Related papers: Quantum Algorithm for the Advection-Diffusion Equa…
This paper introduces a non-variational quantum algorithm designed to solve a wide range of combinatorial optimisation problems, including constrained and non-binary problems. The algorithm leverages an engineered interference process…
Many standard linear algebra problems can be solved on a quantum computer by using recently developed quantum linear algebra algorithms that make use of block encodings and quantum eigenvalue/singular value transformations. A block encoding…
The Quantum Lattice Boltzmann Method (QLBM) is one of the most promising approaches for realizing the potential of quantum computing in simulating computational fluid dynamics. Many recent works mostly focus on classical simulation, and…
Combinatorial optimization is a promising application for near-term quantum computers, however, identifying performant algorithms suited to noisy quantum hardware remains as an important goal to potentially realizing quantum computational…
Routing problems are a common optimization problem in industrial applications, which occur on a large scale in supply chain planning. Due to classical limitations for solving NP-hard problems, quantum computing hopes to improve upon speed…
We assess the convergence of the Carleman linearization of advection-diffusion-reaction (ADR) equations with a logistic nonlinearity. It is shown that five Carleman iterates provide a satisfactory approximation of the original ADR across a…
A semi-implicit, residual-based variational multiscale (VMS) formulation is developed for the incompressible Navier--Stokes equations. The approach linearizes convection using an extrapolated (Oseen-type) convecting velocity, producing a…
We present the mapping of a class of simplified air traffic management (ATM) problems (strategic conflict resolution) to quadratic unconstrained boolean optimization (QUBO) problems. The mapping is performed through an original…
We apply the framework of block-encodings, introduced by Low and Chuang (under the name standard-form), to the study of quantum machine learning algorithms and derive general results that are applicable to a variety of input models,…
We develop a semi-implicit algorithm for time-accurate simulation of the compressible Navier-Stokes equations, with special reference to wall-bounded flows. The method is based on linearization of the partial convective fluxes associated…
Variational quantum algorithms have attracted attention for their potential to solve combinatorial optimization problems. We study how the choice of encoding affects the resource requirements and optimization behavior of a variational…
We propose an iterative algorithm to simulate the dynamics generated by any $n$-qubit Hamiltonian. The simulation entails decomposing the unitary time evolution operator $U$ (unitary) into a product of different time-step unitaries. The…
Two quantum algorithms are presented for the numerical solution of a linear one-dimensional advection-diffusion equation with periodic boundary conditions. Their accuracy and performance with increasing qubit number are compared…
We describe a quantum algorithm for preparing states that encode solutions of non-homogeneous linear partial differential equations. The algorithm is a continuous-variable version of matrix inversion: it efficiently inverts differential…
To simulate highly-resolved flow fields, we extend the Quantum Lattice Boltzmann Method (QLBM) to be able to simulate multiple time steps without state extraction or reinitialization. We adjust and extend given QLBM approaches from the…
We developed and applied a machine-learned discretization for one-dimensional (1-D) horizontal passive scalar advection, which is an operator component common to all chemical transport models (CTMs). Our learned advection scheme resembles a…
Nonautonomous linear ordinary differential equations of the form $\dot{v}(t) = A(t)\, v(t)$, where $A(t)$ is non-skew-symmetric, are often used to describe nonunitary dynamics in a variety of fields that range from open quantum system…
This article proposes a Variational Quantum Algorithm to solve linear and nonlinear thermofluid dynamic transport equations. The hybrid classical-quantum framework is applied to problems governed by the heat, wave, and Burgers' equation in…
Simulating the dynamics and the non-equilibrium steady state of an open quantum system are hard computational tasks on conventional computers. For the simulation of the time evolution, several efficient quantum algorithms have recently been…
The multiple-quantum operator algebra formalism has been exploited to construct generally an unsorted quantum search algorithm. The exponential propagator and its corresponding effective Hamiltonian are constructed explicitly that describe…