Related papers: Gaussian Generating functionals on easy quantum gr…
Quantum walks function as essential means to implement quantum simulators, allowing one to study complex and often directly inaccessible quantum processes in controllable systems. In this contribution, the notion of a driven Gaussian…
In this note, we study non-transitive graphs and prove a number of results when they satisfy a coarse version of transitivity. Also, for each finitely generated group $G$, we produce continuum many pairwise non-quasi-isometric regular…
We study a generating function for the sum over fatgraphs with specified valences of vertices and faces, inversely weighted by the order of their symmetry group. A compact expression is found for general (i.e. non necessarily connected)…
Gaussian processes are a versatile framework for learning unknown functions in a manner that permits one to utilize prior information about their properties. Although many different Gaussian process models are readily available when the…
Quantum algorithms are sequences of abstract operations, performed on non-existent computers. They are in obvious need of categorical semantics. We present some steps in this direction, following earlier contributions of Abramsky, Coecke…
We generalize categories of spatial partitions in the sense of C\'ebron-Weber by introducing new base partitions. This allows us to construct additional examples of free orthogonal quantum groups but yields the same class of spatial…
Gaussian processes (GPs) are Bayesian nonparametric generative models that provide interpretability of hyperparameters, admit closed-form expressions for training and inference, and are able to accurately represent uncertainty. To model…
We provide new examples of groups without rational cross-sections (also called regular normal forms), using connections with bounded generation and rational orders on groups. Specifically, our examples are extensions of infinite torsion…
In this work we first collect and generalize several existing non-perturbative models for the interaction between a single two-level qubit detector and a relativistic quantum scalar field in arbitrary curved spacetimes, where the time…
We call a (q-1)-th Kummer extension of a cyclotomic function field a quasi-cyclotomic function field if it is Galois, but non-abelian, over the rational function field with the constant field of q elements. In this paper, we determine the…
In this paper, we study a family of generating functions whose coefficients are polynomials that enumerate partitions in lower order ideals of Young's lattice. Our main result is that this family satisfies a rational recursion and are…
Usually the generators of a quantum group are assumed to be commutative with the noncommuting coordinates of a quantum plane. We have relaxed the assumption and investigated its consequences. Not only does a two-parameter quantum group…
We narrow in on the number of graphical partitions for which there is no known generating function by manipulating the well known generating function for Frobenius partitions.
The generating functional is suggested for multiparticle generation processes. In mean field approximation of high density QCD two equations for new generating functional are derived: linear functional equation for an arbitrary initial…
Let $a$ be a non-invertible transformation of a finite set and let $G$ be a group of permutations on that same set. Then $\genset{G, a}\setminus G$ is a subsemigroup, consisting of all non-invertible transformations, in the semigroup…
Motivated by Quantum Mechanics considerations, we expose some cross product constructions on a groupoid structure. Furthermore, critical remarks are made on some basic formal aspects of the Hopf algebra structure.
The linear optical creation of Gaussian cluster states, a potential resource for universal quantum computation, is investigated. We show that for any Gaussian cluster state, the canonical generation scheme in terms of QND-type interactions,…
The generating function of a Hamiltonian $H$ is defined as $F(t)=\langle e^{-itH}\rangle$, where $t$ is the time and where the expectation value is taken on a given initial quantum state. This function gives access to the different moments…
Despite rapid recent advances in quantum machine learning, the field is in many ways stuck. Existing approaches can exhibit serious limitations, and we still lack learning frameworks that are simple, interpretable, scalable, and naturally…
This paper provides an alternative approach to the problem of preparing pure Gaussian states in a linear quantum system. It is shown that any pure Gaussian state can be generated by a cascade of one-dimensional open quantum harmonic…