Related papers: Geodesics in CAT(0) Cubical Complexes
Quantum computational complexity estimates the difficulty of constructing quantum states from elementary operations, a problem of prime importance for quantum computation. Surprisingly, this quantity can also serve to study a completely…
We introduce the notion of coupled link cube complex (CLCC) as a means of constructing interesting cocompactly cubulated groups. CLCCs are defined locally, making them a useful tool when precise control over the links is required. In this…
In geophysics, inverse modelling can be applied to a wide range of goals, including, for instance, mapping the distribution of rock physical parameters in applied geophysics and calibrating models to forecast the behaviour of natural…
We present a quantum algorithm for computing the period lattice of infrastructures of fixed dimension. The algorithm applies to infrastructures that satisfy certain conditions. The latter are always fulfilled for infrastructures obtained…
Abstract geometrical computation can solve hard combinatorial problems efficiently: we showed previously how Q-SAT can be solved in bounded space and time using instance-specific signal machines and fractal parallelization. In this article,…
We describe in detail a general strategy for implementing a conditional geometric phase between two spins. Combined with single-spin operations, this simple operation is a universal gate for quantum computation, in that any unitary…
A general scheme for determining and studying hydrodynamic type systems describing integrable deformations of algebraic curves is applied to cubic curves. Lagrange resolvents of the theory of cubic equations are used to derive and…
A configuration of $n$ unit-cube-shaped \textit{modules} (or \textit{robots}) is a lattice-aligned placement of the $n$ modules so that their union is face-connected. The reconfiguration problem aims at finding a sequence of moves that…
Quantum complexity quantifies the difficulty of preparing a state or implementing a unitary transformation with limited resources. Applications range from quantum computation to condensed matter physics and quantum gravity. We seek to…
We prove the arborescence of any locally finite complex that is $CAT(0)$ with a polyhedral metric for which all vertex stars are convex. In particular locally finite $CAT(0)$ cube complexes or equilateral simplicial complexes are…
A horoboundary is one of the attempts to compactify metric spaces, and is constructed using continuous functions on metric spaces. It is a concept that includes global information of metric spaces, and its correspondence with an ideal…
The existence of the limiting pair correlation for angles between reciprocal geodesics on the modular surface is established. An explicit formula is provided, which captures geometric information about the length of reciprocal geodesics, as…
Topological quantum computation is a promising technique to achieve large-scale, error-corrected computation. Quantum hardware is used to create a large, 3-dimensional lattice of entangled qubits while performing computation requires…
In many singular metric spaces, the regularity of a shortest-length curve is unknown. Algebraic varieties, or more generally sets defined by finitely many polynomial or real analytic equalities or inequalities, all locally partition into…
A canonical quantisation of the coordinates of the spacetime within the general relativity theory is proposed. This quantisation will depend on the observer but it provides an interesting perspective on the problem of relating the…
This article provides a discussion on the construction of conformal Gaussian gauge systems to study the evolution of solutions to the Einstein field equations with positive Cosmological constant. This is done by means of a gauge based on…
We introduce graphical complexes of groups, which can be thought of as a generalisation of Coxeter systems with 1-dimensional nerves. We show that these complexes are strictly developable, and we equip the resulting Basic Construction with…
We introduce an algorithm for computing geodesics on sampled manifolds that relies on simulation of quantum dynamics on a graph embedding of the sampled data. Our approach exploits classic results in semiclassical analysis and the…
This paper presents two new direct symbolic-numerical algorithms for the transformation of Cartesian coordinates into geodetic coordinates considering the general case of a triaxial reference ellipsoid. The problem in both algorithms is…
A finite-dimensional CAT(0) cube complex $X$ is equipped with several well-studied boundaries. These include the Tits boundary (which depends on the CAT(0) metric), the Roller boundary (which depends only on the combinatorial structure),…