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.
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.
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.
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.
To realize the full potential of quantum technologies, finding good strategies to control quantum information processing devices in real time becomes increasingly important. Usually these strategies require a precise understanding of the device itself, which is generally not available. Model-free reinforcement learning circumvents this need by discovering control strategies from scratch without relying on an accurate description of the quantum system. Furthermore, important tasks like state preparation, gate teleportation and error correction need feedback at time scales much shorter than the coherence time, which for superconducting circuits is in the microsecond range. Developing and training a deep reinforcement learning agent able to operate in this real-time feedback regime has been an open challenge. Here, we have implemented such an agent in the form of a latency-optimized deep neural network on a field-programmable gate array (FPGA). We demonstrate its use to efficiently initialize a superconducting qubit into a target state. To train the agent, we use model-free reinforcement learning that is based solely on measurement data. We study the agent's performance for strong and weak measurements, and for three-level readout, and compare with simple strategies based on thresholding. This demonstration motivates further research towards adoption of reinforcement learning for real-time feedback control of quantum devices and more generally any physical system requiring learnable low-latency feedback control.
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.
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.
Quantum state stabilization is a pivotal element in the realm of quantum control, forming the bedrock for various quantum tasks. To achieve the stabilization of a quantum state, it is imperative to formulate effective control channels (represented by control Hamiltonians) and devise the appropriate control signals. In this study, we introduce a novel approach, the selection of control Hamiltonians through Deep reinforcement learning (SCH-DRL), to address the challenge of control Hamiltonian selection in quantum control. Deep reinforcement learning (DRL) is employed to generate control signals corresponding to control Hamiltonians, and SCH-DRL utilizes these control signals to recognize a set of simple and efficient control Hamiltonians, depending on different target states. This approach not only provides a method for control Hamiltonian selection in quantum state stabilization but also unveils the untapped potential of DRL for a broad spectrum of applications in the field of quantum information. Through applications in two-qubit and three-qubit scenarios, we demonstrate how the SCH-DRL method adeptly selects the quantity of control Hamiltonians for achieving the desired stability of quantum states.