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QGHNN: A quantum graph Hamiltonian neural network
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Abstract
Representing and learning from graphs is essential for developing effective machine learning models tailored to non-Euclidean data. While Graph Neural Networks (GNNs) strive to address the challenges posed by complex, high-dimensional graph data, Quantum Neural Networks (QNNs) present a compelling alternative due to their potential for quantum parallelism. However, much of the current QNN research tends to overlook the vital connection between quantum state encoding and graph structures, which limits the full exploitation of quantum computational advantages. To address these challenges, this paper introduces a quantum graph Hamiltonian neural network (QGHNN) to enhance graph representation and learning on noisy intermediate-scale quantum computers. Concretely, a quantum graph Hamiltonian learning method (QGHL) is first created by mapping graphs to the Hamiltonian of the topological quantum system. Then, QGHNN based on QGHL is presented, which trains parameters by minimizing the loss function and uses the gradient descent method to learn the graph. Experiments on the PennyLane quantum platform reveal that QGHNN outperforms all assessment metrics, achieving the lowest mean squared error of \textbf{0.004} and the maximum cosine similarity of \textbf{}, which shows that QGHNN not only excels in representing and learning graph information, but it also has high robustness ability. QGHNN can reduce the impact of quantum noise and has significant potential application in future research of quantum knowledge graphs and recommendation systems.
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The Self-Attention Mechanism (SAM) excels at distilling important information from the interior of data to improve the computational efficiency of models. Nevertheless, many Quantum Machine Learning (QML) models lack the ability to distinguish the intrinsic connections of information like SAM, which limits their effectiveness on massive high-dimensional quantum data. To tackle the above issue, a Quantum Kernel Self-Attention Mechanism (QKSAM) is introduced to combine the data representation merit of Quantum Kernel Methods (QKM) with the efficient information extraction capability of SAM. Further, a Quantum Kernel Self-Attention Network (QKSAN) framework is proposed based on QKSAM, which ingeniously incorporates the Deferred Measurement Principle (DMP) and conditional measurement techniques to release half of quantum resources by mid-circuit measurement, thereby bolstering both feasibility and adaptability. Simultaneously, the Quantum Kernel Self-Attention Score (QKSAS) with an exponentially large characterization space is spawned to accommodate more information and determine the measurement conditions. Eventually, four QKSAN sub-models are deployed on PennyLane and IBM Qiskit platforms to perform binary classification on MNIST and Fashion MNIST, where the QKSAS tests and correlation assessments between noise immunity and learning ability are executed on the best-performing sub-model. The paramount experimental finding is that the QKSAN subclasses possess the potential learning advantage of acquiring impressive accuracies exceeding 98.05% with far fewer parameters than classical machine learning models. Predictably, QKSAN lays the foundation for future quantum computers to perform machine learning on massive amounts of data while driving advances in areas such as quantum computer vision.
Natural language processing (NLP) may face the inexplicable “black-box” problem of parameters and unreasonable modeling for lack of embedding of some characteristics of natural language, while the quantum-inspired models based on quantum theory may provide a potential solution. However, the essential prior knowledge and pretrained text features are often ignored at the early stage of the development of quantum-inspired models. To attacking the above challenges, a pretrained quantum-inspired deep neural network is proposed in this work, which is constructed based on quantum theory for carrying out strong performance and great interpretability in related NLP fields. Concretely, a quantum-inspired pretrained feature embedding (QPFE) method is first developed to model superposition states for words to embed more textual features. Then, a QPFE-ERNIE model is designed by merging the semantic features learned from the prevalent pretrained model ERNIE, which is verified with two NLP downstream tasks: 1) sentiment classification and 2) word sense disambiguation (WSD). In addition, schematic quantum circuit diagrams are provided, which has potential impetus for the future realization of quantum NLP with quantum device. Finally, the experiment results demonstrate QPFE-ERNIE is significantly better for sentiment classification than gated recurrent unit (GRU), BiLSTM, and TextCNN on five datasets in all metrics and achieves better results than ERNIE in accuracy, F1-score, and precision on two datasets (CR and SST), and it also has advantage for WSD over the classical models, including BERT (improves F1-score by
5.2
on average) and ERNIE (improves F1-score by
4.2
on average) and improves the F1-score by
8.7
on average compared with a previous quantum-inspired model QWSD. QPFE-ERNIE provides a novel pretrained quantum-inspired model for solving NLP problems, and it lays a foundation for exploring more quantum-inspired models in the future.
We study the problem of learning the parameters for the Hamiltonian of a quantum many-body system, given limited access to the system. In this work, we build upon recent approaches to Hamiltonian learning via derivative estimation. We propose a protocol that improves the scaling dependence of prior works, particularly with respect to parameters relating to the structure of the Hamiltonian (e.g., its locality k). Furthermore, by deriving exact bounds on the performance of our protocol, we are able to provide a precise numerical prescription for theoretically optimal settings of hyperparameters in our learning protocol, such as the maximum evolution time (when learning with unitary dynamics) or minimum temperature (when learning with Gibbs states). Thanks to these improvements, our protocol has practical scaling for large problems: we demonstrate this with a numerical simulation of our protocol on an 80-qubit system.
The Hamiltonian of an isolated quantum-mechanical system determines its dynamics and physical behavior. This study investigates the possibility of learning and utilizing a system's Hamiltonian and its variational thermal state estimation for data analysis techniques. For this purpose, we employ the method of quantum Hamiltonian-based models for the generative modeling of simulated Large Hadron Collider data and demonstrate the representability of such data as a mixed state. In a further step, we use the learned Hamiltonian for anomaly detection, showing that different sample types can form distinct dynamical behaviors once treated as a quantum many-body system. We exploit these characteristics to quantify the difference between sample types. Our findings show that the methodologies designed for field theory computations can be utilized in machine learning applications to employ theoretical approaches in data analysis techniques.
Heterogeneous attribute data composed of attributes with different types of values are quite common in a variety of real-world applications. As data annotation is usually expensive, clustering has provided a promising way for processing unlabeled data, where the adopted similarity measure plays a key role in determining the clustering accuracy. However, it is a very challenging task to appropriately define the similarity between data objects with heterogeneous attributes because the values from heterogeneous attributes are generally with very different characteristics. Specifically, numerical attributes are with quantitative values, while categorical attributes are with qualitative values. Furthermore, categorical attributes can be categorized into nominal and ordinal ones according to the order information of their values. To circumvent the awkward gap among the heterogeneous attributes, this article will propose a new dissimilarity metric for cluster analysis of such data. We first study the connections among the heterogeneous attributes and build graph representations for them. Then, a metric is proposed, which computes the dissimilarities between attribute values under the guidance of the graph structures. Finally, we develop a new
k
-means-type clustering algorithm associated with this proposed metric. It turns out that the proposed method is competent to perform cluster analysis of datasets composed of an arbitrary combination of numerical, nominal, and ordinal attributes. Experimental results show its efficacy in comparison with its counterparts.
Hamiltonian learning, as an important quantum machine learning technique, provides a significant approach for determining an accurate quantum system. This paper establishes parameterized Hamiltonian learning (PHL) and explores its application and implementation on quantum computers. A parameterized quantum circuit for Hamiltonian learning is first created by decomposing unitary operators to excite the system evolution. Then, a PHL algorithm is developed to prepare a specific Hamiltonian system by iteratively updating the gradient of the loss function about circuit parameters. Finally, the experiments are conducted on Origin Pilot, and it demonstrates that the PHL algorithm can deal with the image segmentation problem and provide a segmentation solution accurately. Compared with the classical Grabcut algorithm, the PHL algorithm eliminates the requirement of early manual intervention. It provides a new possibility for solving practical application problems with quantum devices, which also assists in solving increasingly complicated problems and supports a much wider range of application possibilities in the future.
Variational quantum algorithms (VQAs) are expected to be a path to quantum advantages on noisy intermediate-scale quantum devices. However, both empirical and theoretical results exhibit that the deployed ansatz heavily affects the performance of VQAs such that an ansatz with a larger number of quantum gates enables a stronger expressivity, while the accumulated noise may render a poor trainability. To maximally improve the robustness and trainability of VQAs, here we devise a resource and runtime efficient scheme termed quantum architecture search (QAS). In particular, given a learning task, QAS automatically seeks a near-optimal ansatz (i.e., circuit architecture) to balance benefits and side-effects brought by adding more noisy quantum gates to achieve a good performance. We implement QAS on both the numerical simulator and real quantum hardware, via the IBM cloud, to accomplish data classification and quantum chemistry tasks. In the problems studied, numerical and experimental results show that QAS cannot only alleviate the influence of quantum noise and barren plateaus but also outperforms VQAs with pre-selected ansatze.
Reconstructing complex networks from observed data is a fundamental problem in network science. Compressive sensing, widely used for recovery of sparse signals, has also been used for network reconstruction under the assumption that networks are sparse. However, heterogeneous networks are not exactly sparse. Moreover, when using compressive sensing to recover signals, the projection matrix is usually a random matrix that satisfies the restricted isometry property (RIP) condition. This condition is much harder to satisfy during network reconstruction because the projection matrix depends on time-series data of network dynamics. To overcome these shortcomings, we devised a novel approach by adapting the alternating direction method of multipliers to find a candidate adjacency matrix. Then we used clustering to identify high-degree nodes. Finally, we replaced the elements of the candidate adjacency vectors of high-degree nodes, which are likely to be incorrect, with the corresponding elements of small-degree nodes, which are likely to be correct. The proposed method thus overcomes the shortcomings of compressive sensing and is suitable for reconstructing heterogeneous networks. Experiments with both artificial scale-free and empirical networks showed that the proposed method is accurate and robust.
Computational quantum technologies are entering a new phase in which noisy intermediate-scale quantum computers are available, but are still too small to benefit from active error correction. Even with a finite coherence budget to invest in quantum information processing, noisy devices with about 50 qubits are expected to experimentally demonstrate quantum supremacy in the next few years. Defined in terms of artificial tasks, current proposals for quantum supremacy, even if successful, will not help to provide solutions to practical problems. Instead, we believe that future users of quantum computers are interested in actual applications and that noisy quantum devices may still provide value by approximately solving hard combinatorial problems via hybrid classical-quantum algorithms. To lower bound the size of quantum computers with practical utility, we perform realistic simulations of the Quantum Approximate Optimization Algorithm and conclude that quantum speedup will not be attainable, at least for a representative combinatorial problem, until several hundreds of qubits are available.
Recent progress implies that a crossover between machine learning and quantum information processing benefits both fields. Traditional machine learning has dramatically improved the benchmarking and control of experimental quantum computing systems, including adaptive quantum phase estimation and designing quantum computing gates. On the other hand, quantum mechanics offers tantalizing prospects to enhance machine learning, ranging from reduced computational complexity to improved generalization performance. The most notable examples include quantum enhanced algorithms for principal component analysis, quantum support vector machines, and quantum Boltzmann machines. Progress has been rapid, fostered by demonstrations of midsized quantum optimizers which are predicted to soon outperform their classical counterparts. Further, we are witnessing the emergence of a physical theory pinpointing the fundamental and natural limitations of learning. Here we survey the cutting edge of this merger and list several open problems.
Identifying an accurate model for the dynamics of a quantum system is a
vexing problem that underlies a range of problems in experimental physics and
quantum information theory. Recently, a method called quantum Hamiltonian
learning has been proposed by the present authors that uses quantum simulation
as a resource for modeling an unknown quantum system. This approach can, under
certain circumstances, allow such models to be efficiently identified. A major
caveat of that work is the assumption of that all elements of the protocol are
noise-free. Here, we show that quantum Hamiltonian learning can tolerate
substantial amounts of depolarizing noise and show numerical evidence that it
can tolerate noise drawn from other realistic models. We further provide
evidence that the learning algorithm will find a model that is maximally close
to the true model in cases where the hypothetical model lacks terms present in
the true model. Finally, we also provide numerical evidence that the algorithm
works for non-commuting models. This work illustrates that quantum Hamiltonian
learning can be performed using realistic resources and suggests that even
imperfect quantum resources may be valuable for characterizing quantum systems.
The reachability of quantum games refers to the ability of two players to reach a certain subspace of Hilbert spaces in a quantum game modeled by a newly proposed quantum game process (QGP). We refer to this as quantum reachability games (QRGs). Reachability analysis is crucial in studying the strategic behavior and decision-making processes of players in quantum games, as it aids in devising optimal strategies to achieve desired objectives. In a QRG, players make decisions based on their quantum strategies related to decision epochs, which are represented by quantum operations or quantum measurements. We present an algorithm for evaluating two-player strategies, and investigate the optimal QRG for two players, where the goal of player 1 is to maximize his/her probability of reaching a given target subspace, while player 2 aims to minimize it. We show that any optimal QRG are determined, i.e., both of the two players have the same probability of winning in non-cooperative reachability games. Furthermore, our results also demonstrate that reachability games in the quantum world can be undecidable in certain cases. These findings are significantly distinct from those in the probabilistic or classical scenarios. Finally, we present three case studies, penny flipover, ambushing quantum walk and peer-to-peer scheme game on quantum network, to illustrate the potential applications and implications of QRGs.
Graph neural networks (GNN) suffer from severe inefficiency due to the exponential growth of node dependency with the increase of layers. It extremely limits the application of stochastic optimization algorithms so that the training of GNN is usually time-consuming. To address this problem, we propose to decouple a multi-layer GNN as multiple simple modules for more efficient training, which is comprised of classical
forward training
(
FT
) and designed
backward training
(
BT
). Under the proposed framework, each module can be trained efficiently in FT by stochastic algorithms without distortion of graph information owing to its simplicity. To avoid the only unidirectional information delivery of FT and sufficiently train shallow modules with the deeper ones, we develop a backward training mechanism that makes the former modules perceive the latter modules, inspired by the classical backward propagation algorithm. The backward training introduces the reversed information delivery into the decoupled modules as well as the forward information delivery. To investigate how the decoupling and greedy training affect the representational capacity, we theoretically prove that the error produced by linear modules will not accumulate on unsupervised tasks in most cases. The theoretical and experimental results show that the proposed framework is highly efficient with reasonable performance, which may deserve more investigation.
This article proposes a quantum spatial graph convolutional neural network (QSGCN) model that is implementable on quantum circuits, providing a novel avenue to processing non-Euclidean type data based on the state-of-the-art parameterized quantum circuit (PQC) computing platforms. Four basic blocks are constructed to formulate the whole QSGCN model, including the quantum encoding, the quantum graph convolutional layer, the quantum graph pooling layer, and the network optimization. In particular, the trainability of the QSGCN model is analyzed through discussions on the barren plateau phenomenon. Simulation results from various types of graph data are presented to demonstrate the learning, generalization, and robustness capabilities of the proposed quantum neural network (QNN) model.
A vast amount of textual and structural information is required for knowledge graph construction and its downstream tasks. However, most of the current knowledge graphs are incomplete due to the difficulty of knowledge acquisition and integration. Knowledge Graph Completion (KGC) is used to predict missing connections. In previous studies, textual information and graph structural information are utilized independently, without an effective method for fusing these two types of information. In this paper, we propose a graph structure enhanced pre-training language model for knowledge graph completion. Firstly, we design a graph sampling algorithm and a Graph2Seq module for constructing sub-graphs and their corresponding contexts to support large-scale knowledge graph learning and parallel training. It is also the basis for fusing textual data and graph structure. Next, two pre-training tasks based on masked modeling are designed for capturing accurate entity-level and relation-level information. Furthermore, this paper proposes a novel asymmetric Encoder-Decoder architecture to restore masked components, where the encoder is a Pre-trained Language Model (PLM) and the decoder is a multi-relational Graph Neural Network (GNN). The purpose of the architecture is to integrate textual information effectively with graph structural information. Finally, the model is fine-tuned for KGC tasks on two widely used public datasets. The experiments show that the model achieves excellent performance and outperforms baselines in most metrics, which demonstrate the effectiveness of our approach by fusing the structure and semantic information to knowledge graph.
A major drawback in Magnetic Resonance Imaging (MRI) is the long scan times necessary to acquire complete K-space matrices using phase encoding. This paper proposes a transformer-based deep Reinforcement Learning (RL) framework (called TITLE) to reduce the scan time by sequentially selecting partial phases in real-time so that a slice can be accurately reconstructed from the resultant slice-specific incomplete K-space matrix. As a deep learning based slice-specific method, the TITLE method has the following characteristic and merits: (1) It is real-time because the decision of which phase to be encoded in next time can be made within the period between the time at which an echo signal is obtained and the time at which the next 180° RF pulse is activated. (2) It exploits the powerful feature representation ability of transformer, a self-attention based neural network, for predicting phases with the mechanism of deep reinforcement learning. (3) Both historically selected phases (called phase-indicator vector) and the corresponding undersampled image of the slice being scanned are used for extracting features by transformer. Experimental results on the fastMRI dataset demonstrate that the proposed method is 150 times faster than the state-of-the-art reinforcement learning based method and outperforms the state-of-the-art deep learning based methods in reconstruction accuracy. The source codes are available.
Knowledge graph (KG) is increasingly important in improving recommendation performance and handling item cold-start. A recent research hotspot is designing end-to-end models based on information propagation schemes. However, existing these methods do not highlight key collaborative signals hidden in user-item bipartite graphs, which leads to two problems: (1) the collaborative signal of user collaborative neighbors is not modeled and (2) the incompleteness of KG and the behavioral similarity of item collaborative neighbors are not considered. In this paper, we design a new model called
Knowledge Graph Collaborative Neighbor Awareness network
(KGCNA) in order to resolve the above problems. KGCNA models the top-k collaborative neighbors of users and items to extract the collaborative preference of the user's top-k collaborative neighbors, the missing attributes of items, and the behavioral similarity of the item's top-k collaborative neighbors, respectively. At the same time, KGCNA designs a novel information aggregation method, which adopts different aggregation methods for users and items to capture the user's item-based behavior preference and the item's long-distance knowledge association in KG, respectively. Furthermore, KGCNA uses an information-gated aggregation mechanism to extract discriminative signals to better study user behavior intent. Experimental results on three benchmark datasets demonstrate that KGCNA significantly improves over state-of-the-art techniques such as CKAN, KGIN, and KGAT.
For accurate forecasting of multivariate time series, it is essential to consider the relationship between temporal and spatial dimensions. Graph neural networks (GNNs) have gained popularity in recent years due to their ability to capture spatio-temporal correlations in a graph topology from multivariate time series. However, most existing GNN-based algorithms rely on predefined sensor distributions, limiting their applicability. Moreover, models that generate graphs without prior knowledge may overlook local conditions while constructing adjacency matrices. In this paper, we propose a multi-task learning approach that utilizes an AutoEncoder architecture for multivariate time series forecasting. Our method dynamically generates an adjacency matrix that is more focused on local changes in addition to a global graph structure that captures overall trends. The dynamic graph generation mechanism adaptively generates the adjacency matrix, and the two generated graphs are fused to avoid the issue of fixed matrices. We conducted experiments on publicly available datasets and introduced two new civil engineering datasets on tunnel boring machines to validate the effectiveness of our proposed model. Results demonstrate that our approach outperforms other baselines in terms of predictive performance.
Determining Hamiltonian parameters from noisy experimental measurements is a key task for the control of experimental quantum systems. An interesting experimental platform where precise knowledge of device parameters is useful is the quantum-dot-based Kitaev chain. In these systems, the fine tuning of Hamiltonian parameters is crucial in order to reach the desired regime with stable midgap modes. In this work, we demonstrate an adversarial machine-learning algorithm to determine the parameters of a quantum-dot-based Kitaev chain. We train a convolutional conditional generative adversarial neural network (CCGAN) with simulated differential conductance data and use the model to predict the parameters at which Majorana bound states are predicted to appear. In particular, the CCGAN model facilitates a rapid, numerically efficient exploration of the phase diagram describing the transition between elastic co-tunneling and crossed Andreev reflection regimes. We verify the theoretical predictions of the model by applying it to experimentally measured conductance obtained from a minimal Kitaev chain consisting of two spin-polarized quantum dots coupled by a superconductor-semiconductor hybrid. Our model accurately predicts, with an average success probability of 97%, whether the measurement was taken in the elastic co-tunneling or crossed Andreev reflection-dominated regime. Our work constitutes a stepping stone towards fast, reliable parameter prediction for tuning quantum dot systems into distinct Hamiltonian regimes. Ultimately, our results yield a strategy to support Kitaev-chain tuning that is scalable to longer chains.
Deep reinforcement learning (DRL) has been widely used in many quantum control tasks, in which rewards are used to guide the agent in acquiring an optimal control strategy. However, designing suitable rewards is usually challenging, which seriously affects the DRL's application performance, especially for complex quantum control tasks. In this article, we propose a simple and general reward design method by constructing some events, where events are defined by fidelity intervals. In the proposed event-based DRL (EDRL), events are used to describe the evolution of a quantum system. Rewards are designed according to several defined events rather than a large number of specific evolved quantum states, thereby resulting in a reduction in dimensions to be considered. With designed event-attributed rewards, the agent can capture the main evolution characteristics of a quantum system, and then obtain an effective control strategy. The effectiveness of the proposed EDRL method is verified by three quantum systems: i.e., 1) the one-qubit closed quantum system, 2) the two-qubit closed quantum system, and 3) the two-level open quantum system. Numerical comparisons demonstrate that the proposed EDRL outperforms the traditional DRL algorithms (deep Q-network and proximal policy optimization) with some representative reward methods for solving quantum control problems.
The future development of quantum technologies relies on creating and manipulating quantum systems of increasing complexity, with key applications in computation, simulation and sensing. This poses severe challenges in the efficient control, calibration and validation of quantum states and their dynamics. Although the full simulation of large-scale quantum systems may only be possible on a quantum computer, classical characterization and optimization methods still play an important role. Here, we review different approaches that use classical post-processing techniques, possibly combined with adaptive optimization, to learn quantum systems, their correlation properties, dynamics and interaction with the environment. We discuss theoretical proposals and successful implementations across different multiple-qubit architectures such as spin qubits, trapped ions, photonic and atomic systems, and superconducting circuits. This Review provides a brief background of key concepts recurring across many of these approaches with special emphasis on the Bayesian formalism and neural networks. Although the complexity of quantum systems scales exponentially with their size, classical algorithms and optimization strategies can still play an important role in the characterization of quantum states, their dynamics and the detection process. The complexity of quantum systems increases exponentially with their size, but in many practical contexts there are assumptions (such as low rank, sparsity, or a specific type of expected dynamics) that enable classical algorithms to be efficient in the characterization of quantum states, dynamics and measurements.Bayesian inference provides a robust approach to learning models for quantum systems, while preserving physical intuition about the processes involved.Neural networks enable the characterization of complex systems, at the expense of physical intuition.Adaptive approaches, which select the next measurement based on knowledge acquired earlier in the estimation, can speed up the characterization process.Classical optimization and learning algorithms can improve the performance of quantum sensors. The complexity of quantum systems increases exponentially with their size, but in many practical contexts there are assumptions (such as low rank, sparsity, or a specific type of expected dynamics) that enable classical algorithms to be efficient in the characterization of quantum states, dynamics and measurements. Bayesian inference provides a robust approach to learning models for quantum systems, while preserving physical intuition about the processes involved. Neural networks enable the characterization of complex systems, at the expense of physical intuition. Adaptive approaches, which select the next measurement based on knowledge acquired earlier in the estimation, can speed up the characterization process. Classical optimization and learning algorithms can improve the performance of quantum sensors.
The scene classification of remote sensing (RS) images plays an essential role in the RS community, aiming to assign the semantics to different RS scenes. With the increase of spatial resolution of RS images, high-resolution RS (HRRS) image scene classification becomes a challenging task because the contents within HRRS images are diverse in type, various in scale, and massive in volume. Recently, deep convolution neural networks (DCNNs) provide the promising results of the HRRS scene classification. Most of them regard HRRS scene classification tasks as single-label problems. In this way, the semantics represented by the manual annotation decide the final classification results directly. Although it is feasible, the various semantics hidden in HRRS images are ignored, thus resulting in inaccurate decision. To overcome this limitation, we propose a semantic-aware graph network (SAGN) for HRRS images. SAGN consists of a dense feature pyramid network (DFPN), an adaptive semantic analysis module (ASAM), a dynamic graph feature update module, and a scene decision module (SDM). Their function is to extract the multi-scale information, mine the various semantics, exploit the unstructured relations between diverse semantics, and make the decision for HRRS scenes, respectively. Instead of transforming single-label problems into multi-label issues, our SAGN elaborates the proper methods to make full use of diverse semantics hidden in HRRS images to accomplish scene classification tasks. The extensive experiments are conducted on three popular HRRS scene data sets. Experimental results show the effectiveness of the proposed SAGN. Our source codes are available at
https://github.com/TangXu-Group/SAGN
.
This study develops a concrete near-term quantum algorithm for Hamiltonian learning and demonstrates its effectiveness. In particular, we show that learning the spectrum of Hamiltonians during the learning process could produce high-precision estimates of the target interaction coefficients. Our work may have applications in quantum device certification, quantum simulation, and quantum machine learning.
Image-text matching of natural scenes has been a popular research topic in both computer vision and natural language processing communities. Recently, fine-grained image-text matching has shown its significant advance in inferring the high-level semantic correspondence by aggregating pairwise region-word similarity, but it remains challenging mainly due to insufficient representation of high-order semantic concepts and their explicit connections in one modality as its matched in another modality. To tackle this issue, we propose a relationship-enhanced semantic graph (ReSG) model, which can improve the image-text representations by learning their locally discriminative semantic concepts and then organizing their relationships in a contextual order. To be specific, two tailored graph encoders, visual relationship-enhanced graph (VReG) and textual relationship-enhanced graph (TReG), are respectively exploited to encode the high-level semantic concepts of corresponding instances and their semantic relationships. Meanwhile, the representations of each graph node are optimized by aggregating semantically contextual information to enhance the node-level semantic correspondence. Further, the hard-negative triplet ranking loss, center hinge loss, and positive-negative margin loss are jointly leveraged to learn the fine-grained correspondence between the ReSG representations of image and text, whereby the discriminative cross-modal embeddings can be explicitly obtained to benefit various image-text matching tasks in a more interpretable way. Extensive experiments verify the advantages of the proposed fine-grained graph matching approach, by achieving the state-of-the-art image-text matching results on public benchmark datasets.
Quantum technology promises to revolutionize how we learn about the physical world. An experiment that processes quantum data with a quantum computer could have substantial advantages over conventional experiments in which quantum states are measured and outcomes are processed with a classical computer. We proved that quantum machines could learn from exponentially fewer experiments than the number required by conventional experiments. This exponential advantage is shown for predicting properties of physical systems, performing quantum principal component analysis, and learning about physical dynamics. Furthermore, the quantum resources needed for achieving an exponential advantage are quite modest in some cases. Conducting experiments with 40 superconducting qubits and 1300 quantum gates, we demonstrated that a substantial quantum advantage is possible with today's quantum processors.
Electron transport in realistic physical and chemical systems often involves the nontrivial exchange of energy with a large environment, requiring the definition and treatment of open quantum systems. Because the time evolution of an open quantum system employs a nonunitary operator, the simulation of open quantum systems presents a challenge for universal quantum computers constructed from only unitary operators or gates. Here, we present a general algorithm for implementing the action of any nonunitary operator on an arbitrary state on a quantum device. We show that any quantum operator can be exactly decomposed as a linear combination of at most four unitary operators. We demonstrate this method on a two-level system in both zero and finite temperature amplitude damping channels. The results are in agreement with classical calculations, showing promise in simulating nonunitary operations on intermediate-term and future quantum devices.
This paper proposes a new Quantum Spatial Graph Convolutional Neural Network (QSGCNN) model that can directly learn a classification function for graphs of arbitrary sizes. Unlike state-of-the-art Graph Convolutional Neural Network (GCNN) models, the proposed QSGCNN model incorporates the process of identifying transitive aligned vertices between graphs and transforms arbitrary sized graphs into fixed-sized aligned vertex grid structures. In order to learn representative graph characteristics, a new quantum spatial graph convolution is proposed and employed to extract multi-scale vertex features, in terms of quantum information propagation between grid vertices of each graph. Since the quantum spatial convolution preserves the grid structures of the input vertices (i.e., the convolution layer does not alter the original spatial position of vertices), the proposed QSGCNN model allows to directly employ the traditional convolutional neural network architecture to further learn from the global graph topology, providing an end-to-end deep learning architecture that integrates the graph representation and learning in the quantum spatial graph convolution layer and the traditional convolutional layer for graph classifications. We indicate the effectiveness of the proposed QSGCNN model in relation to existing state-of-the-art methods. Experiments on benchmark graph classification datasets demonstrate the effectiveness of the proposed QSGCNN model.
Finding the multiple longest common subsequences (MLCS) among many long sequences (i.e., the large scale MLCS problem) has many important applications, such as gene alignment, disease diagnosis, and documents similarity check, etc. It is an NP-hard problem (Maier et al., 1978). The key bottle neck of this problem is that the existing state-of-the-art algorithms must construct a huge graph (called direct acyclic graph, briefly DAG), and the computer usually has no enough space to store and handle this graph. Thus the existing algorithms cannot solve the large scale MLCS problem. In order to quickly solve the large-scale MLCS problem within limited computer resources, this paper therefore proposes a branch and bound irredundant graph algorithm called Big-MLCS, which constructs a much smaller DAG (called Small-DAG) than the existing algorithms do by a branch and bound method, and designs a new data structure to efficiently store and handle Small-DAG. By these schemes, Big-MLCS is more efficient than the existing algorithms. Also, we compare the proposed algorithm with two state-of-the-art algorithms through the experiments, and the results show that the proposed algorithm outperforms the compared algorithms and is more suitable to large-scale MLCS problems.
A restricted Boltzmann machine (RBM) is a generative model that could be used in effectively balancing a cybersecurity dataset because the synthetic data a RBM generates follows the probability distribution of the training data. RBM training can be performed using contrastive divergence (CD) and quantum annealing (QA). QA-based RBM training is fundamentally different from CD and requires samples from a quantum computer. We present a real-world application that uses a quantum computer. Specifically, we train a RBM using QA for cybersecurity applications. The D-Wave 2000Q has been used to implement QA. RBMs are trained on the ISCX data, which is a benchmark dataset for cybersecurity. For comparison, RBMs are also trained using CD. CD is a commonly used method for RBM training. Our analysis of the ISCX data shows that the dataset is imbalanced. We present two different schemes to balance the training dataset before feeding it to a classifier. The first scheme is based on the undersampling of benign instances. The imbalanced training dataset is divided into five sub-datasets that are trained separately. A majority voting is then performed to get the result. Our results show the majority vote increases the classification accuracy up from 90.24% to 95.68%, in the case of CD. For the case of QA, the classification accuracy increases from 74.14% to 80.04%. In the second scheme, a RBM is used to generate synthetic data to balance the training dataset. We show that both QA and CD-trained RBM can be used to generate useful synthetic data. Balanced training data is used to evaluate several classifiers. Among the classifiers investigated, K-Nearest Neighbor (KNN) and Neural Network (NN) perform better than other classifiers. They both show an accuracy of 93%. Our results show a proof-of-concept that a QA-based RBM can be trained on a 64-bit binary dataset. The illustrative example suggests the possibility to migrate many practical classification problems to QA-based techniques. Further, we show that synthetic data generated from a RBM can be used to balance the original dataset.
Graph-based clustering aims to partition the data according to a similarity graph, which has shown impressive performance on various kinds of tasks. The quality of similarity graph largely determines the clustering results, but it is difficult to produce a high-quality one, especially when data contain noises and outliers. To solve this problem, we propose a robust rank constrained sparse learning (RRCSL) method in this article. The
-norm is adopted into the objective function of sparse representation to learn the optimal graph with robustness. To preserve the data structure, we construct an initial graph and search the graph within its neighborhood. By incorporating a rank constraint, the learned graph can be directly used as the cluster indicator, and the final results are obtained without additional postprocessing. In addition, the proposed method cannot only be applied to single-view clustering but also extended to multiview clustering. Plenty of experiments on synthetic and real-world datasets have demonstrated the superiority and robustness of the proposed framework.
Online social network is popular and graph pattern matching (GPM) has been significant in many social network based applications, such as experts finding and social position detection. However, the existing GPM methods do not consider the multiple constraints of the social contexts in GPM, which are commonly found in various applications, or they do not consider the changes of graph structure in the index maintenance of GPM, leading to low efficiency. In this paper, we first propose a
multi-constrained simulation
based on the bounded graph simulation, and propose a multi-constrained graph pattern matching (MC-GPM) problem. To improve the efficiency of MC-GPM in large social graphs, we propose a new concept, strong social graph (SSG), that contains the users who have strong social connections. Then, we propose an SSG-index method to index the reachability, the graph patterns, and the social contexts of social graphs. Finally, we propose an incremental algorithm to maintain the SSG-index, which can greatly save the execution time when faced with the change of the structures of SSGs. Moreover, by combining SSG-index, we develop a heuristic algorithm, called SSG-MGPM, to identify MC-GPM results effectively and efficiently. An empirical study over five real-world social graphs has demonstrated the superiority of our approach in terms of efficiency and effectiveness.
This paper proposes a new graph convolutional neural network architecture based on a depth-based representation of graph structure deriving from quantum walks, which we refer to as the quantum-based subgraph convolutional neural network (QS-CNNs). This new architecture captures both the global topological structure and the local connectivity structure within a graph. Specifically, we commence by establishing a family of K-layer expansion subgraphs for each vertex of a graph by quantum walks, which captures the global topological arrangement information for substructures contained within a graph. We then design a set of fixed-size convolution filters over the subgraphs, which helps to characterise multi-scale patterns residing in the data. The idea is to apply convolution filters sliding over the entire set of subgraphs rooted at a vertex to extract the local features analogous to the standard convolution operation on grid data. Experiments on eight graph-structured datasets demonstrate that QS-CNNs architecture is capable of outperforming fourteen state-of-the-art methods for the tasks of node classification and graph classification.
In recent years, along with the overwhelming advances in the field of neural information processing, quantum information processing (QIP) has shown significant progress in solving problems that are intractable on classical computers. Quantum machine learning (QML) explores the ways in which these fields can learn from one another. We propose quantum walk neural networks (QWNN), a new graph neural network architecture based on quantum random walks, the quantum parallel to classical random walks. A QWNN learns a quantum walk on a graph to construct a diffusion operator which can be applied to a signal on a graph. We demonstrate the use of the network for prediction tasks for graph structured signals.
