Related papers: Quantum Filter Diagonalization with Double-Factori…
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),…
The numerical emulation of quantum physics and quantum chemistry often involves an intractable number of degrees of freedom and admits no known approximation in general form. In practice, representing quantum-mechanical states using…
Accurate computation of multiple eigenvalues of quantum Hamiltonians is essential in quantum chemistry, materials science, and molecular spectroscopy. Estimating excited-state energies is challenging for classical algorithms due to…
Quantum simulation, the simulation of quantum processes on quantum computers, suggests a path forward for the efficient simulation of problems in condensed-matter physics, quantum chemistry, and materials science. While the majority of…
Quantum chemistry and materials science are among the most promising areas for demonstrating algorithmic quantum advantage and quantum utility due to their inherent quantum mechanical nature. Still, large-scale simulations of quantum…
Starting from the Kirchhoff-Huygens representation and Duhamel's principle of time-domain wave equations, we propose novel butterfly-compressed Hadamard integrators for self-adjoint wave equations in both time and frequency domain in an…
Quantum Fourier transform (QFT) is a widely used building block for quantum algorithms, whose scalable implementation is challenging in experiments. Here, we propose a protocol of quadratic quantum Fourier transform (QQFT), considering cold…
The time-dependent Hartree-Fock (TDHF) method is an approach to simulate the mean field dynamics of electrons within the assumption that the electrons move independently in their self-consistent average field and within the space of single…
Partial differential equations (PDEs) are central to computational electromagnetics (CEM) and photonic design, but classical solvers face high costs for large or complex structures. Quantum Hamiltonian simulation provides a framework to…
Fueled by applications in sensor networks, these years have witnessed a surge of interest in distributed estimation and filtering. A new approach is hereby proposed for the Distributed Kalman Filter (DKF) by integrating a local covariance…
Many quantum algorithms, including recently proposed hybrid classical/quantum algorithms, make use of restricted tomography of the quantum state that measures the reduced density matrices, or marginals, of the full state. The most…
Electronic structure calculation of atoms and molecules, in the past few decades has largely been dominated by density functional methods. This is primarily due to the fact that this can account for electron correlation effects in a…
We generalize Schroedinger's factorization method for Hydrogen from the conventional separation into angular and radial coordinates to a Cartesian-based factorization. Unique to this approach, is the fact that the Hamiltonian is represented…
Quantum subspace diagonalization methods are an exciting new class of algorithms for solving large\rev{-}scale eigenvalue problems using quantum computers. Unfortunately, these methods require the solution of an ill-conditioned generalized…
We present a quantum electronic embedding method derived from the exact factorization approach to calculate static properties of a many-electron system. The method is exact in principle but the practical power lies in utilizing input from a…
We consider a reformulation of QED in which covariant Green functions are used to solve for the electromagnetic field in terms of the fermion fields. The resulting modified Hamiltonian contains the photon propagator directly. A simple…
A quantum thermodynamic system is described by a Hamiltonian and a list of conserved, non-commuting charges, and a fundamental goal is to determine the minimum energy of the system subject to constraints on the charges. Recently, [Liu et…
This paper introduces a quantum-inspired denoising framework that integrates the Quantum Fourier Transform (QFT) into classical audio enhancement pipelines. Unlike conventional Fast Fourier Transform (FFT) based methods, QFT provides a…
We present an extension of many-body downfolding methods to reduce the resources required in the quantum phase estimation (QPE) algorithm. In this paper, we focus on the Schrieffer--Wolff (SW) transformation of the electronic Hamiltonians…
Quantum computing presents a promising alternative for the direct simulation of quantum systems with the potential to explore chemical problems beyond the capabilities of classical methods. However, current quantum algorithms are…