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Quantum computation is one of the most promising new paradigms for the simulation of physical systems composed of electrons and atomic nuclei, with applications in chemistry, solid-state physics, materials science, and molecular biology.…
Quantum algorithms to integrate nonlinear PDEs governing flow problems are challenging to discover but critical to enhancing the practical usefulness of quantum computing. We present here a near-optimal, robust, and end-to-end quantum…
Many methods solve Poisson equations by using grid techniques which discretize the problem in each dimension. Most of these algorithms are subject to the curse of dimensionality, so that they need exponential runtime. In the paper "Quantum…
The Doi formalism treats a reaction-diffusion process as a quantum many-body problem. We use this second quantized formulation as a starting point to derive a numerical scheme for simulating $X\to 0$ reaction-diffusion processes, following…
Solving linear ordinary differential equations (ODE) is one of the most promising applications for quantum computers to demonstrate exponential advantages. The challenge of designing a quantum ODE algorithm is how to embed non-unitary…
In this work, we developed an efficient quantum algorithm for the simulation of non-Markovian quantum dynamics, based on the Feynman path integral formulation. The algorithm scales polynomially with the number of native gates and the number…
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…
This paper provides a theoretical framework of deriving the forward and backward Feynman-Kac equations for the distribution of functionals of the path of a particle undergoing both diffusion and chemical reaction. Very general forms of the…
The finite element method is used to approximately solve boundary value problems for differential equations. The method discretises the parameter space and finds an approximate solution by solving a large system of linear equations. Here we…
Quantum algorithms have the potential to revolutionize our understanding of open quantum systems in chemistry. In this work, we demonstrate that a repeated interaction model, which could serve as the foundation for a digital quantum…
Carleman linearization is a technique that embeds systems of ordinary differential equations with polynomial nonlinearities into infinite dimensional linear systems in a procedural way. In this paper we generalize the method for systems of…
To overcome the fast oscillatory behavior of correlation functions for extracting scattering phase shift in real-time quantum simulations encountered in Ref.\cite{Guo:2026qkx}, we propose and test two solutions in the present work. One is…
Group convolutions and cross-correlations, which are equivariant to the actions of group elements, are commonly used in mathematics to analyze or take advantage of symmetries inherent in a given problem setting. Here, we provide efficient…
We present a new algorithm which is named the Dynamical Functional Particle Method, DFPM. It is based on the idea of formulating a finite dimensional damped dynamical system whose stationary points are the solution to the original…
Computational fluid dynamics (CFD) is a cornerstone of classical scientific computing, and there is growing interest in whether quantum computers can accelerate such simulations. To date, the existing proposals for fault-tolerant quantum…
We propose a new solvable class of multidimensional quantum harmonic oscillators for a linear diffusive particle and a quadratic energy absorbing well associated with a semi-definite positive matrix force. Under natural and easily checked…
A three-level explicit time-split MacCormack scheme is proposed for solving the two-dimensional nonlinear reaction-diffusion equations. The computational cost is reduced thank to the splitting and the explicit MacCormack scheme. Under the…
Quantum computers have the potential to efficiently solve a system of nonlinear ordinary differential equations (ODEs), which play a crucial role in various industries and scientific fields. However, it remains unclear which system of…
The method of differential equations has been proven to be a powerful tool for the computation of multi-loop Feynman integrals appearing in quantum field theory. It has been observed that in many instances a canonical basis can be chosen,…
We present a novel approach to solve the advection-diffusion equation under arbitrary transporting fields using a quantum-inspired 'Schrodingerisation' technique for Hamiltonian simulation. Although numerous methods exist for solving…