Related papers: Layer-by-layer disentangling two-dimensional topol…

Kitaev's quantum double models in 2D provide some of the most commonly studied examples of topological quantum order. In particular, the ground space is thought to yield a quantum error-correcting code. We offer an explicit proof that this…

In this chapter we discuss aspects of the quantum critical behavior that occurs at a quantum phase transition separating a topological phase from a conventionally ordered one. We concentrate on a family of quantum lattice models, namely…

Quantum information science has leaped forward with the exploration of high-dimensional quantum systems, offering greater potential than traditional qubits in quantum communication and quantum computing. To advance the field of…

We show that the evolution of two-component particles governed by a two-dimensional spin-orbit lattice Hamiltonian can reveal transitions between topological phases. A kink in the mean width of the particle distribution signals the closing…

We derive formulas and algorithms for Kitaev's invariants in the periodic table for topological insulators and superconductors for finite disordered systems on lattices with boundaries. We find that K-theory arises as an obstruction to…

We investigate the quantum phase transitions of the extended Hubbard model at half-filling with periodic boundary conditions employing the entanglement of particles, as opposed to the more traditional entanglement of modes. Our results show…

To every compact oriented surface that is composed entirely out of 2-dimensional 0- and 1-handles, we construct a dg category using structures arising in Khovanov homology. These dg categories form part of the 2-dimensional layer (a.k.a.…

We give a pedagogical introduction to topologically ordered states of matter, with the aim of familiarizing the reader with their axiomatic topological quantum field theory description. We introduce basic noninteracting topological phases…

Disentangled Graph Convolutional Network (DisenGCN) is an encouraging framework to disentangle the latent factors arising in a real-world graph. However, it relies on disentangling information heavily from a local range (i.e., a node and…

Nonlocality is the defining feature of quantum entanglement. Entangled states with multiple particles are of crucial importance in fundamental tests of quantum physics as well as in many quantum information tasks. One of the archetypal…

Entanglement is known to serve as an order parameter for true topological order in two-dimensional systems. We show how entanglement of disconnected partitions defines topological invariants for one-dimensional topological superconductors.…

We propose a scalable protocol in the Rydberg atomic system to generate the Greenberger-Horne-Zeilinger (GHZ) states, where the qubits are encoded on the hyperfine ground levels. Our system is featured with off-resonant driving fields…

We briefly review the advanced mathematical language of fiber bundle structures and how they can be used to classify two-level quantum systems based on the analysis of the topological properties of their sets of state vectors. The…

We establish an intriguing connection between quantum phase transitions and bifurcations in the reduced fidelity between two different reduced density matrices for quantum lattice many-body systems with symmetry-breaking orders. Our finding…

The tenfold classification provides a powerful framework for organizing topological phases of matter based on symmetry and spatial dimension. However, it does not offer a systematic method for transitioning between classes or engineering…

Nonlinear topological insulators have garnered substantial recent attention as they have both enabled the discovery of new physics due to interparticle interactions, and may have applications in photonic devices such as topological lasers…

Tensor networks provide compact and scalable representations of high-dimensional data, enabling efficient computation in fields such as quantum physics, numerical partial differential equations (PDEs), and machine learning. This paper…

The familiar Greenberger-Horne-Zeilinger (GHZ) states can be rewritten by entangling the Bell states for two qubits with a state of the third qubit, which is dubbed entangled entanglement. We show that in this way we obtain all 8…

The Kitaev toric code is widely considered one of the leading candidates for error correction in fault-tolerant quantum computation. However, direct methods to increase its logical dimensions, such as lattice surgery or introducing…

The Greenberger-Horne-Zeilinger (GHZ) entanglement, originally introduced to uncover the extreme violation of local realism against quantum mechanics, is an important resource for multiparty quantum communication tasks. But the low…