Related papers: Quantum Algorithms for Stochastic Differential Equ…
Quantum computing uses the physical principles of very small systems to develop computing platforms which can solve problems that are intractable on conventional supercomputers. There are challenges not only in building the required…
Recent breakthroughs have opened the possibility to intermediate-scale quantum computing with tens to hundreds of qubits, and shown the potential for solving classical challenging problems, such as in chemistry and condensed matter physics.…
In this article we introduce an algorithm for mitigating the adverse effects of noise on gradient descent in variational quantum algorithms. This is accomplished by computing a {\emph{regularized}} local classical approximation to the…
The Schrodinger equation is one of the most important equations in physics and chemistry and can be solved in the simplest cases by computer numerical methods. Since the beginning of the 70s of the last century the computer began to be used…
Quantum computers have the potential for an exponential speedup of classical molecular computations. However, existing algorithms have limitations; quantum phase estimation (QPE) algorithms are intractable on current hardware while…
The Schr\"odingerisation method combined with the autonomozation technique in \cite{cjL23} converts general non-autonomous linear differential equations with non-unitary dynamics into systems of autonomous Schr\"odinger-type equations, via…
With rapid advances in quantum hardware, a central question is whether quantum devices with or without full error correction can outperform classical computers on practically relevant problems. Variational Quantum Algorithms (VQAs) have…
Quantum computers have the potential of solving certain problems exponentially faster than classical computers. Recently, Harrow, Hassidim and Lloyd proposed a quantum algorithm for solving linear systems of equations: given an $N\times{N}$…
Quantum dynamics, typically expressed in the form of a time-dependent Schr\"odinger equation with a Hermitian Hamiltonian, is a natural application for quantum computing. However, when simulating quantum dynamics that involves the emission…
Quantum computing in the Noisy Intermediate-Scale Quantum (NISQ) era presents significant challenges in differentiating quantum software bugs from hardware noise. Traditional debugging techniques from classical software engineering cannot…
Noise is ubiquitous in real quantum systems, leading to non-Hermitian quantum dynamics, and may affect the fundamental states of matter. Here we report in experiment a quantum simulation of the two-dimensional non-Hermitian quantum…
We present a quantum algorithm for systems of (possibly inhomogeneous) linear ordinary differential equations with constant coefficients. The algorithm produces a quantum state that is proportional to the solution at a desired final time.…
The quest for improved sampling methods to solve statistical mechanics problems of physical and chemical interest proceeds with renewed efforts since the invention of the Metropolis algorithm, in 1953. In particular, the understanding of…
We study a new method - called Schrodingerisation introduced in [Jin, Liu, Yu, arXiv: 2212.13969] - for solving general linear partial differential equations with quantum simulation. This method converts linear partial differential…
We present substantially generalized and improved quantum algorithms over prior work for inhomogeneous linear and nonlinear ordinary differential equations (ODE). Specifically, we show how the norm of the matrix exponential characterizes…
In this paper, we present two Hamiltonian simulation algorithms for multiscale linear transport equations, combining the Schr\"odingerization method [S. Jin, N. Liu and Y. Yu, Phys. Rev. Lett, 133 (2024), 230602][S. Jin, N. Liu and Y. Yu,…
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…
A recently proposed variational quantum algorithm has expanded the horizon of variational quantum computing to nonlinear physics and fluid dynamics. In this work, we probe the ability of such approaches to capture the ground state of the…
This letter presents a novel \textit{quantum algorithm} for signal denoising, which performs a thresholding in the frequency domain through amplitude amplification and using an adaptive threshold determined by local mean values. The…
While quantum computing can accomplish tasks that are classically intractable, the presence of noise may destroy this advantage in the absence of fault tolerance. In this work, we present a classical algorithm that runs in…