Related papers: Grobner Bases for Finite-temperature Quantum Compu…
Attention is focused on antisymmetrized versions of quantum spaces that are of particular importance in physics, i.e. two-dimensional quantum plane, q-deformed Euclidean space in three or four dimensions as well as q-deformed Minkowski…
An approach is proposed enabling to effectively describe the behaviour of a bosonic system. The approach uses the quantum group $GL_{p,q}(2)$ formalism. In effect, considering a bosonic Hamiltonian in terms of the $GL_{p,q}(2)$ generators,…
The computation of Gr\"obner bases is an established hard problem. By contrast with many other problems, however, there has been little investigation of whether this hardness is robust. In this paper, we frame and present results on the…
A discussion is given of recent developments in canonical gravity that assimilates the conformal analysis of gravitational degrees of freedom. The work is motivated by the problem of time in quantum gravity and is carried out at the metric…
A C# package is presented that allows a user for an input quantum circuit to generate a set of multivariate polynomials over the finite field Z_2 whose total number of solutions in Z_2 determines the output of the quantum computation…
Despite its enormous empirical success, the formalism of quantum theory still raises fundamental questions: why is nature described in terms of complex Hilbert spaces, and what modifications of it could we reasonably expect to find in some…
Computing the critical points of a polynomial function $q\in\mathbb Q[X_1,\ldots,X_n]$ restricted to the vanishing locus $V\subset\mathbb R^n$ of polynomials $f_1,\ldots, f_p\in\mathbb Q[X_1,\ldots, X_n]$ is of first importance in several…
The modern quantum theory is based on the assumption that quantum states are represented by elements of a complex Hilbert space. It is expected that in future quantum theory the number field will be not postulated but derived from more…
We investigate strongly correlated many-body systems composed of bosons and fermions with a fully quantum treatment using the path-integral ground state method, PIGS. To account for the Fermi-Dirac statistics, we implement the fixed-node…
In a recent work [10], Poulin and one of us presented a quantum algorithm for preparing thermal Gibbs states of interacting quantum systems. This algorithm is based on Grovers's technique for quantum state engineering, and its running time…
The quantum cohomology ring of the Grassmannian is determined by the quantum Pieri rule for multiplying by Schubert classes indexed by row or column-shaped partitions. We provide a direct equivariant generalization of Postnikov's quantum…
We present an effective algorithm for computing the standard cohomology spaces of finitely generated Lie (super) algebras over a commutative field K of characteristic zero. In order to reach explicit representatives of some generators of…
The maximal minors of a p by (m + p) matrix of univariate polynomials of degree n with indeterminate coefficients are themselves polynomials of degree np. The subalgebra generated by their coefficients is the coordinate ring of the quantum…
Based on the theory of Dunkl operators, this paper presents a general concept of multivariable Hermite polynomials and Hermite functions which are associated with finite reflection groups on $\b R^N$. The definition and properties of these…
We construct for each choice of a quiver $Q$, a cohomology theory $A$ and a poset $P$ a "loop Grassmannian" $\mathcal{G}^P(Q,A)$. This generalizes loop Grassmannians of semisimple groups and the loop Grassmannians of based quadratic forms.…
In this work, we systematically analyse Feynman integrals in the `t Hooft-Veltman scheme. We write an explicit reduction resulting from partial fractioning the high-multiplicity integrands to a finite basis of topologies at any given loop…
We apply the theory of Groebner bases to the computation of free resolutions over a polynomial ring, the defining equations of a canonically embedded curve, and the unirationality of the moduli space of curves of a fixed genus.
In this paper we give a method to associate a graph with an arbitrary density matrix referred to a standard orthonormal basis in the Hilbert space of a finite dimensional quantum system. We study the related issues like classification of…
We demonstrate the applicability of integration-by-parts (IBP) identities in finite-temperature field theory. As a concrete example, we perform 3-loop computations for the thermodynamic pressure of QCD in general covariant gauges, and…
Motivated on the one hand by recent results on isochronous dynamical systems, and on the other by quantum gravity applications of complex metrics, we show that, if such enlarged class of metrics is considered, one can easily obtain periodic…