Learning Informative Latent Representation for Quantum State Tomography

Quantum state tomography (QST) is the process of reconstructing the complete state of a quantum system (mathematically described as a density matrix) through a series of different measurements. These measurements are performed on a number of identical copies of the quantum system, with outcomes gathered as frequencies. QST aims to recover the density matrix and the corresponding properties of the quantum state from the measured frequencies. Although an informationally complete set of measurements can specify quantum state accurately in an ideal scenario with a large number of identical copies, both measurements and identical copies are restricted and imperfect in practical scenarios, making QST highly ill-posed. The conventional QST methods usually assume adequate or accurate measured frequencies or rely on manually designed regularizers to handle the ill-posed reconstruction problem, suffering from limited applications in realistic scenarios. Recent advances in deep neural networks (DNNs) led to the emergence of deep learning (DL) in QST. However, existing DL-based QST approaches often employ generic DNN models that are not optimized for imperfect conditions of QST. In this paper, we propose a transformer-based autoencoder architecture tailored for QST with imperfect measurement data. Our method leverages a transformer-based encoder to extract an informative latent representation (ILR) from imperfect measurement data and employs a decoder to predict the quantum states based on the ILR. We anticipate that the high-dimensional ILR will capture more comprehensive information about quantum states. To achieve this, we conduct pre-training of the encoder using a pretext task that involves reconstructing high-quality frequencies from measured frequencies. Extensive simulations and experiments demonstrate the remarkable ability of the ILR in dealing with imperfect measurement data in QST.

Attention-Based Transformer Networks for Quantum State Tomography

Neural networks have been actively explored for quantum state tomography (QST) due to their favorable expressibility. To further enhance the efficiency of reconstructing quantum states, we explore the similarity between language modeling and quantum state tomography and propose an attention-based QST method that utilizes the Transformer network to capture the correlations between measured results from different measurements. Our method directly retrieves the density matrices of quantum states from measured statistics, with the assistance of an integrated loss function that helps minimize the difference between the actual states and the retrieved states. Then, we systematically trace different impacts within a bag of common training strategies involving various parameter adjustments on the attention-based QST method. Combining these techniques, we establish a robust baseline that can efficiently reconstruct pure and mixed quantum states. Furthermore, by comparing the performance of three popular neural network architectures (FCNs, CNNs, and Transformer), we demonstrate the remarkable expressiveness of attention in learning density matrices from measured statistics.

Auxiliary Task-based Deep Reinforcement Learning for Quantum Control

Due to its property of not requiring prior knowledge of the environment, reinforcement learning has significant potential for quantum control problems. In this work, we investigate the effectiveness of continuous control policies based on deep deterministic policy gradient. To solve the sparse reward signal in quantum learning control problems, we propose an auxiliary task-based deep reinforcement learning (AT-DRL) for quantum control. In particular, we first design a guided reward function based on the fidelity of quantum states that enables incremental fidelity improvement. Then, we introduce the concept of an auxiliary task whose network shares parameters with the main network to predict the reward provided by the environment (called the main task). The auxiliary task learns synchronously with the main task, allowing one to select the most relevant features of the environment, thus aiding the agent in comprehending how to achieve the desired state. The numerical simulations demonstrate that the proposed AT-DRL can provide a solution to the sparse reward in quantum systems, and has great potential in designing control pulses that achieve efficient quantum state preparation.

A Dirichlet Process Mixture of Robust Task Models for Scalable Lifelong Reinforcement Learning

While reinforcement learning (RL) algorithms are achieving state-of-the-art performance in various challenging tasks, they can easily encounter catastrophic forgetting or interference when faced with lifelong streaming information. In the paper, we propose a scalable lifelong RL method that dynamically expands the network capacity to accommodate new knowledge while preventing past memories from being perturbed. We use a Dirichlet process mixture to model the non-stationary task distribution, which captures task relatedness by estimating the likelihood of task-to-cluster assignments and clusters the task models in a latent space. We formulate the prior distribution of the mixture as a Chinese restaurant process (CRP) that instantiates new mixture components as needed. The update and expansion of the mixture are governed by the Bayesian non-parametric framework with an expectation maximization (EM) procedure, which dynamically adapts the model complexity without explicit task boundaries or heuristics. Moreover, we use the domain randomization technique to train robust prior parameters for the initialization of each task model in the mixture, thus the resulting model can better generalize and adapt to unseen tasks. With extensive experiments conducted on robot navigation and locomotion domains, we show that our method successfully facilitates scalable lifelong RL and outperforms relevant existing methods.

Efficient Bayesian Policy Reuse with a Scalable Observation Model in Deep Reinforcement Learning

Bayesian policy reuse (BPR) is a general policy transfer framework for selecting a source policy from an offline library by inferring the task belief based on some observation signals and a trained observation model. In this paper, we propose an improved BPR method to achieve more efficient policy transfer in deep reinforcement learning (DRL). First, most BPR algorithms use the episodic return as the observation signal that contains limited information and cannot be obtained until the end of an episode. Instead, we employ the state transition sample, which is informative and instantaneous, as the observation signal for faster and more accurate task inference. Second, BPR algorithms usually require numerous samples to estimate the probability distribution of the tabular-based observation model, which may be expensive and even infeasible to learn and maintain, especially when using the state transition sample as the signal. Hence, we propose a scalable observation model based on fitting state transition functions of source tasks from only a small number of samples, which can generalize to any signals observed in the target task. Moreover, we extend the offline-mode BPR to the continual learning setting by expanding the scalable observation model in a plug-and-play fashion, which can avoid negative transfer when faced with new unknown tasks. Experimental results show that our method can consistently facilitate faster and more efficient policy transfer.

Depthwise Convolution for Multi-Agent Communication with Enhanced Mean-Field Approximation

Multi-agent settings remain a fundamental challenge in the reinforcement learning (RL) domain due to the partial observability and the lack of accurate real-time interactions across agents. In this paper, we propose a new method based on local communication learning to tackle the multi-agent RL (MARL) challenge within a large number of agents coexisting. First, we design a new communication protocol that exploits the ability of depthwise convolution to efficiently extract local relations and learn local communication between neighboring agents. To facilitate multi-agent coordination, we explicitly learn the effect of joint actions by taking the policies of neighboring agents as inputs. Second, we introduce the mean-field approximation into our method to reduce the scale of agent interactions. To more effectively coordinate behaviors of neighboring agents, we enhance the mean-field approximation by a supervised policy rectification network (PRN) for rectifying real-time agent interactions and by a learnable compensation term for correcting the approximation bias. The proposed method enables efficient coordination as well as outperforms several baseline approaches on the adaptive traffic signal control (ATSC) task and the StarCraft II multi-agent challenge (SMAC).

Path Planning for Cellular-Connected UAV: A DRL Solution with Quantum-Inspired Experience Replay

In cellular-connected unmanned aerial vehicle (UAV) network, a minimization problem on the weighted sum of time cost and expected outage duration is considered. Taking advantage of UAV's adjustable mobility, an intelligent UAV navigation approach is formulated to achieve the aforementioned optimization goal. Specifically, after mapping the navigation task into a Markov decision process (MDP), a deep reinforcement learning (DRL) solution with novel quantum-inspired experience replay (QiER) framework is proposed to help the UAV find the optimal flying direction within each time slot, and thus the designed trajectory towards the destination can be generated. Via relating experienced transition's importance to its associated quantum bit (qubit) and applying Grover iteration based amplitude amplification technique, the proposed DRL-QiER solution can commit a better trade-off between sampling priority and diversity. Compared to several representative baselines, the effectiveness and supremacy of the proposed DRL-QiER solution are demonstrated and validated in numerical results.

Residual Tensor Train: a Flexible and Efficient Approach for Learning Multiple Multilinear Correlations

Tensor Train (TT) approach has been successfully applied in the modelling of the multilinear interaction of features. Nevertheless, the existing models lack flexibility and generalizability, as they only model a single type of high-order correlation. In practice, multiple multilinear correlations may exist within the features. In this paper, we present a novel Residual Tensor Train (ResTT) which integrates the merits of TT and residual structure to capture the multilinear feature correlations, from low to higher orders, within the same model. In particular, we prove that the fully-connected layer in neural networks and the Volterra series can be taken as special cases of ResTT. Furthermore, we derive the rule for weight initialization that stabilizes the training of ResTT based on a mean-field analysis. We prove that such a rule is much more relaxed than that of TT, which means ResTT can easily address the vanishing and exploding gradient problem that exists in the current TT models. Numerical experiments demonstrate that ResTT outperforms the state-of-the-art tensor network approaches, and is competitive with the benchmark deep learning models on MNIST and Fashion-MNIST datasets.

Rule-Based Reinforcement Learning for Efficient Robot Navigation with Space Reduction

For real-world deployments, it is critical to allow robots to navigate in complex environments autonomously. Traditional methods usually maintain an internal map of the environment, and then design several simple rules, in conjunction with a localization and planning approach, to navigate through the internal map. These approaches often involve a variety of assumptions and prior knowledge. In contrast, recent reinforcement learning (RL) methods can provide a model-free, self-learning mechanism as the robot interacts with an initially unknown environment, but are expensive to deploy in real-world scenarios due to inefficient exploration. In this paper, we focus on efficient navigation with the RL technique and combine the advantages of these two kinds of methods into a rule-based RL (RuRL) algorithm for reducing the sample complexity and cost of time. First, we use the rule of wall-following to generate a closed-loop trajectory. Second, we employ a reduction rule to shrink the trajectory, which in turn effectively reduces the redundant exploration space. Besides, we give the detailed theoretical guarantee that the optimal navigation path is still in the reduced space. Third, in the reduced space, we utilize the Pledge rule to guide the exploration strategy for accelerating the RL process at the early stage. Experiments conducted on real robot navigation problems in hex-grid environments demonstrate that RuRL can achieve improved navigation performance.

Deep Reinforcement Learning with Quantum-inspired Experience Replay

In this paper, a novel training paradigm inspired by quantum computation is proposed for deep reinforcement learning (DRL) with experience replay. In contrast to traditional experience replay mechanism in DRL, the proposed deep reinforcement learning with quantum-inspired experience replay (DRL-QER) adaptively chooses experiences from the replay buffer according to the complexity and the replayed times of each experience (also called transition), to achieve a balance between exploration and exploitation. In DRL-QER, transitions are first formulated in quantum representations, and then the preparation operation and the depreciation operation are performed on the transitions. In this progress, the preparation operation reflects the relationship between the temporal difference errors (TD-errors) and the importance of the experiences, while the depreciation operation is taken into account to ensure the diversity of the transitions. The experimental results on Atari 2600 games show that DRL-QER outperforms state-of-the-art algorithms such as DRL-PER and DCRL on most of these games with improved training efficiency, and is also applicable to such memory-based DRL approaches as double network and dueling network.