Related papers: Form factor expansion for large graphs: a diagramm…
We introduce a notion of quantum function, and develop a compositional framework for finite quantum set theory based on a 2-category of quantum sets and quantum functions. We use this framework to formulate a 2-categorical theory of quantum…
A general framework is presented which unifies the treatment of wavelet-like, quasidistribution, and tomographic transforms. Explicit formulas relating the three types of transforms are obtained. The case of transforms associated to the…
An integral representation for form-factors of exponential fields in the sine-Gordon model is proposed.
We consider a free (2 k)-form gauge-field on a Euclidean (4 k + 2)-manifold. The parameters needed to specify the action and the gauge-invariant observables take their values in spaces with natural complex structures. We show that the…
We study how the number $c(X)$ of components of a graph $X$ can be expressed through the number and properties of the components of a quotient graph $X/\sim.$ We partially rely on classic qualifications of graph homomorphisms such as…
A quantum trajectory describes the evolution of a quantum system undergoing indirect measurement. In the discrete-time setting, the state of the system is updated by applying Kraus operators according to the measurement results. From an…
We connect quantum graphs with infinite leads, and turn them to scattering systems. We show that they display all the features which characterize quantum scattering systems with an underlying classical chaotic dynamics: typical poles, delay…
We investigate 1-factorisations in which the 2-regular graphs that occur as the union of a pair of 1-factors appear an equal number of times across the unions of all pairs of 1-factors in the 1-factorisation. We call such 1-factorisations…
We formulate a notion of the quantum automorphism group of a $2$-graph. After some preliminary computations, we define quantum isomorphism between a pair of $2$-graphs. We produce a `non-trivial' example of a pair of $2$-graphs that are not…
Lifted probabilistic inference exploits symmetries in probabilistic graphical models to allow for tractable probabilistic inference with respect to domain sizes. To exploit symmetries in, e.g., factor graphs, it is crucial to identify…
We study the spectral statistics for extended yet finite quasi 1-d systems which undergo a transition from periodicity to disorder. In particular we compute the spectral two-point form factor, and the resulting expression depends on the…
In QCD sum-rule methods, the fundamental field-theoretical quantities are correlation functions of composite operators that serve as hadronic interpolating fields. One of the challenges of loop corrections to QCD correlation functions in…
Exploiting the indistinguishability of objects in a probabilistic graphical model such as a factor graph is key to lifted probabilistic inference algorithms and allows for tractable probabilistic inference problems with respect to domain…
We present the Boolean dimension of a graph, we relate it with the notions of inner, geometric and symplectic dimensions, and with the rank and minrank of a graph. We obtain an exact formula for the Boolean dimension of a tree in terms of a…
Quantum counting is a key quantum algorithm that aims to determine the number of marked elements in a database. This algorithm is based on the quantum phase estimation algorithm and uses the evolution operator of Grover's algorithm because…
We evaluate the variance of coefficients of the characteristic polynomial for binary quantum graphs using a dynamical approach. This is the first example where a spectral statistic can be evaluated in terms of periodic orbits for a system…
We reformulate quantum computation in terms of Lagrangian (sum-over-path) formalism, in contrast to the widely used Hamiltonian (unitary gate) formulation. We exemplify this formalism with some widely-studied models, including the standard…
A generalization of the coadjoint orbit action describes the dynamics of an observer (or instrument). We consider how this fits in with the view of observables in field theory being correlations of read-outs of instruments and show how one…
Quantum algorithm is an algorithm for solving mathematical problems using quantum systems encoded as information, which is found to outperform classical algorithms in some specific cases. The objective of this study is to develop a quantum…
The purpose of this work is to present a method based on the factorizations used in one dimensional quantum mechanics in order to find the symmetries of quantum and classical superintegrable systems in higher dimensions. We apply this…