Related papers: Synthesis of a quantum tree Weyl matrix
We introduce an efficient way, called Newton algorithm, to study arbitrary ideals in C[[x,y]], using a finite succession of Newton polygons. We codify most of the data of the algorithm in a useful combinatorial object, the Newton tree. For…
An algorithm for quantum computing Hamiltonian cycles of simple, cubic, bipartite graphs is discussed. It is shown that it is possible to evolve a quantum computer into an entanglement of states which map onto the set of all possible paths…
A framework allowing for perturbative calculations to be carried out for quantum field theories with arbitrary smoothly curved boundaries is described. It is based on an expansion of the heat kernel derived earlier for arbitrary mixed…
The process of translating a quantum algorithm into a form suitable for implementation on a quantum computing platform is crucial but yet challenging. This entails specifying quantum operations with precision, a typically intricate task. In…
The Weyl-Wigner correspondence prescription, which makes large use of Fourier duality, is reexamined from the point of view of Kac algebras, the most general background for noncommutative Fourier analysis allowing for that property. It is…
A new version of hidden variables theory founded on the generalisation of world's geometry is proposed. The quantum-mechanical motion as the motion in some "inner space", which has a structure of the integrable Weyl space is examined.…
Motivated by Weyl algebra analogues of the Jacobian conjecture and the Tame Generators problem, we prove quantum versions of these problems for a family of analogues to the Weyl algebras. In particular, our results cover the Weyl-Hayashi…
Time series data are essential for a wide range of applications, particularly in developing robust machine learning models. However, access to high-quality datasets is often limited due to privacy concerns, acquisition costs, and labeling…
We demonstrate that any self-adjoint coupling in a quantum graph vertex can be approximated by a family of magnetic Schroedinger operators on a tubular network built over the graph. If such a manifold has a boundary, Neumann conditions are…
In quantum field theory the path integral is usually formulated in the wave picture, i.e., as a sum over field evolutions. This path integral is difficult to define rigorously because of analytic problems whose resolution may ultimately…
A nonlinear Wightman field is taken to be a nonlinear map from a linear space of test functions to a linear space of Hilbert space operators, with inessential modifications to other axioms only to the extent dictated by the introduction of…
Using von Neumann algebras, we extend the theory of quantum computation on a graph to a theory of computation on an arbitrary topological space.
The Fast Fourier Transform is extended to functions on finite graphs whose edges are identified with intervals of finite length. Spectral and pseudospectral methods are developed to solve a wide variety of time dependent partial…
The process algebra has been used successfully to provide a novel formulation of quantum mechanics in which non-relativistic quantum mechanics (NRQM) emerges as an effective theory asymptotically. The process algebra is applied here to the…
Based on our previous works, and in order to relate them with the theory of quantum graphs and the quantum computing principles, we once again try to introduce some newly developed technical structures just by relying on our toy example,…
In this paper, we develop a two-stage distributed algorithm that enables nodes in a graph to cooperatively estimate the spectrum of a matrix $W$ associated with the graph, which includes the adjacency and Laplacian matrices as special…
In this article the geometry of quantum gravity is quantized in the sense of being noncommutative (first quantization) but it is also quantized in the sense of being emergent (second quantization). A new mechanism for quantum geometry is…
A numerical matrix methodology is applied to quantum problems with periodic potentials. The procedure consists essentially in replacing the true potential by an alternative one, restricted by an infinite square well, and in expressing the…
Recently developed quantum algorithms address computational challenges in numerical analysis by performing linear algebra in Hilbert space. Such algorithms can produce a quantum state proportional to the solution of a $d$-dimensional system…
We present algorithms to compute generalized root systems of Nichols algebras of diagonal type and of contragredient Lie superalgebras. As a consequence, we obtain an algorithm to compute the Lyndon words in the Kharchenko PBW basis…