Related papers: Quantum Algorithm for the Advection-Diffusion Equa…
A quantum algorithm for solving the advection equation by embedding the discrete time-marching operator into Hamiltonian simulations is presented. One-dimensional advection can be simulated directly since the central finite difference…
We present a quantum algorithm for the simulation of the linear advection-diffusion equation based on block encodings of high order finite-difference operators and the quantum singular value transform. Our complexity analysis shows that the…
This article presents the first complete application of a quantum time-marching algorithm for simulating multidimensional linear transport phenomena with arbitrary boundaries, whereby the success probabilities are problem intrinsic. The…
The mixing of scalar substances in fluid flows by stirring and diffusion is ubiquitous in natural flows, chemical engineering, and microfluidic drug delivery. Here, we present a spectral quantum algorithm for scalar mixing by solving the…
The advection-diffusion equation is simulated on a superconducting quantum computer via several quantum algorithms. Three formulations are considered: (1) Trotterization, (2) variational quantum time evolution (VarQTE), and (3) adaptive…
This article introduces a novel framework for developing quantum algorithms for the Lattice Boltzmann Method (LBM) applied to the advection-diffusion equation. We formulate the collision-streaming evolution of the LBM as a compact…
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…
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…
Matrices with the displacement structures of circulant, Toeplitz, and Hankel types as well as matrices with structures generalizing these types are omnipresent in computations of sciences and engineering. In this paper, we present efficient…
In this study, two initial boundary value problems for one dimensional advection-dispersion equation are solved by differential quadrature method based on sine cardinal functions. Pure advection problem modeling transport of conservative…
The extent to which quantum computers can simulate physical phenomena and solve the partial differential equations (PDEs) that govern them remains a central open question. In this work, one of the most fundamental PDEs is addressed: the…
Simulating differential equations on classical computers becomes an intractable problem if the grid size is extremely large. Quantum computers are believed to achieve a possibly exponential speedup in the matrix operation. In this paper, we…
Transport phenomena play a key role in a variety of application domains, and efficient simulation of these dynamics remains an outstanding challenge. While quantum computers offer potential for significant speedups, existing algorithms…
In this work we propose an approach for implementing time-evolution of a quantum system using product formulas. The quantum algorithms we develop have provably better scaling (in terms of gate complexity and circuit depth) than a naive…
Constraints in power consumption and computational power limit the skill of operational numerical weather prediction by classical computing methods. Quantum computing could potentially address both of these challenges. Herein, we present…
We present a quantum algorithm for computational fluid dynamics based on the Lattice-Boltzmann method. Our approach involves a novel encoding strategy and a modified collision operator, assuming full relaxation to the local equilibrium…
We present quantum algorithms for the estimation of n-time correlation functions, the local and non-local density of states, and dynamical linear response functions. These algorithms are all based on block-encodings - a versatile technique…
Block encoding is a successful technique used in several powerful quantum algorithms. In this work we provide an explicit quantum circuit for block encoding a sparse matrix with a periodic diagonal structure. The proposed methodology is…
Block encoding is a key ingredient in the recently developed quantum singular value transformation (QSVT) framework, which provides a unifying description for many quantum algorithms. Initially introduced to simplify and optimize resource…
We propose an efficient block-encoding technique for the implementation of the Linear Combination of Hamiltonian Simulations (LCHS) for simulating dissipative initial-value problems. This algorithm approximates a target nonunitary operator…