Related papers: Permutation Equivalence Classes of Kronecker Produ…
In this paper, we present an overview of constrained PARAFAC models where the constraints model linear dependencies among columns of the factor matrices of the tensor decomposition, or alternatively, the pattern of interactions between…
Using integration by parts relations, Feynman integrals can be represented in terms of coupled systems of differential equations. In the following we suppose that the unknown Feynman integrals can be given in power series representations,…
We study right exact tensor products on the category of finitely presented functors. As our main technical tool, we use a multilinear version of the universal property of so-called Freyd categories. Furthermore, we compare our constructions…
We present an infinite number of construction schemes involving unitary error bases, Hadamard matrices, quantum Latin squares and controlled families, many of which have not previously been described. Our results rely on biunitary…
We study unital operator spaces endowed with a partially defined product. We give a matrix-norm characterization of such products that allows for a representation theorem where the partial product is realized as composition of operators on…
We study infinite products of reproducing kernels with view to their use in dynamics (of iterated function systems), in harmonic analysis, and in stochastic processes. On the way, we construct a new family of representations of the Cuntz…
We consider universal aspects of two problems: (i) the slow purification of a large number of qubits by repeated quantum measurements, and (ii) the singular value structure of a product ${m_t m_{t-1}\ldots m_1}$ of many large random…
We focus upon the relationship between Hamiltonian cycle products and efficient vectors for a reciprocal matrix $A$, to more deeply understand the latter. This facilitates a new description of the set of efficient vectors (as a union of…
Let A and B be normal matrices with coefficients that are continuous complex-valued functions on a topological space X that has the homotopy type of a CW complex, and suppose these matrices have the same distinct eigenvalues at each point…
We present a quantum solver for partial differential equations based on a flexible matrix product operator representation. Utilizing mid-circuit measurements and a state-dependent norm correction, this scheme overcomes the restriction of…
The quantum Fourier transform (QFT) is a powerful tool in quantum computing. The main ingredients of QFT are formed by the Walsh-Hadamard transform H and phase shifts P(.), both of which are 2x2 unitary matrices as operators on the…
Tensor Kronecker products, the natural generalization of the matrix Kronecker product, are independently emerging in multiple research communities. Like their matrix counterpart, the tensor generalization gives structure for implicit…
In symmetric groups, studies of permutation factorizations or triples of permutations satisfying certain conditions have a long history. One particular interesting case is when two of the involved permutations are long cycles, for which…
The approximation of matrices to the sum of tensor products of Hermitian matrices is studied. A minimum decomposition of matrices on tensor space $H_1\otimes H_2$ in terms of the sum of tensor products of Hermitian matrices on $H_1$ and…
Leveraging the decomposability of the fast Fourier transform, I propose a new class of tensor network that is efficiently contractible and able to represent many-body systems with local entanglement that is greater than the area law.…
The products of weak values of quantum observables are shown to be of value in deriving quantum uncertainty and complementarity relations, for both weak and strong measurement statistics. First, a 'product representation formula' allows the…
We significantly enhance the simulation accuracy of initial Trotter circuits for Hamiltonian simulation of quantum systems by integrating first-order Riemannian optimization with tensor network methods. Unlike previous approaches, our…
We have generalised the properties with the tensor product, of one 4x4 matrix which is a permutation matrix, and we call a tensor commutation matrix. Tensor commutation matrices can be constructed with or without calculus. A formula allows…
We propose a Kronecker product model for correlation or covariance matrices in the large dimensional case. The number of parameters of the model increases logarithmically with the dimension of the matrix. We propose a minimum distance (MD)…
In this article, we propose an algorithm for approximating the action of $\varphi-$functions of matrices against vectors, which is a key operation in exponential time integrators. In particular, we consider matrices with Kronecker sum…