相关论文: Exactly unitary discrete representations of the me…
We exhibit an explicit, deterministic algorithm for finding a canonical form for a positive definite matrix under unimodular integral transformations. We use characteristic sets of short vectors and partition-backtracking graph software.…
We analyze effective approximation of unitary matrices. In our formulation, a unitary matrix is represented as a product of rotations in two-dimensional subspaces, so-called Givens rotations. Instead of the quadratic dimension dependence…
This paper presents a novel intrinsic image transfer (IIT) algorithm for illumination manipulation, which creates a local image translation between two illumination surfaces. This model is built on an optimization-based framework consisting…
The evolution of quantum light through linear optical devices can be described by the scattering matrix $S$ of the system. For linear optical systems with $m$ possible modes, the evolution of $n$ input photons is given by a unitary matrix…
This paper is devoted to a discussion of the Discrete Fourier Transform (DFT) representation of a chaotic finite-duration sequence. This representation has the advantage that is itself a finite-duration sequence corresponding to samples…
As an extension of the 2D fractional Fourier transform (FRFT) and a special case of the 2D linear canonical transform (LCT), the gyrator transform was introduced to produce rotations in twisted space/spatial-frequency planes. It is a useful…
We introduce a novel concept of the {\em pseudo} parity-time ($\mathcal{PT}$) symmetry in periodically modulated optical systems with balanced gain and loss. We demonstrate that whether the original system is $\mathcal{PT}$-symmetric or…
We introduce and theoretically demonstrate a quantum metamaterial made of dense ultracold neutral atoms loaded into an inherently defect-free artificial crystal of light, immune to well-known critical chal- lenges inevitable in conventional…
In recent years, multiple Light Detection and Ranging (LiDAR) systems have grown in popularity due to their enhanced accuracy and stability from the increased field of view (FOV). However, integrating multiple LiDARs can be challenging,…
We propose a new and completely data-driven approach for generating a photo-consistent image transform. We show that simple classical algorithms which operate in the transform domain become extremely resilient to illumination changes. This…
Visual-inertial fusion is crucial for a large amount of intelligent and autonomous applications, such as robot navigation and augmented reality. To bootstrap and achieve optimal state estimation, the spatial-temporal displacements between…
An effective hamiltonian is derived exactly for the one-dimensional periodic Anderson model via a canonical transformation. The canonical transformation has been calculated up to infinite order, thus an exact transformation was performed in…
Motivated by various applications, unbounded Hamiltonian simulation has recently garnered great attention. Quantum Magnus algorithms, designed to achieve commutator scaling for time-dependent Hamiltonian simulation, have been found to be…
This article presents the first complete application of a quantum time-marching algorithm for simulating multidimensional linear transport phenomena with arbitrary boundaries, whereby the success probabilities are problem intrinsic. The…
The efficient computation of parametric solution sensitivities is a key challenge in the integration of learning-enhanced methods with nonlinear model predictive control (MPC), as their availability is crucial for many learning algorithms.…
In this work, we introduce a definition of the Discrete Fourier Transform (DFT) on Euclidean lattices in $\R^n$, that generalizes the $n$-th fold DFT of the integer lattice $\Z^n$ to arbitrary lattices. This definition is not applicable for…
Deep Neural Networks (DNNs) have achieved remarkable success in a variety of tasks, especially when it comes to prediction accuracy. However, in complex real-world scenarios, particularly in safety-critical applications, high accuracy alone…
Nonuniform Fourier data are routinely collected in applications such as magnetic resonance imaging, synthetic aperture radar, and synthetic imaging in radio astronomy. To acquire a fast reconstruction that does not require an online inverse…
We consider finite approximations of a fractal generated by an iterated function system of affine transformations on $\mathbb{R}^d$ as a discrete set of data points. Considering a signal supported on this finite approximation, we propose a…
We both review and augment the lightcone conformal truncation (LCT) method. LCT is a Hamiltonian truncation method for calculating dynamical quantities in QFT in infinite volume. This document is a self-contained, pedagogical introduction…