Related papers: Fast Phase Factor Finding for Quantum Signal Proce…
Quantum computing can provide speedups in solving many problems as the evolution of a quantum system is described by a unitary operator in an exponentially large Hilbert space. Such unitary operators change the phase of their eigenstates…
Using a perturbative solution for a periodically driven two-level quantum system, we show how to obtain phase factors for both a two-level quantum system and two two-level quantum systems non-interacting and interacting. The method is…
Many problems on signal processing reduce to nonparametric function estimation. We propose a new methodology, piecewise convex fitting (PCF), and give a two-stage adaptive estimate. In the first stage, the number and location of the change…
Phase estimation is a quantum algorithm for measuring the eigenvalues of a Hamiltonian. We propose and rigorously analyse a randomized phase estimation algorithm with two distinctive features. First, our algorithm has complexity independent…
Building quantum devices using fixed operators is a must to simplify the hardware construction. Quantum search engine is not an exception. In this paper, a fixed phase quantum search algorithm that searches for M matches in an unstructured…
We introduce a new statistical and variational approach to the phase estimation algorithm (PEA). Unlike the traditional and iterative PEAs which return only an eigenphase estimate, the proposed method can determine any unknown…
High-dimensional fractional reaction-diffusion equations have numerous applications in the fields of biology, chemistry, and physics, and exhibit a range of rich phenomena. While classical algorithms have an exponential complexity in the…
In this article, we study algorithms for nonnegative matrix factorization (NMF) in various applications involving streaming data. Utilizing the continual nature of the data, we develop a fast two-stage algorithm for highly efficient and…
Quantum information processing and its subfield, quantum image processing, are rapidly growing fields as a result of advancements in the practicality of quantum mechanics. In this paper, we propose a quantum algorithm for processing…
LU and Cholesky matrix factorization algorithms are core subroutines used to solve systems of linear equations (SLEs) encountered while solving an optimization problem. Standard factorization algorithms are highly efficient but remain…
The characterization of a quantum device is a crucial step in the development of quantum experiments. This is accomplished via Quantum Process Tomography, which combines the outcomes of different projective measurements to deliver a…
Quaternionic signal processing provides powerful tools for efficiently managing color signals by preserving the intrinsic correlations among signal dimensions through quaternion algebra. In this paper, we address the quaternionic phase…
The paper considers the phase retrieval problem in N-dimensional complex vector spaces. It provides two sets of deterministic measurement vectors which guarantee signal recovery for all signals, excluding only a specific subspace and a…
This contribution proposes a two stage strategy to allow for phase retrieval in state of the art sub-Nyquist sampling schemes for sparse multiband signals. The proposed strategy is based on data acquisition via modulated wideband converters…
The quantum phase estimation (QPE) is one of the fundamental algorithms based on the quantum Fourier transform. It has applications in order-finding, factoring, and finding the eigenvalues of unitary operators. The major challenge in…
Quantum signal processing (QSP) has emerged as a unifying subroutine in quantum algorithms. In QSP, we are given a function $f$ and a unitary black-box $U$, and the goal is to construct a quantum circuit for implementing $f(U)$ to a given…
Fluid flow simulations marshal our most powerful computational resources. In many cases, even this is not enough. Quantum computers provide an opportunity to speed up traditional algorithms for flow simulations. We show that lattice-based…
The Cholesky decomposition is a fundamental tool for solving linear systems with symmetric and positive definite matrices which are ubiquitous in linear algebra, optimization, and machine learning. Its numerical stability can be improved by…
We present a quantum eigenstate filtering algorithm based on quantum signal processing (QSP) and minimax polynomials. The algorithm allows us to efficiently prepare a target eigenstate of a given Hamiltonian, if we have access to an initial…
Phase retrieval is in general a non-convex and non-linear task and the corresponding algorithms struggle with the issue of local minima. We consider the case where the measurement samples within typically very small and disconnected subsets…