Approximate combinatorial optimisation has emerged as one of the most promising application areas for quantum computers, particularly those in the near term. In this work, we focus on the quantum approximate optimisation algorithm (QAOA) for solving the MaxCut problem. Specifically, we address two problems in the QAOA, how to initialise the algorithm, and how to subsequently train the parameters to find an optimal solution. For the former, we propose graph neural networks (GNNs) as a warm-starting technique for QAOA. We demonstrate that merging GNNs with QAOA can outperform both approaches individually. Furthermore, we demonstrate how graph neural networks enables warm-start generalisation across not only graph instances, but also to increasing graph sizes, a feature not straightforwardly available to other warm-starting methods. For training the QAOA, we test several optimisers for the MaxCut problem up to 16 qubits and benchmark against vanilla gradient descent. These include quantum aware/agnostic and machine learning based/neural optimisers. Examples of the latter include reinforcement and meta-learning. With the incorporation of these initialisation and optimisation toolkits, we demonstrate how the optimisation problems can be solved using QAOA in an end-to-end differentiable pipeline.
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The ideal realization of quantum teleportation relies on having access to a maximally entangled state; however, in practice, such an ideal state is typically not available and one can instead only realize an approximate teleportation. With this in mind, we present a method to quantify the performance of approximate teleportation when using an arbitrary resource state. More specifically, after framing the task of approximate teleportation as an optimization of a simulation error over one-way local operations and classical communication (LOCC) channels, we establish a semi-definite relaxation of this optimization task by instead optimizing over the larger set of two-PPT-extendible channels. The main analytical calculations in our paper consist of exploiting the unitary covariance symmetry of the identity channel to establish a significant reduction of the computational cost of this latter optimization. Next, by exploiting known connections between approximate teleportation and quantum error correction, we also apply these concepts to establish bounds on the performance of approximate quantum error correction over a given quantum channel. Finally, we evaluate our bounds for various examples of resource states and channels.
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.
We consider a discrete-time multi-channel network where the destination collects time-sensitive packets from multiple sources with sided channel information. The popular metric, Age of Information (AoI), is applied to measure the data freshness at the destination. Due to the interference constraint, only disjoint source-channel pairs can be chosen for transmission in each time slot, and the decision maker should choose the optimal scheduling pairs to minimize the average AoI at the destination. To learn the optimal channel selection, we apply the linear contextual bandit (LCB) framework by utilizing the sided information provided by pilots. Concretely, we establish the relationship between AoI regret and sub-optimal channel selection times and propose both age-independent and age-dependent algorithms. The former method is proven to achieve the sub-linear AoI regret but is outperformed by the latter algorithm both in the linear and non-linear contextual model in simulation.
Explainability of Graph Neural Networks (GNNs) is critical to various GNN applications but remains an open challenge. A convincing explanation should be both necessary and sufficient simultaneously. However, existing GNN explaining approaches focus on only one of the two aspects, necessity or sufficiency, or a trade-off between the two. To search for the most necessary and sufficient explanation, the Probability of Necessity and Sufficiency (PNS) can be applied since it can mathematically quantify the necessity and sufficiency of an explanation. Nevertheless, the difficulty of obtaining PNS due to non-monotonicity and the challenge of counterfactual estimation limits its wide use. To address the non-identifiability of PNS, we resort to a lower bound of PNS that can be optimized via counterfactual estimation, and propose Necessary and Sufficient Explanation for GNN (NSEG) via optimizing that lower bound. Specifically, we employ nearest neighbor matching to generate counterfactual samples for the features, which is different from the random perturbation. In particular, NSEG combines the edges and node features to generate an explanation, where the common edge explanation is a special case of the combined explanation. Empirical study shows that NSEG achieves excellent performance in generating the most necessary and sufficient explanations among a series of state-of-the-art methods.
We consider the problem of estimating an unknown parameter vector ${\boldsymbol \theta}\in{\mathbb R}^n$, given noisy observations ${\boldsymbol Y} = {\boldsymbol \theta}{\boldsymbol \theta}^{\top}/\sqrt{n}+{\boldsymbol Z}$ of the rank-one matrix ${\boldsymbol \theta}{\boldsymbol \theta}^{\top}$, where ${\boldsymbol Z}$ has independent Gaussian entries. When information is available about the distribution of the entries of ${\boldsymbol theta}$, spectral methods are known to be strictly sub-optimal. Past work characterized the asymptotics of the accuracy achieved by the optimal estimator. However, no polynomial-time estimator is known that achieves this accuracy. It has been conjectured that this statistical-computation gap is fundamental, and moreover that the optimal accuracy achievable by polynomial-time estimators coincides with the accuracy achieved by certain approximate message passing (AMP) algorithms. We provide evidence towards this conjecture by proving that no estimator in the (broader) class of constant-degree polynomials can surpass AMP.
Function approximation is widely used in reinforcement learning to handle the computational difficulties associated with very large state spaces. However, function approximation introduces errors which may lead to instabilities when using approximate dynamic programming techniques to obtain the optimal policy. Therefore, techniques such as lookahead for policy improvement and m-step rollout for policy evaluation are used in practice to improve the performance of approximate dynamic programming with function approximation. We quantitatively characterize, for the first time, the impact of lookahead and m-step rollout on the performance of approximate dynamic programming (DP) with function approximation: (i) without a sufficient combination of lookahead and m-step rollout, approximate DP may not converge, (ii) both lookahead and m-step rollout improve the convergence rate of approximate DP, and (iii) lookahead helps mitigate the effect of function approximation and the discount factor on the asymptotic performance of the algorithm. Our results are presented for two approximate DP methods: one which uses least-squares regression to perform function approximation and another which performs several steps of gradient descent of the least-squares objective in each iteration.
Structural data well exists in Web applications, such as social networks in social media, citation networks in academic websites, and threads data in online forums. Due to the complex topology, it is difficult to process and make use of the rich information within such data. Graph Neural Networks (GNNs) have shown great advantages on learning representations for structural data. However, the non-transparency of the deep learning models makes it non-trivial to explain and interpret the predictions made by GNNs. Meanwhile, it is also a big challenge to evaluate the GNN explanations, since in many cases, the ground-truth explanations are unavailable. In this paper, we take insights of Counterfactual and Factual (CF^2) reasoning from causal inference theory, to solve both the learning and evaluation problems in explainable GNNs. For generating explanations, we propose a model-agnostic framework by formulating an optimization problem based on both of the two casual perspectives. This distinguishes CF^2 from previous explainable GNNs that only consider one of them. Another contribution of the work is the evaluation of GNN explanations. For quantitatively evaluating the generated explanations without the requirement of ground-truth, we design metrics based on Counterfactual and Factual reasoning to evaluate the necessity and sufficiency of the explanations. Experiments show that no matter ground-truth explanations are available or not, CF^2 generates better explanations than previous state-of-the-art methods on real-world datasets. Moreover, the statistic analysis justifies the correlation between the performance on ground-truth evaluation and our proposed metrics.
Graph neural networks (GNNs) is widely used to learn a powerful representation of graph-structured data. Recent work demonstrates that transferring knowledge from self-supervised tasks to downstream tasks could further improve graph representation. However, there is an inherent gap between self-supervised tasks and downstream tasks in terms of optimization objective and training data. Conventional pre-training methods may be not effective enough on knowledge transfer since they do not make any adaptation for downstream tasks. To solve such problems, we propose a new transfer learning paradigm on GNNs which could effectively leverage self-supervised tasks as auxiliary tasks to help the target task. Our methods would adaptively select and combine different auxiliary tasks with the target task in the fine-tuning stage. We design an adaptive auxiliary loss weighting model to learn the weights of auxiliary tasks by quantifying the consistency between auxiliary tasks and the target task. In addition, we learn the weighting model through meta-learning. Our methods can be applied to various transfer learning approaches, it performs well not only in multi-task learning but also in pre-training and fine-tuning. Comprehensive experiments on multiple downstream tasks demonstrate that the proposed methods can effectively combine auxiliary tasks with the target task and significantly improve the performance compared to state-of-the-art methods.
Co-saliency detection aims to discover the common and salient foregrounds from a group of relevant images. For this task, we present a novel adaptive graph convolutional network with attention graph clustering (GCAGC). Three major contributions have been made, and are experimentally shown to have substantial practical merits. First, we propose a graph convolutional network design to extract information cues to characterize the intra- and interimage correspondence. Second, we develop an attention graph clustering algorithm to discriminate the common objects from all the salient foreground objects in an unsupervised fashion. Third, we present a unified framework with encoder-decoder structure to jointly train and optimize the graph convolutional network, attention graph cluster, and co-saliency detection decoder in an end-to-end manner. We evaluate our proposed GCAGC method on three cosaliency detection benchmark datasets (iCoseg, Cosal2015 and COCO-SEG). Our GCAGC method obtains significant improvements over the state-of-the-arts on most of them.
Graph neural networks (GNNs) are a popular class of machine learning models whose major advantage is their ability to incorporate a sparse and discrete dependency structure between data points. Unfortunately, GNNs can only be used when such a graph-structure is available. In practice, however, real-world graphs are often noisy and incomplete or might not be available at all. With this work, we propose to jointly learn the graph structure and the parameters of graph convolutional networks (GCNs) by approximately solving a bilevel program that learns a discrete probability distribution on the edges of the graph. This allows one to apply GCNs not only in scenarios where the given graph is incomplete or corrupted but also in those where a graph is not available. We conduct a series of experiments that analyze the behavior of the proposed method and demonstrate that it outperforms related methods by a significant margin.
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