相关论文: Quantum simulation of the Fokker-Planck equation v…
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 develop a quantum algorithm for solving high-dimensional time-fractional heat equations. By applying the dimension extension technique from [FKW23], the $d+1$-dimensional time-fractional equation is reformulated as a local partial…
This paper explores the feasibility of quantum simulation for partial differential equations (PDEs) with physical boundary or interface conditions. Semi-discretisation of such problems does not necessarily yield Hamiltonian dynamics and…
This paper explores the explicit design of quantum circuits for quantum simulation of partial differential equations (PDEs) with physical boundary conditions. These equations and/or their discretized forms usually do not evolve via unitary…
We present a simple new way - called Schrodingerisation - to simulate general linear partial differential equations via quantum simulation. Using a simple new transform, referred to as the warped phase transformation, any linear partial…
We analyze the Schr\"odingerization method for quantum simulation of a general class of non-unitary dynamics with inhomogeneous source terms. The Schr\"odingerization technique, introduced in [31], transforms any linear ordinary and partial…
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…
Hamiltonian simulation is a fundamental algorithm in quantum computing that has attracted considerable interest owing to its potential to efficiently solve the governing equations of large-scale classical systems. Exponential speedup…
Quantum simulation is known to be capable of simulating certain dynamical systems in continuous time -- Schrodinger's equations being the most direct and well-known -- more efficiently than classical simulation. Any linear dynamical system…
This paper investigates quantum simulation algorithms for the Liouville equation in geometrical optics with partial transmission and reflection at sharp interfaces, based on the Schr\"odingerization method. By means of a warped phase…
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…
We propose an explicit, oracle-free quantum framework for numerically simulating general linear partial differential equations (PDEs), extending previous work to incorporate (a) Robin boundary conditions - which include Neumann and…
Recently, Jin et al. proposed a quantum simulation technique for ANY linear partial differential equations (PDEs), called Schr\"{o}dingerisation [1,2,3]. In this paper, the Schr\"{o}dingerisation technique for quantum simulation is expanded…
In this paper we study quantum simulation algorithms on the elastic wave equations using the Schr\"odingerisation method. The Schr\"odingerisation method transforms any linear PDEs into a system of Schr\"odinger-type PDEs -with unitary…
We consider the time discretization based on Lie-Trotter splitting, for the nonlinear Schrodinger equation, in the semi-classical limit, with initial data under the form of WKB states. We show that both the exact and the numerical solutions…
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…
Quantum computing has emerged as a promising avenue for achieving significant speedup, particularly in large-scale PDE simulations, compared to classical computing. One of the main quantum approaches involves utilizing Hamiltonian…
The Fokker_Planck equation can be derived in a consistent manner through a microscopic approach based on a unified scheme of classical and quantum mechanics. Here we shall derive it through a purely quantum mechanical approach based on the…
The solution of option-pricing problems may turn out to be computationally demanding due to non-linear and path-dependent payoffs, the high dimensionality arising from multiple underlying assets, and sophisticated models of price dynamics.…
We demonstrate a method that merges the quantum filter diagonalization (QFD) approach for hybrid quantum/classical solution of the time-independent electronic Schr\"odinger equation with a low-rank double factorization (DF) approach for the…