Some variational recipes for quantum field theories

Rapid developments of quantum information technology show promising opportunities for simulating quantum field theory in near-term quantum devices. In this work, we formulate the theory of (time-dependent) variational quantum simulation of the 1+1 dimensional $\lambda \phi^4$ quantum field theory including encoding, state preparation, and time evolution, with several numerical simulation results. These algorithms could be understood as near-term variational analogs of the Jordan-Lee-Preskill algorithm, the basic algorithm for simulating quantum field theory using universal quantum devices. Besides, we highlight the advantages of encoding with harmonic oscillator basis based on the LSZ reduction formula and several computational efficiency such as when implementing a bosonic version of the unitary coupled cluster ansatz to prepare initial states. We also discuss how to circumvent the "spectral crowding" problem in the quantum field theory simulation and appraise our algorithm by both state and subspace fidelities.Comment: 28 pages, many figures. v2: modified style, add references, clear typos. v3: significant change, authors adde

On the Super-exponential Quantum Speedup of Equivariant Quantum Machine Learning Algorithms with SU(dd) Symmetry

We introduce a framework of the equivariant convolutional algorithms which is tailored for a number of machine-learning tasks on physical systems with arbitrary SU($d$) symmetries. It allows us to enhance a natural model of quantum computation--permutational quantum computing (PQC) [Quantum Inf. Comput., 10, 470-497 (2010)] --and defines a more powerful model: PQC+. While PQC was shown to be effectively classically simulatable, we exhibit a problem which can be efficiently solved on PQC+ machine, whereas the best known classical algorithms runs in $O(n!n^2)$ time, thus providing strong evidence against PQC+ being classically simulatable. We further discuss practical quantum machine learning algorithms which can be carried out in the paradigm of PQC+.Comment: A shorter version established based on arXiv:2112.07611, presented in TQC 202

Path Integral Based Convolution and Pooling for Graph Neural Networks

Graph neural networks (GNNs) extends the functionality of traditional neural networks to graph-structured data. Similar to CNNs, an optimized design of graph convolution and pooling is key to success. Borrowing ideas from physics, we propose a path integral based graph neural networks (PAN) for classification and regression tasks on graphs. Specifically, we consider a convolution operation that involves every path linking the message sender and receiver with learnable weights depending on the path length, which corresponds to the maximal entropy random walk. It generalizes the graph Laplacian to a new transition matrix we call maximal entropy transition (MET) matrix derived from a path integral formalism. Importantly, the diagonal entries of the MET matrix are directly related to the subgraph centrality, thus providing a natural and adaptive pooling mechanism. PAN provides a versatile framework that can be tailored for different graph data with varying sizes and structures. We can view most existing GNN architectures as special cases of PAN. Experimental results show that PAN achieves state-of-the-art performance on various graph classification/regression tasks, including a new benchmark dataset from statistical mechanics we propose to boost applications of GNN in physical sciences.Comment: 15 pages, 4 figures, 6 tables. arXiv admin note: text overlap with arXiv:1904.1099

Unifying O(3) Equivariant Neural Networks Design with Tensor-Network Formalism

Many learning tasks, including learning potential energy surfaces from ab initio calculations, involve global spatial symmetries and permutational symmetry between atoms or general particles. Equivariant graph neural networks are a standard approach to such problems, with one of the most successful methods employing tensor products between various tensors that transform under the spatial group. However, as the number of different tensors and the complexity of relationships between them increase, maintaining parsimony and equivariance becomes increasingly challenging. In this paper, we propose using fusion diagrams, a technique widely employed in simulating SU($2$)-symmetric quantum many-body problems, to design new equivariant components for equivariant neural networks. This results in a diagrammatic approach to constructing novel neural network architectures. When applied to particles within a given local neighborhood, the resulting components, which we term "fusion blocks," serve as universal approximators of any continuous equivariant function defined in the neighborhood. We incorporate a fusion block into pre-existing equivariant architectures (Cormorant and MACE), leading to improved performance with fewer parameters on a range of challenging chemical problems. Furthermore, we apply group-equivariant neural networks to study non-adiabatic molecular dynamics of stilbene cis-trans isomerization. Our approach, which combines tensor networks with equivariant neural networks, suggests a potentially fruitful direction for designing more expressive equivariant neural networks.Comment: 10 pages + 12-page supplementary materials, many figure

A Feasible Methodological Framework for Uncertainty Analysis and Diagnosis of Atmospheric Chemical Transport Models

The current state of quantifying uncertainty in chemical transport models (CTM) is often limited and insufficient due to numerous uncertainty sources and inefficient or inaccurate uncertainty propagation methods. In this study, we proposed a feasible methodological framework for CTM uncertainty analysis, featuring sensitivity analysis to filter for important model inputs and a new reduced-form model (RFM) that couples the high-order decoupled direct method (HDDM) and the stochastic response surface model (SRSM) to boost uncertainty propagation. Compared with the SRSM, the new RFM approach is 64% more computationally efficient while maintaining high accuracy. The framework was applied to PM2.5 simulations in the Pearl River Delta (PRD) region and found five precursor emissions, two pollutants in lateral boundary conditions (LBCs), and three meteorological inputs out of 203 model inputs to be important model inputs based on sensitivity analysis. Among these selected inputs, primary PM2.5 emissions, PM2.5 concentrations of LBCs, and wind speed were identified as key uncertainty sources, which collectively contributed 81.4% to the total uncertainty in PM2.5 simulations. Also, when evaluated against observations, we found that there were systematic underestimates in PM2.5 simulations, which can be attributed to the two-product method that describes the formation of secondary organic aerosol

Dual-Channel Multiplex Graph Neural Networks for Recommendation

Efficient recommender systems play a crucial role in accurately capturing user and item attributes that mirror individual preferences. Some existing recommendation techniques have started to shift their focus towards modeling various types of interaction relations between users and items in real-world recommendation scenarios, such as clicks, marking favorites, and purchases on online shopping platforms. Nevertheless, these approaches still grapple with two significant shortcomings: (1) Insufficient modeling and exploitation of the impact of various behavior patterns formed by multiplex relations between users and items on representation learning, and (2) ignoring the effect of different relations in the behavior patterns on the target relation in recommender system scenarios. In this study, we introduce a novel recommendation framework, Dual-Channel Multiplex Graph Neural Network (DCMGNN), which addresses the aforementioned challenges. It incorporates an explicit behavior pattern representation learner to capture the behavior patterns composed of multiplex user-item interaction relations, and includes a relation chain representation learning and a relation chain-aware encoder to discover the impact of various auxiliary relations on the target relation, the dependencies between different relations, and mine the appropriate order of relations in a behavior pattern. Extensive experiments on three real-world datasets demonstrate that our \model surpasses various state-of-the-art recommendation methods. It outperforms the best baselines by 10.06\% and 12.15\% on average across all datasets in terms of R@10 and N@10 respectively