Abstract Investigating quantum advantage in the NISQ era is a challenging problem whereas quantum machine learning becomes the most promising application that can be resorted to. However, no proposal has been investigated for arguably challenging inverse reinforcement learning to demonstrate the potential advantage. In this work, we propose a hybrid quantum–classical inverse reinforcement learning algorithm based on the variational quantum circuit with the generative adversarial framework. We find an important connection between the quantum gradient anomaly and the performance degradation, which suggest a gradient clipping strategy to stabilize the training process. In light of the algorithm, we study three classic control problems and the Hamiltonian parameter estimation in quantum sensing with shallow quantum circuits. The numerical results showcase that the control-enhanced quantum sensor can saturate quantum Cramér-Rao bound only with a single variational layer, empirically demonstrating a parameter complexity advantage over the classical learning control. The proposed generative adversarial reinforcement learning algorithm achieves state-of-the-art performance in classical and quantum sensor control in terms of required number of parameters.
Abstract Investigating quantum advantage in the NISQ era is a challenging problem whereas quantum machine learning becomes the most promising application that can be resorted to. However, no proposal has been investigated for arguably challenging inverse reinforcement learning to demonstrate the potential advantage. In this work, we propose a hybrid quantum–classical inverse reinforcement learning algorithm based on the variational quantum circuit with the generative adversarial framework. We find an important connection between the quantum gradient anomaly and the performance degradation, which suggest a gradient clipping strategy to stabilize the training process. In light of the algorithm, we study three classic control problems and the Hamiltonian parameter estimation in quantum sensing with shallow quantum circuits. The numerical results showcase that the control-enhanced quantum sensor can saturate quantum Cramér-Rao bound only with a single variational layer, empirically demonstrating a parameter complexity advantage over the classical learning control. The proposed generative adversarial reinforcement learning algorithm achieves state-of-the-art performance in classical and quantum sensor control in terms of required number of parameters.
Despite remarkable successes in solving various complex decision-making tasks, training an imitation learning (IL) algorithm with deep neural networks (DNNs) suffers from the high-computational burden. In this work, we propose quantum IL (QIL) with a hope to utilize quantum advantage to speed up IL. Concretely, we develop two QIL algorithms: quantum behavioral cloning (Q-BC) and quantum generative adversarial IL (Q-GAIL). Q-BC is trained with a negative log-likelihood (NLL) loss in an offline manner that suits extensive expert data cases, whereas Q-GAIL works in an inverse reinforcement learning (IRL) scheme, which is online, on-policy, and is suitable for limited expert data cases. For both QIL algorithms, we adopt variational quantum circuits (VQCs) in place of DNNs for representing policies, which are modified with data reuploading and scaling parameters to enhance the expressivity. We first encode classical data into quantum states as inputs, then perform VQCs, and finally measure quantum outputs to obtain control signals of agents. Experiment results demonstrate that both Q-BC and Q-GAIL can achieve comparable performance compared to classical counterparts, with the potential of quantum speedup. To our knowledge, we are the first to propose the concept of QIL and conduct pilot studies, which paves the way for the quantum era.
Variational quantum circuits have recently gained popularity as quantum machine learning models. While considerable effort has been invested to train them in supervised and unsupervised learning settings, relatively little attention has been given to their potential use in reinforcement learning. In this work, we leverage the understanding of quantum policy gradient algorithms in a number of ways. First, we investigate how to construct and train reinforcement learning policies based on variational quantum circuits. We propose several designs for quantum policies, provide their learning algorithms, and test their performance on classical benchmarking environments. Second, we show the existence of task environments with a provable separation in performance between quantum learning agents and any polynomial-time classical learner, conditioned on the widely-believed classical hardness of the discrete logarithm problem. We also consider more natural settings, in which we show an empirical quantum advantage of our quantum policies over standard neural-network policies. Our results constitute a first step towards establishing a practical near-term quantum advantage in a reinforcement learning setting. Additionally, we believe that some of our design choices for variational quantum policies may also be beneficial to other models based on variational quantum circuits, such as quantum classifiers and quantum regression models.
Quantum computing has a superior advantage in tackling specific problems, such as integer factorization and Simon's problem. For more general tasks in machine learning, by applying variational quantum circuits, more and more quantum algorithms have been proposed recently, especially in supervised learning and unsupervised learning. However, little work has been done in reinforcement learning, arguably more important and challenging. Previous work in quantum reinforcement learning mainly focuses on discrete control tasks where the action space is discrete. In this work, we develop a quantum reinforcement learning algorithm based on soft actor-critic -- one of the state-of-the-art methods for continuous control. Specifically, we use a hybrid quantum-classical policy network consisting of a variational quantum circuit and a classical artificial neural network. Tested in a standard reinforcement learning benchmark, we show that this quantum version of soft actor-critic is comparable with the original soft actor-critic, using much less adjustable parameters. Furthermore, we analyze the effect of different hyper-parameters and policy network architectures, pointing out the importance of architecture design for quantum reinforcement learning.
Abstract Variational quantum circuits are being used as versatile quantum machine learning models. Some empirical results exhibit an advantage in supervised and generative learning tasks. However, when applied to reinforcement learning, less is known. In this work, we considered a variational quantum circuit composed of a low-depth hardware-efficient ansatz as the parameterized policy of a reinforcement learning agent. We show that an 𝜖-approximation of the policy gradient can be obtained using a logarithmic number of samples concerning the total number of parameters. We empirically verify that such quantum models behave similarly to typical classical neural networks used in standard benchmarking environments and quantum control, using only a fraction of the parameters. Moreover, we study the barren plateau phenomenon in quantum policy gradients using the Fisher information matrix spectrum.
Recent advancements in machine learning have revolutionised research across various fields. Despite their success, conventional learning techniques are hindered by their significant computational resources and energy requirements. Prompted by recent experimental breakthroughs in quantum computing, variational quantum machine learning (QML) – machine learning integrated with variational quantum circuits (VQCs) – has emerged as a promising alternative. Nonetheless, the theoretical framework underpinning the advantages of variational QML is still rudimentary. Specifically, the training of VQCs faces several challenges, such as the barren plateau problem, where the gradient diminishes exponentially with an increasing qubits. A related issue arises in variational QML training, where the convergence rate is exponentially small. In this thesis, we present theoretically guaranteed solutions to these challenges. First, we construct innovative circuit architectures to address the vanishing gradient problem in deep VQCs. We propose quantum controlled-layer and quantum ResNet structures, demonstrating that the expected gradient norm's lower bound is unaffected by the increase in qubits and circuit depth. Next, we introduce an initialization strategy to mitigate the vanishing gradient issue in general deep quantum circuits. We prove that Gaussian-initialized parameters ensure the gradient norm's decay rate remains inversely polynomial despite the increase in qubit numbers and circuit depth. Finally, we propose a novel and effective theory for analysing the training of quantum neural networks with moderate depths. We prove that, under certain randomness conditions in the circuits and datasets, training converges linearly with a rate inversely proportional to the dataset size. Our approach surpasses previous results, achieving exponentially larger convergence rates with modest depth, or conversely, requiring exponentially less depth for equivalent rates.
Quantum computing offers efficient encapsulation of high-dimensional states. In this work, we propose a novel quantum reinforcement learning approach that combines the Advantage Actor-Critic algorithm with variational quantum circuits by substituting parts of the classical components. This approach addresses reinforcement learning's scalability concerns while maintaining high performance. We empirically test multiple quantum Advantage Actor-Critic configurations with the well known Cart Pole environment to evaluate our approach in control tasks with continuous state spaces. Our results indicate that the hybrid strategy of using either a quantum actor or quantum critic with classical post-processing yields a substantial performance increase compared to pure classical and pure quantum variants with similar parameter counts. They further reveal the limits of current quantum approaches due to the hardware constraints of noisy intermediate-scale quantum computers, suggesting further research to scale hybrid approaches for larger and more complex control tasks.