Related papers: Holographic Transformation for Quantum Factor Grap…
Group convolutions and cross-correlations, which are equivariant to the actions of group elements, are commonly used in mathematics to analyze or take advantage of symmetries inherent in a given problem setting. Here, we provide efficient…
A quantum bit encoding converter between qubits of different forms is experimentally demonstrated, paving the way to efficient networks for optical quantum computing and communication.
We introduce the partition function of edge-colored graph homomorphisms, of which the usual partition function of graph homomorphisms is a specialization, and present an efficient algorithm to approximate it in a certain domain. Corollaries…
Quantum renormalization group scheme provides a microscopic understanding of holography through a general mapping between the beta functions of underlying quantum field theories and the holographic actions in the bulk. We show that the…
Shor's algorithms for factorization and discrete logarithms on a quantum computer employ Fourier transforms preceding a final measurement. It is shown that such a Fourier transform can be carried out in a semi-classical way in which a…
The increasing demand for Fourier transforms on geometric algebras has resulted in a large variety. Here we introduce one single straight forward definition of a general geometric Fourier transform covering most versions in the literature.…
The present work attempts both a review of previous methods for transferring digital and symbolic computations in an analog or optical substrate and also to offer certain alternatives not yet fully explored. The essential difference from…
The quantum Fourier transform (QFT) is a fundamental primitive in quantum computation and quantum information. In this work, we generalize the QFT for finite groups to a QFT for finite-dimensional semisimple algebras, and give efficient…
Holographic algorithms introduced by Valiant are composed of two ingredients: matchgates, which are gadgets realizing local constraint functions by weighted planar perfect matchings, and holographic reductions, which show equivalences among…
Holographic duality describes gravitational theories in terms of quantum many-body systems. In holography, quantum information theory provides a crucial tool that directly connects microscopic structures of these systems to the geometries…
The discovery of an algorithm for factoring which runs in polynomial time on a quantum computer has given rise to a concerted effort to understand the principles, advantages, and limitations of quantum computing. At the same time, many…
Varying the curvature, quantum phase transitions are investigated in holographic confining QFTs defined on a fixed constant positive curvature background. We find a competition between two branches of solutions and a phase transition as one…
In quantum mechanics, one can express the evolution operator and other quantities in terms of functional integrals. The main goal of this paper is to prove corresponding results in the geometric approach to quantum theory. We apply these…
Quantum process tomography is an experimental technique to fully characterize an unknown quantum process. Standard quantum process tomography suffers from exponentially scaling of the number of measurements with the increasing system size.…
This paper presents a novel methodology that transforms discrete-time quantum walks into a graph embedding technique, offering a fresh perspective on graph representation methods.Through mathematical manipulations, the approach of this…
In this paper we aim to generalize results obtained in the framework of fractional calculus by the way of reformulating them in terms of operator theory. In its own turn, the achieved generalization allows us to spread the obtained…
The holographic principle posits that all quantum information in a region of spacetime is encoded on its boundary. While there is strong evidence for this principle in certain models of quantum gravity in asymptotically anti-de Sitter…
There is compelling theoretical evidence that quantum physics will change the face of information science. Exciting progress has been made during the last two decades towards the building of a large scale quantum computer. A quantum group…
Quantum computing is currently gaining significant attention, not only from the academic community but also from industry, due to its potential applications across several fields for addressing complex problems. For any practical problem…
Tomograms are obtained as probability distributions and are used to reconstruct a quantum state from experimentally measured values. We study the evolution of tomograms for different quantum systems, both finite and infinite dimensional. In…