相关论文: Tensor Network States with Three-Site Correlators

We present a general graph-based Projected Entangled-Pair State (gPEPS) algorithm to approximate ground states of nearest-neighbor local Hamiltonians on any lattice or graph of infinite size. By introducing the structural-matrix which…

Tensor networks (TNs) enable compact representations of large tensors through shared parameters. Their use in probabilistic modeling is particularly appealing, as probabilistic tensor networks (PTNs) allow for tractable computation of…

We study tensor network varieties associated with the triangular graph, with a focus on the case where one of the physical dimensions is 2. This allows us to interpret the tensors as pencils of matrices. We provide a complete…

Projected entangled-pair states (PEPS) have become a powerful tool for studying quantum many-body systems in the condensed matter and quantum materials context, particularly with advances in variational energy optimization methods. A key…

The success of tensor network approaches in simulating strongly correlated quantum systems crucially depends on whether the many body states that are relevant for the problem can be encoded in a local tensor network. Despite numerous…

Multivariate Time Series Classification (MTSC) enables the analysis if complex temporal data, and thus serves as a cornerstone in various real-world applications, ranging from healthcare to finance. Since the relationship among variables in…

We introduce two-dimensional tensor network representations of finite groups carrying a 4-cocycle index. We characterize the associated gapped (2+1)D phases that emerge when these anomalous symmetries act on tensor network ground states. We…

The curse of dimensionality associated with the Hilbert space of spin systems provides a significant obstruction to the study of condensed matter systems. Tensor networks have proven an important tool in attempting to overcome this…

It is challenging to reduce the complexity of neural networks while maintaining their generalization ability and robustness, especially for practical applications. Conventional solutions for this problem incorporate quantum-inspired neural…

Tensor Networks are non-trivial representations of high-dimensional tensors, originally designed to describe quantum many-body systems. We show that Tensor Networks are ideal vehicles to connect quantum mechanical concepts to machine…

The performance of tensor network methods has seen constant improvements over the last few years. We add to this effort by introducing a new algorithm that efficiently applies tree tensor network operators to tree tensor network states…

Graph Neural Networks (GNNs) excel in various graph learning tasks but face computational challenges when applied to large-scale graphs. A promising solution is to remove non-essential edges to reduce the computational overheads in GNN.…

We introduce a protocol to classify three-qubit pure states into different entanglement classes and implement it on an NMR quantum processor. The protocol is designed in such a way that the experiments performed to classify the states can…

We introduce a new class of states for bosonic quantum fields which extend tensor network states to the continuum and generalize continuous matrix product states (cMPS) to spatial dimensions $d\geq 2$. By construction, they are Euclidean…

Graph Neural Networks (GNNs) have made significant advancements in node classification, but their success relies on sufficient labeled nodes per class in the training data. Real-world graph data often exhibits a long-tail distribution with…

Graph states represent a significant class of multi-partite entangled quantum states with applications in quantum error correction, quantum communication, and quantum computation. In this work, we introduce a novel formalism called the…

We introduce a general method for achieving robust group-invariance in group-equivariant convolutional neural networks ($G$-CNNs), which we call the $G$-triple-correlation ($G$-TC) layer. The approach leverages the theory of the…

AC State Estimation (ACSE) is widely recognized as a practical approach for determining the grid states in steady-state conditions. It serves as a fundamental analysis to ensure grid security and is a reference for market dispatch. As grid…

By taking inspiration from the backflow transformation for correlated systems, we introduce a novel tensor network ansatz which extend the well-established Matrix Product State representation of a quantum-many body wave function. This new…

In many real world applications, data are characterized by a complex structure, that can be naturally encoded as a graph. In the last years, the popularity of deep learning techniques has renewed the interest in neural models able to…