Related papers: Quantum algorithm for solving high-dimensional lin…
Vector set orthogonal normalization and matrix QR decomposition are fundamental problems in matrix analysis with important applications in many fields. We know that Gram-Schmidt process is a widely used method to solve these two problems.…
It has recently been shown that there are efficient algorithms for quantum computers to solve certain problems, such as prime factorization, which are intractable to date on classical computers. The chances for practical implementation,…
Differential equations (DEs) serve as the cornerstone for a wide range of scientific endeavors, their solutions weaving through the core of diverse fields such as structural engineering, fluid dynamics, and financial modeling. DEs are…
While quantum algorithms for solving large scale systems of linear equations offer potentially exponential speedups, their application has largely been confined to sparse matrices. This work extends the scope of these algorithms to a broad…
Noisy quantum simulation is challenging since one has to take into account the stochastic nature of the process. The dominating method for it is the density matrix approach. In this paper, we evaluate conditions for which this method is…
The Fokker-Planck equation models rare events across sciences, but its high-dimensional nature challenges classical computers. Quantum algorithms for such non-unitary dynamics often suffer from exponential {decay in} success probability. We…
Classical simulations of noisy quantum circuits are instrumental to our understanding of the behavior of real-world quantum systems and the identification of regimes where one expects quantum advantage. In this work, we present a highly…
Many real-world problems, like modelling environment dynamics, physical processes, time series etc., involve solving Partial Differential Equations (PDEs) parameterised by problem-specific conditions. Recently, a deep learning architecture…
Quantum computing has the potential to speed up some optimization methods. One can use quantum computers to solve linear systems via Quantum Linear System Algorithms (QLSAs). QLSAs can be used as a subroutine for algorithms that require…
In this paper, we propose a deep learning-based method, deep Euler method (DEM) to solve ordinary differential equations. DEM significantly improves the accuracy of the Euler method by approximating the local truncation error with deep…
This manuscript explores a variational quantum formulation for nonlinear elasticity problems arising from hyperelastic material models, targeting near term noisy intermediate scale quantum (NISQ) devices. The approach leverages the…
In this work, we propose a novel backward differential deep learning-based algorithm for solving high-dimensional nonlinear backward stochastic differential equations (BSDEs), where the deep neural network (DNN) models are trained not only…
Quantum computing holds significant promise for scientific computing due to its potential for polynomial to even exponential speedups over classical methods, which are often hindered by the curse of dimensionality. While neural networks…
We show how a quantum computer may efficiently simulate a disordered Hamiltonian, by incorporating a pseudo-random number generator directly into the time evolution circuit. This technique is applied to quantum simulation of few-body…
Most problems in uncertainty quantification, despite its ubiquitousness in scientific computing, applied mathematics and data science, remain formidable on a classical computer. For uncertainties that arise in partial differential equations…
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 $N\times{N}$…
Linear optical quantum circuits with photon number resolving (PNR) detectors are used for both Gaussian Boson Sampling (GBS) and for the preparation of non-Gaussian states such as Gottesman-Kitaev-Preskill (GKP), cat and NOON states. They…
This paper presents a quantum algorithm for the solution of prototypical second-order linear elliptic partial differential equations discretized by $d$-linear finite elements on Cartesian grids of a bounded $d$-dimensional domain. An…
High-dimensional partial-differential equations (PDEs) arise in a number of fields of science and engineering, where they are used to describe the evolution of joint probability functions. Their examples include the Boltzmann and…
We establish improved complexity estimates of quantum algorithms for linear dissipative ordinary differential equations (ODEs) and show that the time dependence can be fast-forwarded to be sub-linear. Specifically, we show that a quantum…