We generalize a standard benchmark of reinforcement learning, the classical cartpole balancing problem, to the quantum regime by stabilizing a particle in an unstable potential through measurement and feedback. We use state-of-the-art deep reinforcement learning to stabilize a quantum cartpole and find that our deep learning approach performs comparably to or better than other strategies in standard control theory. Our approach also applies to measurement-feedback cooling of quantum oscillators, showing the applicability of deep learning to general continuous-space quantum control.
We generalize a standard benchmark of reinforcement learning, the classical cartpole balancing problem, to the quantum regime by stabilizing a particle in an unstable potential through measurement and feedback. We use state-of-the-art deep reinforcement learning to stabilize a quantum cartpole and find that our deep learning approach performs comparably to or better than other strategies in standard control theory. Our approach also applies to measurement-feedback cooling of quantum oscillators, showing the applicability of deep learning to general continuous-space quantum control.
Feedback-based control is the de-facto standard when it comes to controlling classical stochastic systems and processes. However, standard feedback-based control methods are challenged by quantum systems due to measurement induced backaction and partial observability. Here we remedy this by using weak quantum measurements and model-free reinforcement learning agents to perform quantum control. By comparing control algorithms with and without state estimators to stabilize a quantum particle in an unstable state near a local potential energy maximum, we show how a trade-off between state estimation and controllability arises. For the scenario where the classical analogue is highly nonlinear, the reinforcement learned controller has an advantage over the standard controller. Additionally, we demonstrate the feasibility of using transfer learning to develop a quantum control agent trained via reinforcement learning on a classical surrogate of the quantum control problem. Finally, we present results showing how the reinforcement learning control strategy differs from the classical controller in the non-linear scenarios.
In this thesis, we consider two simple but typical control problems and apply deep reinforcement learning to them, i.e., to cool and control a particle which is subject to continuous position measurement in a one-dimensional quadratic potential or in a quartic potential. We compare the performance of reinforcement learning control and conventional control strategies on the two problems, and show that the reinforcement learning achieves a performance comparable to the optimal control for the quadratic case, and outperforms conventional control strategies for the quartic case for which the optimal control strategy is unknown. To our knowledge, this is the first time deep reinforcement learning is applied to quantum control problems in continuous real space. Our research demonstrates that deep reinforcement learning can be used to control a stochastic quantum system in real space effectively as a measurement-feedback closed-loop controller, and our research also shows the ability of AI to discover new control strategies and properties of the quantum systems that are not well understood, and we can gain insights into these problems by learning from the AI, which opens up a new regime for scientific research.
With the development of experimental quantum technology, quantum control has attracted increasing attention due to the realization of controllable artificial quantum systems. However, because quantum-mechanical systems are often too difficult to analytically deal with, heuristic strategies and numerical algorithms which search for proper control protocols are adopted, and, deep learning, especially deep reinforcement learning (RL), is a promising generic candidate solution for the control problems. Although there have been a few successful applications of deep RL to quantum control problems, most of the existing RL algorithms suffer from instabilities and unsatisfactory reproducibility, and require a large amount of fine-tuning and a large computational budget, both of which limit their applicability. To resolve the issue of instabilities, in this dissertation, we investigate the non-convergence issue of Q-learning. Then, we investigate the weakness of existing convergent approaches that have been proposed, and we develop a new convergent Q-learning algorithm, which we call the convergent deep Q network (C-DQN) algorithm, as an alternative to the conventional deep Q network (DQN) algorithm. We prove the convergence of C-DQN and apply it to the Atari 2600 benchmark. We show that when DQN fail, C-DQN still learns successfully. Then, we apply the algorithm to the measurement-feedback cooling problems of a quantum quartic oscillator and a trapped quantum rigid body. We establish the physical models and analyse their properties, and we show that although both C-DQN and DQN can learn to cool the systems, C-DQN tends to behave more stably, and when DQN suffers from instabilities, C-DQN can achieve a better performance. As the performance of DQN can have a large variance and lack consistency, C-DQN can be a better choice for researches on complicated control problems.
Closed loop quantum control uses measurement to control the dynamics of a quantum system to achieve either a desired target state or target dynamics. In the case when the quantum Hamiltonian is quadratic in x and p, there are known optimal control techniques to drive the dynamics toward particular states, e.g., the ground state. However, for nonlinear Hamiltonian such control techniques often fail. We apply deep reinforcement learning (DRL), where an artificial neural agent explores and learns to control the quantum evolution of a highly nonlinear system (double well), driving the system toward the ground state with high fidelity. We consider a DRL strategy which is particularly motivated by experiment where the quantum system is continuously but weakly measured. This measurement is then fed back to the neural agent and used for training. We show that the DRL can effectively learn counterintuitive strategies to cool the system to a nearly pure "cat" state, which has a high overlap fidelity with the true ground state.
The stabilization of quantum states is a fundamental problem for realizing various quantum technologies. Measurement-based-feedback strategies have demonstrated powerful performance, and the construction of quantum control signals using measurement information has attracted great interest. However, the interaction between quantum systems and the environment is inevitable, especially when measurements are introduced, which leads to decoherence. To mitigate decoherence, it is desirable to stabilize quantum systems faster, thereby reducing the time of interaction with the environment. In this paper, we utilize information obtained from measurement and apply deep reinforcement learning (DRL) algorithms, without explicitly constructing specific complex measurement-control mappings, to rapidly drive random initial quantum state to the target state. The proposed DRL algorithm has the ability to speed up the convergence to a target state, which shortens the interaction between quantum systems and their environments to protect coherence. Simulations are performed on two-qubit and three-qubit systems, and the results show that our algorithm can successfully stabilize random initial quantum system to the target entangled state, with a convergence time faster than traditional methods such as Lyapunov feedback control and several DRL algorithms with different reward functions. Moreover, it exhibits robustness against imperfect measurements and delays in system evolution.
Real-time feedback control of quantum systems is often limited by partial observations, nonlinear dynamics and measurement noise, which make accurate model-based controllers difficult to design. Here we show that deep reinforcement learning can cool the motion of a single neutral atom coupled to a high-finesse optical cavity using only the continuously monitored cavity transmission. We first train the controller in simulation and then transfer it to the experiment, where online fine-tuning adapts it to unmodeled experimental dynamics. The learned policy damps the atom's motion in real time and achieves a cooling time constant of 388 +/- 14 microseconds, corresponding to only two motional periods in the trap. It also outperforms a standard linear differentiator controller in cooling speed while maintaining comparable atom retention over a broad range of operating conditions. These results establish reinforcement learning as a practical strategy for feedback control in quantum-limited experiments where compact analytical models are incomplete.