Related papers: Synthesis of a quantum tree Weyl matrix

For families of orthogonal and symplectic types quantum matrix (QM-) algebras, we derive corresponding versions of the Cayley-Hamilton theorem. For a wider family of Birman-Murakami-Wenzl type QM-algebras, we investigate a structure of its…

We present a new family of quantum Weyl algebras where the polynomial part is the quantum analog of functions on homogeneous spaces corresponding to symmetric matrices, skew symmetric matrices, and the entire space of matrices of a given…

Construction of graphs with equal eigenvalues (co-spectral graphs) is an interesting problem in spectral graph theory. Seidel switching is a well-known method for generating co-spectral graphs. From a matrix theoretic point of view, Seidel…

We consider an algebraic formulation of Quantum Theory and develop a combinatorial model of the Heisenberg-Weyl algebra structure. It is shown that by lifting this structure to the richer algebra of graph operator calculus, we gain a simple…

While the ability to build quantum computers is improving dramatically, developing quantum algorithms is limited and relies on human insight and ingenuity. Although a number of quantum programming languages have been developed, it is…

In this paper, the problem of synthesizing a general Hermitian quantum gate into a set of primary quantum gates is addressed. To this end, an extended version of the Jacobi approach for calculating the eigenvalues of Hermitian matrices in…

We define a graded graph, called the Schur--Weyl graph, which arises naturally when one considers simultaneously the RSK algorithm and the classical duality between representations of the symmetric and general linear groups. As one of the…

By revisiting the Kirchhoff's Matrix-Tree Theorem, we give an exact formula for the number of spanning trees of a graph in terms of the quantum relative entropy between the maximally mixed state and another state specifically obtained from…

A Lie superalgebrea of Riemannian type leads to a representation of a quadratic Lie algebra into a Weyl algebra. A necessary and sufficient condition that such a representation leads to a Lie superalgebra of Riemannian type is that the…

The theory of quantum symmetric pairs provides a universal K-matrix which is an analogue of the universal R-matrix for quantum groups. The main ingredient in the construction of the universal K-matrix is a quasi K-matrix which has so far…

Weyl algebra is a simple noncommutative system used in quantum mechanics. Here I introduce the weyl package, written in the R computing language, which furnishes functionality for working with univariate and multivariate Weyl algebras. The…

While quantum computing provides an exponential advantage in solving system of linear equations, there is little work to solve system of nonlinear equations with quantum computing. We propose quantum Newton's method (QNM) for solving…

The Weyl-Wigner map yields the entire structure of Moyal quantum mechanics directly from the standard operator formulation. The covariant generalization of Moyal theory, also known as Vey quantum mechanics, was presented in the literature…

We find Weyl upper bounds for the quantum open baker's map in the semiclassical limit. For the number of eigenvalues in an annulus, we derive the asymptotic upper bound $\mathcal O(N^\delta)$ where $\delta$ is the dimension of the trapped…

The synthesis of a quantum circuit consists in decomposing a unitary matrix into a series of elementary operations. In this paper, we propose a circuit synthesis method based on the QR factorization via Householder transformations. We…

We study the inverse problem of recovering a tree graph together with the weights on its edges (equivalently a metric tree) from the knowledge of the Dirichlet-to-Neumann matrix associated with the Laplacian. We prove an explicit formula…

Parameter-dependent quantum systems often exhibit energy degeneracy points, whose comprehensive description naturally lead to the application of methods from singularity theory. A prime example is an electronic band structure where two…

This work provides a quantum-computing-first derivation of the Unitary Coupled Cluster ansatz, showing that its structure emerges naturally from fermionic algebra under unitary constraints. By explicitly connecting second quantization,…

In this paper we study the Dirichlet-to-Neumann map for solutions to mean value formulas on trees. We give two alternative definition of the Dirichlet-to-Neumann map. For the first definition (that involves the product of a "gradient" with…

We introduce the concept of regular quantum graphs and construct connected quantum graphs with discrete symmetries. The method is based on a decomposition of the quantum propagator in terms of permutation matrices which control the way…