Related papers: Holographic Software for Quantum Networks
Photonic systems offer a promising platform for interconnecting quantum processors and enabling scalable, networked architectures. Designing and verifying such architectures requires a unified formalism that integrates linear algebraic…
The Hopfield neural networks and the holographic neural networks are models which were successfully simulated on conventional computers. Starting with these models, an analogous fundamental quantum information processing system is developed…
The Hilbert transform has been one of the foundational transforms in signal processing, finding it's way into multiple disciplines from cryptography to biomedical sciences. However, there does not exist any quantum analogue for the Hilbert…
Physical systems, characterized by an ensemble of interacting elementary constituents, can be represented and studied by different algebras of observables or operators. For example, a fully polarized electronic system can be investigated by…
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…
The promise of artificial intelligence (AI) to process complex datasets has brought about innovative computing paradigms. While recent developments in quantum-photonic computing have reached significant feats, mimicking our brain's ability…
{\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…
Fourier representations play a central role in operator learning methods for partial differential equations and are increasingly being explored in quantum machine learning architectures. The classical fast Fourier transform (FFT),…
We analyze the dynamical response functions of strongly interacting quantum critical states described by conformal field theories (CFTs). We construct a self-consistent holographic model that incorporates the relevant scalar operator…
Holographic quantum error-correcting code, the quantum-information structure hypothesized for the AdS/CFT correspondence, has being attracting increasing attention in new directions interrelating the studies of quantum gravity and quantum…
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…
Quantum information protocols often rely on tomographic techniques to determine the state of the system. A popular method of encoding information is on the different paths a photon may take, for example, parallel waveguides in integrated…
Holography is a cornerstone characterisation and imaging technique that can be applied to the full electromagnetic spectrum, from X-rays to radio waves or even particles such as neutrons. The key property in all these holographic approaches…
We present HoloGraphs, a novel approach for physically representing, explaining, exploring, and interacting with dynamic networks. HoloGraphs addresses the challenges of visualizing and understanding evolving network structures by providing…
We introduce a symbolic operator framework for simulating quantum photonic systems that works directly with the canonical commutation relations and the Weyl algebra. Unlike existing Fock-space or Gaussian simulators, our method treats…
The light's image is the primary source of information carrier in nature. Indeed, a single photon's image possesses a vast information capacity that can be harnessed for quantum information processing. Our scheme for implementing quantum…
We present a number of quantum computing patterns that build on top of fundamental algorithms, that can be applied to solving concrete, NP-hard problems. In particular, we introduce the concept of a quantum dictionary as a summation of…
All-quantum signal processing techniques are at the core of the successful advancement of most information-based quantum technologies. This paper develops coherent and comprehensive methodologies and mathematical models to describe Fourier…
Topological holography is a holographic principle that describes the generalized global symmetry of a local quantum system in terms of a topological order in one higher dimension. This framework separates the topological data from the local…
The Quantum Fourier transform (QFT) is a key ingredient in most quantum algorithms. We have compared various spin-based quantum computing schemes to implement the QFT from the point of view of their actual time-costs and the accuracy of the…