Related papers: Holographic Transformation for Quantum Factor Grap…
The holographic transformation, belief propagation and loop calculus are generalized to problems in generalized probabilistic theories including quantum mechanics. In this work, the partition function of classical factor graph is…
We introduce a pictorial approach to quantum information, called holographic software. Our software captures both algebraic and topological aspects of quantum networks. It yields a bi-directional dictionary to translate between a…
Revisiting the old problem of existence of interacting models of QFT with new conceptual ideas and mathematical tools, one arrives at a novel view about the nature of QFT. The recent success of algebraic methods in establishing the…
Quantum Fourier transformation is important in many quantum algorithms. In this paper, we generalize quantum Fourier transformation over the Abelian group $\mathbb{Z}_N$ from two different points to get more efficient unitary…
This paper stands at the intersection of two distinct lines of research. One line is "holographic algorithms," a powerful approach introduced by Valiant for solving various counting problems in computer science; the other is "normal factor…
The Quantum Fourier Transform (QFT) is a fundamental component of many quantum computing algorithms. In this paper, we present an alternative method for factoring this transformation. Inspired by this approach, we introduce a new quantum…
I present a method of performing geometric quantization using cohomology groups extended via coefficient groups of different types. This is possible according to the Universal Coefficient Theorem (UTC). I also show that by using this method…
In this paper, we focus on Fourier analysis and holographic transforms for signal representation. For instance, in the case of image processing, the holographic representation has the property that an arbitrary portion of the transformed…
[...] In this thesis, we are interested in generalizing factor graphs and the relevant methods toward describing quantum systems. Two generalizations of classical graphical models are investigated, namely double-edge factor graphs (DeFGs)…
Integral transforms are invaluable mathematical tools to map functions into spaces where they are easier to characterize. We introduce the hyperdimensional transform as a new kind of integral transform. It converts square-integrable…
Some properties of the fractional Fourier transform, which is used in information processing, are presented in connection with the tomography transform of optical signals. Relation of the Green function of the quantum harmonic oscillator to…
We derive a holographic description of the simplest quantum mechanical system, a 1d free particle. The dual formulation uses a couple of two-dimensional topological abelian BF theories with appropriate boundary conditions, interactions and…
The conventional Quantum Fourier Transform, with exponential speedup compared to the classical Fast Fourier Transform, has played an important role in quantum computation as a vital part of many quantum algorithms (most prominently, the…
A general framework is presented which unifies the treatment of wavelet-like, quasidistribution, and tomographic transforms. Explicit formulas relating the three types of transforms are obtained. The case of transforms associated to the…
A factor-graph representation of quantum-mechanical probabilities (involving any number of measurements) is proposed. Unlike standard statistical models, the proposed representation uses auxiliary variables (state variables) that are not…
The Quantum Fourier Transformation (QFT) is a well-known subroutine for algorithms on qubit-based universal quantum computers. In this work, the known QFT circuit is used to derive an efficient circuit for the multidimensional QFT. The…
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…
Due to recent technological advances, actual quantum devices are being constructed and used to perform computations. As a result, many classical problems are being restated so as to be solved on quantum computers. Some examples include…
The simulation of the physical movement of multi-body systems at an atomistic level, with forces calculated from a quantum mechanical description of the electrons, motivates a graph partitioning problem studied in this article. Several…
{\em Quantum Fourier analysis} is a new subject that combines an algebraic Fourier transform (pictorial in the case of subfactor theory) with analytic estimates. This provides interesting tools to investigate phenomena such as quantum…