Related papers: Universal Boundary-Modes Localization from Quantum…
We investigate the topological properties of the bond order wave phase arising in the extended Fermi-Hubbard model. In particular, we uncover a topological sector, which remained elusive in previous finite-size numerical studies due to…
The color code is both an interesting example of an exactly solved topologically ordered phase of matter and also among the most promising candidate models to realize fault-tolerant quantum computation with minimal resource overhead. The…
Here, we reveal our recent progress on a geometrical approach of quantum physics and topological crystals linking with Dirac magnetic monopoles and gauge fields through classical electrodynamics. The Bloch sphere of a quantum spin-1/2…
We present the {\em (symmetry-incorporating) formalism of general continuum models with boundary conditions} and apply it to the model with the minimal number of degrees of freedom necessary to have a well-defined boundary: a model with a…
We study topological transport in the steady state of a quantum particle hopping on a one-dimensional lattice in the presence of dissipation. The model exhibits a rich phase structure, with the average particle velocity in the steady state…
In this paper, we will present some ideas to use 3D topology for quantum computing. Topological quantum computing in the usual sense works with an encoding of information as knotted quantum states of topological phases of matter, thus being…
The development of quantum computers has been the stimulus that enables the realization of Quantum Machine Learning (QML), an area that integrates the calculational framework of quantum mechanics with the adaptive properties of classical…
Criticality-based quantum sensing exploits hypersensitive response to system parameters near phase transition points. This work uncovers two metrological advantages offered by topological phase transitions when the probe is prepared as…
As first demonstrated by the characterization of the quantum Hall effect by the Chern number, topology provides a guiding principle to realize robust properties of condensed matter systems immune to the existence of disorder. The…
In a physical system with conformal symmetry, observables depend on cross-ratios, measures of distance invariant under global conformal transformations (conformal geometry for short). We identify a quantum information-theoretic mechanism by…
Quantum machine learning (QML) aims to use quantum computers to enhance machine learning, but it is often limited by the required number of samples due to quantum noise and statistical limits on expectation value estimates. While efforts…
In a scenario of spontaneous symmetry breaking in finite time, topological defects are generated at a density that scale with the driving time according to the Kibble-Zurek mechanism (KZM). Signatures of universality beyond the KZM have…
We treat a quantum walk (QW) on the line whose quantum coin at each vertex tends to be the identity as the distance goes to infinity. We obtain a limit theorem that this QW exhibits localization with not an exponential but a "power-law"…
We propose a mathematically rigorous unified framework for hybrid quantum mechanics that systematically combines algebraic deformation and spatial non-locality within a single operator formalism. By constructing a self-adjoint hybrid…
The quantum geometric tensor (QGT) of a quantum system in a given parameter space captures both the geometry of the state manifold and the topology of the system. While the local QGT elements have been successfully measured in various…
We investigate a family of quasiperiodic continuous elastic beams, the topological properties of their vibrational spectra, and their relation to the existence of localized modes. We specifically consider beams featuring arrays of ground…
The absence of a well-defined Fermi surface in flat-band systems challenges the conventional understanding of instabilities toward Landau order based on nesting. We investigate the existence of an intrinsic nesting structure encoded in the…
Kinetically constrained models were originally introduced to capture slow relaxation in glassy systems, where dynamics are hindered by local constraints instead of energy barriers. Their quantum counterparts have recently drawn attention…
We study the characteristic probability density distribution of random flat band models by machine learning. The models considered here are constructed on the basis of the molecular-orbital representation, which guarantees the existence of…
We study quantum field theories which have quantum groups as global internal symmetries. We show that in such theories operators are generically non-local, and should be thought as living at the ends of topological lines. We describe the…