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We develop a theoretical and computational framework for estimating and correcting non-Abelian geometric distortions in time-bin photonic qudit processing when the relevant encoded object is a transported logical subspace rather than a…
Topological quantum computing promises error-resistant quantum computation without active error correction. However, there is a worry that during the process of executing quantum gates by braiding anyons around each other, extra anyonic…
In our previous works we proved a finiteness property of the radii of convergence functions associated with a vector bundle with connection on $p$-adic analytic curves. We showed that the radii are locally constant functions outside a…
We consider efficiency in the implementation of deep neural networks. Hardware accelerators are gaining interest as machine learning becomes one of the drivers of high-performance computing. In these accelerators, the directed graph…
We consider a finitely generated virtually abelian group $G$ acting properly and without inversions on a CAT(0) cube complex $X$. We prove that $G$ stabilizes a finite dimensional CAT(0) subcomplex $Y \subseteq X$ that is isometrically…
The discovery of the quantised Hall effect, and its subsequent topological explanation, demonstrated the important role topology can play in determining the properties of quantum systems. This realisation led to the development of…
Traffic forecasting is crucial for urban traffic management and guidance. However, existing methods rarely exploit the time-frequency properties of traffic speed observations, and often neglect the propagation of traffic flows from upstream…
We measure the conductance of a quantum point contact (QPC) while the biased tip of a scanning probe microscope induces a depleted region in the electron gas underneath. At finite magnetic field we find plateaus in the real-space maps of…
We investigate the possibility of hidden non-Abelian Local Phase symmetries in large-U doped planar Hubbard antiferromagnets, believed to simulate the physics of two-dimensional (magnetic) superconductors. We present a spin-charge…
We study directionally informed belief propagation (BP) decoding for quantum CSS codes, where anisotropic Tanner-graph structure and biased noise concentrate degeneracy along preferred directions. We formalize this by placing orientation…
Nonadiabatic holonomic quantum computation has robust feature in suppressing control errors because of its holonomic feature. However, this kind of robust feature is challenged since the usual way of realizing nonadiabatic holonomic gates…
Nonadiabatic holonomic quantum computation (NHQC) has been developed to shorten the construction times of geometric quantum gates. However, previous NHQC gates require the driving Hamiltonian to satisfy a set of rather restrictive…
To analyze the electronic band structure of a two-dimensional (2D) crystal under a commensurate perpendicular magnetic field, tight-binding (TB) Hamiltonians are typically constructed using a magnetic unit cell (MUC), which is composed of…
We provide a unified geometrical description for analyzing the stability of holonomic quantum gates in the presence of imprecise driving controls (parametric noise). We consider the situation in which these fluctuations do not affect the…
Van der Waals heterostructures display a rich variety of unique electronic properties. To identify novel transport mechanisms, nonlocal measurements have been widely used, wherein a voltage is measured at contacts placed far away from the…
We theoretically investigate a folded bilayer graphene structure as an experimentally realizable platform to produce the one-dimensional topological zero-line modes. We demonstrate that the folded bilayer graphene under an external gate…
We give a local treatment of finite alignment by identifying the finitely aligned part of any (not necessarily finitely aligned) higher-rank graph. We show the finitely aligned part is itself a constellation and forms a finitely aligned…
Using the adiabatic perturbation theory of driven dynamics [Phys. Rev. A 78, 052508 (2008)] we design a hierarchy of quantum state preparation protocols that systematically increase the fidelity at very long driving times. We test these and…
The aim of this paper is to analyse algorithms for constructing presentations of graph braid groups from the point of view of anyonic quantum statistics on graphs. In the first part of this paper, we provide a comprehensive review of an…
Counterdiabatic (CD) driving enables efficient quantum state preparation, but it requires implementing highly nonlocal adiabatic gauge potentials (AGP) that are impractical to compute and realize in large many-body systems. We introduce a…