Related papers: Layer-by-layer disentangling two-dimensional topol…
Strongly interacting electrons in layered materials give rise to a plethora of emergent phenomena, such as unconventional superconductivity. heavy fermions, and spin textures with non-trivial topology. Similar effects can also be observed…
This article proposes a topological method that extracts hierarchical structures of various amorphous solids. The method is based on the persistence diagram (PD), a mathematical tool for capturing shapes of multiscale data. The input to the…
We present a hierarchy of quantum many-body states among which many examples of topological order can be identified by construction. We define these states in terms of a general, basis-independent framework of tensor networks based on the…
Topological phase transitions, which do not adhere to Landau's phenomenological model (i.e. a spontaneous symmetry breaking process and vanishing local order parameters) have been actively researched in condensed matter physics. Machine…
We use a categorical topological semantics to examine the Deutsch-Jozsa, hidden subgroup and single-shot Grover algorithms. This reveals important structures hidden by conventional algebraic presentations, and allows novel proofs of…
In recent years, there have been many studies on local stabilizer codes. Under the assumption of translation and scale invariance Yoshida classified such codes. His result implies that translation invariant 2D color codes are equivalent to…
Topological phases are unique states of matter incorporating long-range quantum entanglement, hosting exotic excitations with fractional quantum statistics. We report a practical method to identify topological phases in arbitrary realistic…
We investigate the low-energy spectral properties and robustness of the topological phase of color code, which is a quantum spin model for the aim of fault-tolerant quantum computation, in the presence of a uniform magnetic field or Ising…
We study the entanglement structure of the Greenberger-Horne-Zeilinger (GHZ) state as it thermalizes under a strongly-symmetric quantum channel describing the Metropolis-Hastings dynamics for the $d$-dimensional classical Ising model at…
We investigate finite-size scaling of genuine multisite entanglement in the ground state of quantum spin-1/2 Heisenberg ladders. We obtain the ground states of odd- and even-legged Heisenberg ladder Hamiltonians and compute genuine…
The three-dimensional topological insulator (originally called "topological insulators") is the first example in nature of a topologically ordered electronic phase existing in three dimensions that cannot be reduced to multiple copies of…
Topological protection of quantum correlations opens new horizons and opportunities in quantum technologies. A variety of topological effects has recently been observed in qubit networks. However, the experimental identification of the…
Graph Transformers have recently attracted attention for molecular property prediction by combining the inductive biases of graph neural networks (GNNs) with the global receptive field of Transformers. However, many existing hybrid…
Detecting and analyzing the local environment is crucial for investigating the dynamical processes of crystal nucleation and shape colloidal particle self-assembly. Recent developments in machine learning provide a promising avenue for…
Motivated by the recent introduction of a $U(1)$-symmetric toric code model, we investigate symmetry-based deformations of topological order by systematically deconstructing the Gauss-law-enforcing star terms of the toric code (TC)…
We introduce a convolutional neural network for inferring a compact disentangled graphical description of objects from 2D images that can be used for volumetric reconstruction. The network comprises an encoder and a twin-tailed decoder. The…
Here we show the connection between topological order and the geometric entanglement, as measured by the logarithm of the overlap between a given state and its closest product state of blocks, for the topological universality class of the…
Engineering synthetic dimensions, where the physics of additional spatial dimensions is simulated within the internal states of a quantum system, allows the realisation of phenomena not otherwise accessible in experiments. Ultracold…
Perturbation theory (PT) is often used to model statistical observables capturing the translation and rotation-invariant information in cosmological density fields. PT produces higher-order corrections by integration over linear statistics…
Possible generalizations of the topological (or Berezinskii-Kosterlitz-Thouless) phase transition on multicomponent 2D systems with nontrivial vector homotopic group pi_1 are considered. Relations between Ginzburg-Landau like theories,…