Related papers: Topological defect network representations of frac…
The twisted hypercube-like networks($THLNs$) contain several important hypercube variants. This paper is concerned with the fault-tolerant path-embedding of $n$-dimensional($n$-$D$) $THLNs$. Let $G_n$ be an $n$-$D$ $THLN$ and $F$ be a…
We introduce a systematic mathematical language for describing fixed point models and apply it to the study to topological phases of matter. The framework is reminiscent of state-sum models and lattice topological quantum field theories,…
Tensor networks states allow to find the low energy states of local lattice Hamiltonians through variational optimization. Recently, a construction of such states in the continuum was put forward, providing a first step towards the goal of…
In this work, we develop a coupled layer construction of fracton topological orders in $d=3$ spatial dimensions. These topological phases have sub-extensive topological ground-state degeneracy and possess excitations whose movement is…
Convolutional Neural Networks (CNN) have been successful in processing data signals that are uniformly sampled in the spatial domain (e.g., images). However, most data signals do not natively exist on a grid, and in the process of being…
We develop a topological theory for fault-tolerant quantum computation in quantum low-density parity-check (qLDPC) codes. We show that there exist hidden simplicial or CW complex structures encoding the topological data for all qLDPC and…
The ability to identify and temporally segment fine-grained human actions throughout a video is crucial for robotics, surveillance, education, and beyond. Typical approaches decouple this problem by first extracting local spatiotemporal…
Unitary Modular Tensor Categories(UMTC) have a one-to-one correspondence with Topological Quantum Field Theories (TQFT). Different identifications have been made so far associating different physical particle types (anyons) to different…
While conventional methods for sequential learning focus on interaction between consecutive inputs, we suggest a new method which captures composite semantic flows with variable-length dependencies. In addition, the semantic structures…
This work is concerned with tree tensor network operators (TTNOs) for representing quantum Hamiltonians. We first establish a mathematical framework connecting tree topologies with state diagrams. Based on these, we devise an algorithm for…
The study of the electronic properties of charged defects is crucial for our understanding of various electrical properties of materials. However, the high computational cost of density functional theory (DFT) hinders the research on large…
Dynamic graphs (DG) are often used to describe evolving interactions between nodes in real-world applications. Temporal patterns are a natural feature of DGs and are also key to representation learning. However, existing dynamic GCN models…
With the widespread use of power electronic devices, modern distribution networks are turning into flexible distribution networks (FDNs), which have enhanced active and reactive power flexibility at the transmission-distribution-interface…
Braiding defects in topological stabiliser codes has been widely studied as a promising approach to fault-tolerant quantum computing. Here, we explore the potential and limitations of such schemes in codes of all spatial dimensions. We…
We propose Lagrangian Descriptors (LDs) as a diagnostic framework for evaluating neural network models of Hamiltonian systems beyond conventional trajectory-based metrics. Standard error measures quantify short-term predictive accuracy but…
A realistic material may possess defects, which often bring the material new properties that have practical applications. The boundary defects of a two-dimensional topologically ordered system are thought of as an alternative way of…
Graph neural networks (GNNs) have been widely used in representation learning on graphs and achieved state-of-the-art performance in tasks such as node classification and link prediction. However, most existing GNNs are designed to learn…
We present a new way of nano-engineering graphene using defect domains. These regions have ring structures that depart from the usual honeycomb lattice, though each carbon atom still has three nearest neighbors. A set of stable domain…
Transient stability prediction is critically essential to the fast online assessment and maintaining the stable operation in power systems. The wide deployment of phasor measurement units (PMUs) promotes the development of data-driven…
Accurate segmentation of long and thin tubular structures is required in a wide variety of areas such as biology, medicine, and remote sensing. The complex topology and geometry of such structures often pose significant technical…