Related papers: Quantum algorithms for solving a drift-diffusion e…
Most quantum algorithms that give an exponential speedup over classical algorithms exploit the Fourier transform in some way. In Shor's algorithm, sampling from the quantum Fourier spectrum is used to discover periodicity of the modular…
Numerical calculus algorithms which estimate derivatives and integrals from data series acquired either via measurements or by sampling functions are essential in scientific computing. To date, a few quantum algorithms have been developed…
Quantum simulation is a foundational application for quantum computers, projected to offer insights into complex quantum systems beyond the reach of classical computation. However, with the exception of Trotter-based methods, which suffer…
By decomposing the important sampled imaginary time Schr\"odinger evolution operator to fourth order with positive coefficients, we derived a number of distinct fourth order Diffusion Monte Carlo algorithms. These sophisticated algorithms…
We study a quantum computer with fixed and permanent interaction of diagonal type between qubits. It is controlled only by one-qubit quick transformations. It is shown how to implement Quantum Fourier Transform and to solve Shroedinger…
There have been several research works on the hidden shift problem, quantum algorithms for the problem, and their applications. However, all the results have focused on discrete groups with discrete oracle functions. In this paper, we…
We introduce an optimisation method for variational quantum algorithms and experimentally demonstrate a 100-fold improvement in efficiency compared to naive implementations. The effectiveness of our approach is shown by obtaining…
For quantum computers to become useful tools to physicists, engineers and computational scientists, quantum algorithms for solving nonlinear differential equations need to be developed. Despite recent advances, the quest for a solver that…
Linear equations play a pivotal role in many areas of science and engineering, making efficient solutions to linear systems highly desirable. The development of quantum algorithms for solving linear systems has been a significant…
We present a hybrid numerical-quantum method for solving the Poisson equation under homogeneous Dirichlet boundary conditions, leveraging the Quantum Fourier Transform (QFT) to enhance computational efficiency and reduce time and space…
Many claims of computational advantages have been made for quantum computing over classical, but they have not been demonstrated for practical problems. Here, we present algorithms for solving time-dependent PDEs, with particular reference…
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 quantum Fourier transform (QFT) plays an important role in many known quantum algorithms such as Shor's algorithm for prime factorisation. In this paper we show that the QFT algorithm can, on a restricted set of input states, be…
We propose an explicit algorithm based on the Linear Combination of Hamiltonian Simulations technique to simulate both the advection-diffusion equation and a nonunitary discretized version of the Koopman-von Neumann formulation of nonlinear…
The Fast Fourier Transform is extended to functions on finite graphs whose edges are identified with intervals of finite length. Spectral and pseudospectral methods are developed to solve a wide variety of time dependent partial…
Time-dependent linear differential equations are a common type of problem that needs to be solved in classical physics. Here we provide a quantum algorithm for solving time-dependent linear differential equations with logarithmic dependence…
In mathematical physics, the space-fractional diffusion equations are of particular interest in the studies of physical phenomena modelled by L\'{e}vy processes, which are sometimes called super-diffusion equations. In this article, we…
Limited by today's physical devices, quantum circuits are usually noisy and difficult to be designed deeply. The novel computing architecture of distributed quantum computing is expected to reduce the noise and depth of quantum circuits. In…
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…
In this paper, we present quantum algorithms for a class of highly-oscillatory transport equations, which arise in semiclassical computation of surface hopping problems and other related non-adiabatic quantum dynamics, based on the…