Related papers: A level N reduction theory of indefinite binary qu…
Let $Q$ be an acyclic quiver, it is classical that certain truncations of the translation quiver $\mathbb Z Q$ appear in the Auslander-Reiten quiver of the path algebra $kQ$. The stable $n$-translation quiver $\mathbb Z|_{n-1} Q$ is…
Elliptic curves over finite fields GF(2^n) play a prominent role in modern cryptography. Published quantum algorithms dealing with such curves build on a short Weierstrass form in combination with affine or projective coordinates. In this…
We give an algorithm to solve the quantum hidden subgroup problem for maximal cyclic non-normal subgroups of the affine group of a finite field (if the field has order $q$ then the group has order $q(q-1)$) with probability $1-\varepsilon$…
Let F be the imaginary quadratic field of discriminant -3 and OF its ring of integers. Let Gamma be the arithmetic group GL_3 (OF), and for any ideal n subset OF let Gamma_0 (n) be the congruence subgroup of level n consisting of matrices…
We review the large N method of calculating high order information on the renormalization group functions in a quantum field theory which is based on conformal integration methods. As an example these techniques are applied to a typical…
Training quantum neural networks (QNNs) using gradient-based or gradient-free classical optimisation approaches is severely impacted by the presence of barren plateaus in the cost landscapes. In this paper, we devise a framework for…
A method for generating irreducible polynomials of degree n over the finite field GF(2) is proposed. The irreducible polynomials are found by solving a system of equations that brings the information on the internal properties of the…
We describe a simple algorithm for computing the canonical basis of any finite-dimensional $U_{q}(sp_{2n})$-module.
We use Nakajima's geometric approach to representations of quantum affine algebras and recent results on explicit descriptions of specific canonical basis elements, to derive closed positive formulas for certain decomposition numbers of…
We discuss the algebra of $N\times N$ matrices as a reduced quantum plane. A $3-$nilpotent deformed differential calculus involving a complex parameter $q$ is constructed. The two cases, $q$ $3^{rd}$ and $N^{th}$ root of unity are…
We show that the class of every primitive indefinite binary quadratic form is naturally represented by an infinite graph (named \c{c}ark) with a unique cycle embedded on a conformal annulus. This cycle is called the spine of the \c{c}ark.…
Let G be a connected complex simple Lie group with maximal compact subgroup U. Let g be the Lie algebra of G, and X = G/U be the associated Riemannian globally symmetric space of type IV. We have constructed three types of arithmetic…
The two-parametric quantum superalgebra $U_{pq}[gl(2/2)]$ and its representations are considered. All finite-dimensional irreducible representations of this quantum superalgebra can be constructed and classified into typical and nontypical…
Let F* be the finite field of q elements and let P(n,q) be the projective space of dimension n-1 over F*. We construct a family H^{n}_{k,i} of combinatorial homology modules associated to P(n,q) over a coefficient field F field of…
Given an indefinite binary quaternionic Hermitian form $f$ with coefficients in a maximal order of a definite quaternion algebra over $\mathbb Q$, we give a precise asymptotic equivalent to the number of nonequivalent representations,…
We study the model enumeration problem of the function-free, finite domain fragment of first-order logic with two variables ($FO^2$). Specifically, given an $FO^2$ sentence $\Gamma$ and a positive integer $n$, how can one enumerate all the…
In this paper, we propose a novel framework for modeling topological phases of matter using code-based Narain conformal field theories (NCFTs). We show that the algebraic structure of the NCFTs naturally embeds into critical lattice quantum…
This paper proposes a new family of recursive systematic convolutional codes, defined in the non-binary domain over different Galois fields GF(q) and intended to be used as component codes for the design of non-binary turbo codes. A general…
We present a classical algorithm to find approximate solutions to instances of quadratic unconstrained binary optimisation. The algorithm can be seen as an analogue of quantum annealing under the restriction of a product state space, where…
In this paper we focus on the unconstrained binary quadratic optimization model, maximize x^t Qx, x binary, and consider the problem of identifying optimal solutions that are robust with respect to perturbations in the Q matrix.. We are…