相关论文: Unsupervised learning of non-Abelian multi-gap top…

The note introduces a novel concept of non-Abelian patchworking arising as real locus of non-Abelian complex-phase tropical hypersurfaces, the theory of which is now developed enough to allow the proposed spin-off. Although, non-Abelian…

Hopf insulators represent a unique class of topological insulators that exist exclusively in two-band systems and are inherently unstable upon the inclusion of additional bands. Meanwhile, recent studies have shown that non-Hermiticity…

We propose an unsupervised learning methodology with descriptors based on Topological Data Analysis (TDA) concepts to describe the local structural properties of materials at the atomic scale. Based only on atomic positions and without a…

Gate-based quantum computers can in principle simulate the adiabatic dynamics of a large class of Hamiltonians. Here we consider the cyclic adiabatic evolution of a parameter in the Hamiltonian. We propose a quantum algorithm to estimate…

This paper introduces a theoretical framework for understanding the accumulation of non-Abelian geometric phases in rotating nitrogen-vacancy centers in diamond. Specifically, we consider how degenerate states can be achieved and…

The conventional formulation of the non-adiabatic (Aharonov-Anandan) phase is based on the equivalence class $\{e^{i\alpha(t)}\psi(t,\vec{x})\}$ which is not a symmetry of the Schr\"{o}dinger equation. This equivalence class when understood…

We give a gauge description of the adiabatic charge pumping in closed systems, both in Abelian and non-Abelian processes, and by means of asymptotic Wilson loops in a suitable parameter manifold. Our geometric formulation provides new…

Tables are an abundant form of data with use cases across all scientific fields. Real-world datasets often contain anomalous samples that can negatively affect downstream analysis. In this work, we only assume access to contaminated data…

We propose a scheme for detecting noncommutative feature of the non-Abelian geometric phase in circuit QED, which involves three transmon qubits capacitively coupled to an one-dimensional transmission line resonator. By controlling the…

A regular sampling theory in a multiply generated unitary invariant subspace of a separable Hilbert space $\mathcal{H}$ is proposed. This subspace is associated to a unitary representation of a countable discrete abelian group $G$ on…

Chemical relaxation phenomena, including photochemistry and electron transfer processes, form a vigorous area of research in which nonadiabatic dynamics plays a fundamental role. Here, we show that for nonadiabatic dynamics with two…

Designing proper time-dependent control fields for slowly varying the system to the ground state that encodes the problem solution is crucial for adiabatic quantum computation. However, inevitable perturbations in real applications demand…

We develop the theory of the nonadiabatic geometric phase, in both the Abelian and non-Abelian cases, in quaternionic Hilbert space.

The success of current deep saliency detection methods heavily depends on the availability of large-scale supervision in the form of per-pixel labeling. Such supervision, while labor-intensive and not always possible, tends to hinder the…

Quantum technologies based on adiabatic techniques can be highly effective, but often at the cost of being very slow. Here we introduce a set of experimentally realistic, non-adiabatic protocols for spatial state preparation, which yield…

The search for materials with topological properties is an ongoing effort. In this article we propose a systematic statistical method supported by machine learning techniques that is capable of constructing topological models for a generic…

We investigate how isolated quantum many-body systems dynamically equilibrate under non-Abelian gauge-symmetry constraints. By encoding gauge superselection sectors into static $\mathrm{SU}(2)$ background charges, we map out the dynamical…

The non-Abelian geometric phases of the robust degenerate ground states were proposed as physically measurable defining properties of topological order in 1990. In this paper we discuss in detail such a quantitative characterization of…

In a nonlinear three-wave mixing process, the interacting waves can accumulate an adiabatic geometric phase (AGP) if the nonlinear coefficient of the crystal is modulated in a proper manner along the nonlinear crystal. This concept was…

The paradigm shift toward structure-driven molecule generation has been propelled by advances in deep generative models, such as variational auto-encoders and diffusion models. However, these generative models for molecular design remain…