Related papers: Comment on "A Recursive Parametrisation of Unitary…
The variational quantum eigensolver is a prominent hybrid quantum-classical algorithm expected to impact near-term quantum devices. They are usually based on a circuit ansatz consisting of parameterized single-qubit gates and fixed…
We investigate the group gradings on the algebra of upper triangular matrices over an arbitrary field, viewed as a Lie algebra. These results were obtained a few years early by the same authors. We provide streamlined proofs, and present a…
Kliuchnikov, Maslov, and Mosca proved in 2012 that a $2\times 2$ unitary matrix $V$ can be exactly represented by a single-qubit Clifford+$T$ circuit if and only if the entries of $V$ belong to the ring $\mathbb{Z}[1/\sqrt{2},i]$. Later…
Many promising quantum algorithms in economics, medical science, and material science rely on circuits that are parameterized by a large number of angles. To ensure that these algorithms are efficient, these parameterized circuits must be…
We present an explicit construction of a relativistic quantum computing architecture using a variational quantum circuit approach that is shown to allow for universal quantum computing. The variational quantum circuit consists of tunable…
We study the Universality and Membership Problems for gate sets consisting of a finite number of quantum gates. Our approach relies on the techniques from compact Lie groups theory. We also introduce an auxiliary problem called Subgroup…
A theory of canonical basis for a two-parameter quantum algebra is developed in parallel with the one in one-parameter case. A geometric construction of the negative part of a two-parameter quantum algebra is given by using mixed perverse…
We describe a framework for random pairwise comparisons matrices, inspired by selected constructions releted to the so called inconsistency reduction of pairwise comparisons (PC) matrices. In to build up structures on random pairwise…
Recursion formulae are derived for the calculation of two centre matrix elements of a radial function in relativistic quantum mechanics. The recursions are obtained between not necessarily diagonal radial eigensates using arbitrary radial…
We investigate randomized benchmarking in a general setting with quantum gates that form a representation, not necessarily an irreducible one, of a finite group. We derive an estimate for the average fidelity, to which experimental data may…
Reynolds' parametricity originally equips types with proof-irrelevant binary propositional relations over the types. But such relations can also be taken proof-relevant or unary, and described either in an indexed or fibred way.…
Randomized benchmarking is routinely used as an efficient method for characterizing the performance of sets of elementary logic gates in small quantum devices. In the measurement-based model of quantum computation, logic gates are…
This paper presents a sequential randomized lowrank matrix factorization approach for incrementally predicting values of an unknown function at test points using the Gaussian Processes framework. It is well-known that in the Gaussian…
The aim of this paper is to introduce and study a large class of $\mathfrak{g}$-module algebras which we call factorizable by generalizing the Gauss factorization of (square or rectangular) matrices. This class includes coordinate algebras…
We describe the mathematical properties of pairwise comparisons matrices with coefficients in an arbitrary group. We provide a vocabulary adapted for the description of main algebraic properties of inconsistency maps, describe an example…
This paper reveals the relation between the canonical coset decomposition of unitary matrices and the corresponding decomposition via Householder reflections. These results can be used to parametrize unitary matrices via Householder…
One of the principal obstacles on the way to quantum computers is the lack of distinguished basis in the space of unitary evolutions and thus the lack of the commonly accepted set of basic operations (universal gates). A natural choice,…
We discuss characterization of experimental quantum gates by the error matrix, which is similar to the standard process matrix $\chi$ in the Pauli basis, except the desired unitary operation is factored out, by formally placing it either…
Machine learning algorithms based on parametrized quantum circuits are prime candidates for near-term applications on noisy quantum computers. In this direction, various types of quantum machine learning models have been introduced and…
First some old as well as new results about P.I. algebras, Ore extensions, and degrees are presented. Then quantized $n\times r$ matrices as well as quantized factor algebras of $M_q(n)$ are analyzed. The latter are the quantized function…