can compensate for linear, constrained control. Here we show that reinforcement learning can successfully discover such feedback strategies, without prior knowledge. We illustrate this for state preparation in a cavity subject to quantum-non-demolition detection of photon number, with a simple linear drive as control. Fock states can be produced and stabilized at very high fidelity. It is even possible to reach superposition states, provided the measurement rates for different Fock states can be controlled as well.

Quantum control has been of great relevance in recent years, especially due to the spread of quantum computers. Dealing with feedback in quantum control (i.e. using measurements to steer the dynamics) is especially difficult since the control choices get exponentially large. The system studied here can be modelled as a cavity, that can be weakly measured to obtain partial information about each energy level. To prepare and stabilize quantum states in such a cavity, we use reinforcement learning (RL). RL is a branch of machine learning that deals with control problems. In an RL framework, the algorithm tries to maximize an objective function (in this case the fidelity) by interacting with the system via a trial-and-error process. In this work, RL manages to prepare complex superpositions of the Fock state in the cavity, with only very limited linear control. The RL agent also learns to stabilize quantum states against different forms of decay.

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