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Product code construction is a powerful tool for constructing quantum stabilizer codes, which serve as a promising paradigm for realizing fault-tolerant quantum computation. Furthermore, the natural mapping between stabilizer codes and the…
Power delivery network (PDN) design is a nontrivial, time-intensive, and iterative task. Correct PDN design must account for considerations related to power bumps, currents, blockages, and signal congestion distribution patterns. This work…
We formulate a construction of type-I fracton models based on gauging planar subsystem symmetries of topologically ordered two dimensional layers that have been stacked in three ambient spatial dimensions. Via our construction, any defect…
Topological holography is a conjectured correspondence between the symmetry charges and defects of a $D$-dimensional system with the anyons in a $(D+1)$-dimensional topological order: the symmetry topological field theory (SymTFT).…
In cloud computing, software-defined network (SDN) gaining more attention due to its advantages in network configuration to improve network performance and network monitoring. SDN addresses an issue of static architecture in traditional…
We propose a unifying paradigm for analyzing and constructing topological quantum error correcting codes as dynamical circuits of geometrically local channels and measurements. To this end, we relate such circuits to discrete fixed-point…
We introduce a flexible and graphically intuitive framework that constructs complex quantum error correction codes from simple codes or states, generalizing code concatenation. More specifically, we represent the complex code constructions…
The terms of topological and quantum stabilities of low-dimensional crystalline carbon lattices with multiple non-equivalent sublattices are coined using theoretical analysis, multilevel simulations, and available experimental structural…
With the development of 5G, innovative applications requiring bounded transmission delays and zero packet loss emerge, e.g., AR, industrial automation, and smart grid. In this circumstance, time-sensitive networking (TSN) is proposed, which…
Graph neural networks excel at modeling pairwise interactions, but they cannot flexibly accommodate higher-order interactions and features. Topological deep learning (TDL) has emerged recently as a promising tool for addressing this issue.…
Image reconstruction-based anomaly detection has recently been in the spotlight because of the difficulty of constructing anomaly datasets. These approaches work by learning to model normal features without seeing abnormal samples during…
Tunnels are essential elements of transportation infrastructure, but are increasingly affected by ageing and deterioration mechanisms such as cracking. Regular inspections are required to ensure their safety, yet traditional manual…
Recently emerged Topological Deep Learning (TDL) methods aim to extend current Graph Neural Networks (GNN) by naturally processing higher-order interactions, going beyond the pairwise relations and local neighborhoods defined by graph…
Deep learning methods have been shown to be effective in representing ground-state wave functions of quantum many-body systems. Existing methods use convolutional neural networks (CNNs) for square lattices due to their image-like…
Disordered complex networks are of fundamental interest as stochastic models for information transmission over wireless networks. Well-known networks based on the Poisson point process model have limitations vis-a-vis network efficiency,…
Tensor network (TN) methods are well established for computing partition functions in statistical mechanics, though this use has traditionally been limited to lattice models. We extend the scope of TN methodology to interacting particle…
Accurate segmentation of tubular and curvilinear structures, such as blood vessels, neurons, and road networks, is crucial in various applications. A key challenge is ensuring topological correctness while maintaining computational…
We present an alternative derivation of the LTI system underlying the Legendre Delay Network (LDN). To this end, we first construct an LTI system that generates the Legendre polynomials. We then dampen the system by approximating a windowed…
Topological deep learning (TDL) is a rapidly growing field that seeks to leverage topological structure in data and facilitate learning from data supported on topological objects, ranging from molecules to 3D shapes. Most TDL architectures…
This thesis develops advanced Tensor Network (TN) methods to address Hamiltonian Lattice Gauge Theories (LGTs), overcoming limitations in real-time dynamics and finite-density regimes. A novel dressed-site formalism is introduced, enabling…