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

Non-Abelian braiding has attracted significant attention because of its pivotal role in describing the exchange behaviors of anyons--a candidate for realizing quantum logics. The input and outcome of non-Abelian braiding are connected by a…

Qubits in topological quantum computation are built from non-Abelian anyons. Adiabatic braiding of anyons is exploited as topologically protected logical gate operations. Thus, the adiabaticity upon which the notion of quantum statistics is…

Transductive graph-based semi-supervised learning methods usually build an undirected graph utilizing both labeled and unlabeled samples as vertices. Those methods propagate label information of labeled samples to neighbors through their…

We prove that many dynamical properties of group cellular automata (i.e., cellular automata defined on any finite group and with global rule which is an endomorphism), including surjectivity, injectivity, sensitivity to initial conditions,…

The transfer of conserved charges through insulating matter via smooth deformations of the Hamiltonian is known as quantum adiabatic, or Thouless, pumping. Central to this phenomenon are Hamiltonians whose insulating gap is controlled by a…

We study a non-Hermitian non-Abelian topological insulator preserving $PT$ symmetry, where the non-Hermitian term represents nonreciprocal hoppings. As it increases, a spontaneous $PT$ symmetry breaking transition occurs in the perfect-flat…

Machine learning has been successfully used to study phase transitions. One of the most popular approaches to identifying critical points from data without prior knowledge of the underlying phases is the learning-by-confusion scheme. As…

In the context of two-particle interferometry, we construct a parallel transport condition that is based on the maximization of coincidence intensity with respect to local unitary operations on one of the subsystems. The dependence on…

Unsupervised learning is a discipline of machine learning which aims at discovering patterns in big data sets or classifying the data into several categories without being trained explicitly. We show that unsupervised learning techniques…

Non-Abelian toroidal heterotic orbifolds have received comparatively little attention, mainly because of the significant computational challenges they pose, even at the level of computing their matter spectrum. Similarly, the SO(32)…

In this paper, we first study the endomorphisms of free-abelian times surface groups and give a characterization of when they are injective and surjective. Then, we see that free-abelian times hyperbolic groups are Hopfian but not…

Topological classification in our previous paper [K. Shiozaki and M. Sato, Phys. Rev. B ${\bf 90}$, 165114 (2014)] is extended to nonsymmorphic crystalline insulators and superconductors. Using the twisted equivariant $K$-theory, we…

Node classification is one of the core tasks on attributed graphs, but successful graph learning solutions require sufficiently labeled data. To keep annotation costs low, active graph learning focuses on selecting the most qualitative…

We introduce non-abelian cohomology sets of Hopf algebras with coefficients in Hopf modules. We prove that these sets generalize Serre's non-abelian group cohomology theory. Using descent techniques, we establish that our construction…

The recent progress of the Majorana experiments paves a way for the future tests of non-abelian braiding statistics and topologically-protected quantum information processing. However, a deficient design in those tests could be very…

We study a class of translational-invariant insulators with discrete rotational symmetry. These insulators have no spin-orbit coupling, and in some cases have no time-reversal symmetry as well, i.e., the relevant symmetries are purely…

Diffusion models form an important class of generative models today, accounting for much of the state of the art in cutting edge AI research. While numerous extensions beyond image and video generation exist, few of such approaches address…

Generative models have recently undergone significant advancement due to the diffusion models. The success of these models can be often attributed to their use of guidance techniques, such as classifier or classifier-free guidance, which…

We demonstrate the possibility of (sub)exponential quantum speedup via a quantum algorithm that follows an adiabatic path of a gapped Hamiltonian with no sign problem. This strengthens the superpolynomial separation recently proved by…

Complex quantum systems are often multiscale in nature with strong interactions between different scales. We present a novel idea: iteratively suppressing, rather than tracing out, the fast, high-energy degrees of freedom in strongly…