Variational Quantum Solutions to the Advection-Diffusion Equation for Applications in Fluid Dynamics

Abstract

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 one method to perform fluid dynamics calculations that takes advantage of quantum computing. This hybrid quantum-classical method, which combines several algorithms, scales logarithmically with the dimension of the vector space and quadratically with the number of nonzero terms in the linear combination of unitary operators that specifies the linear operator describing the system of interest. As a demonstration, we apply our method to solve the advection-diffusion equation for a small system using IBM quantum computers. We find that reliable solutions of the equation can be obtained on even the noisy quantum computers available today. This and other methods that exploit quantum computers could replace some of our traditional methods in numerical weather prediction as quantum hardware continues to improve.

References in corpus (25)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• A variational eigenvalue solver on a quantum processor
• Cost Function Dependent Barren Plateaus in Shallow Parametrized Quantum Circuits
• Expressibility and entangling capability of parameterized quantum circuits for hybrid quantum-classical algorithms
• Validating quantum computers using randomized model circuits
• Quantum algorithm for systems of linear equations with exponentially improved dependence on precision
• Variational quantum algorithms for nonlinear problems
• Improving data-driven global weather prediction using deep convolutional neural networks on a cubed sphere
• High-order quantum algorithm for solving linear differential equations
• Efficient quantum algorithm for dissipative nonlinear differential equations
• Quantum algorithm for linear differential equations with exponentially improved dependence on precision
• Solving nonlinear differential equations with differentiable quantum circuits
• High-precision quantum algorithms for partial differential equations
• Quantum Algorithm for Simulating the Wave Equation
• Quantum spectral methods for differential equations
• A Quantum Inspired Approach to Exploit Turbulence Structures
• Quantum algorithm for non-homogeneous linear partial differential equations
• A Quantum Algorithm for Solving Linear Differential Equations: Theory and Experiment
• A quantum algorithm to solve nonlinear differential equations
• Quantum algorithm for the Navier Stokes equations by using the streamfunction vorticity formulation and the lattice Boltzmann method
• Practical Quantum Computing: solving the wave equation using a quantum approach
• Linear embedding of nonlinear dynamical systems and prospects for efficient quantum algorithms
• Quantum algorithm for nonlinear differential equations
• Quantum technologies for climate change: Preliminary assessment
• Efficient algorithm for generating Pauli coordinates for an arbitrary linear operator

Cited by in corpus (25)

• Quantum computing of fluid dynamics using the hydrodynamic Schrödinger equation
• Two quantum algorithms for solving the one-dimensional advection-diffusion equation
• Nonlinear dynamics as a ground-state solution on quantum computers
• A Performance Study of Variational Quantum Algorithms for Solving the Poisson Equation on a Quantum Computer
• Simulating unsteady fluid flows on a superconducting quantum processor
• Hamiltonian simulation for hyperbolic partial differential equations by scalable quantum circuits
• Incompressible Navier-Stokes solve on noisy quantum hardware via a hybrid quantum-classical scheme
• Enabling Large-Scale and High-Precision Fluid Simulations on Near-Term Quantum Computers
• A hybrid quantum-classical framework for computational fluid dynamics
• Quantum algorithm for the advection-diffusion equation and the Koopman-von Neumann approach to nonlinear dynamical systems
• Bridging Paradigms: Designing for HPC-Quantum Convergence
• Boundary Treatment for Variational Quantum Simulations of Partial Differential Equations on Quantum Computers
• Self-Adaptive Physics-Informed Quantum Machine Learning for Solving Differential Equations
• Sequential optimal selection of a single-qubit gate and its relation to barren plateau in parameterized quantum circuits
• Numerical solution of nonlinear Schrödinger equation by a hybrid pseudospectral-variational quantum algorithm
• Variational quantum algorithm for generalized eigenvalue problems and its application to the finite element method
• Gate-set evaluation metrics for closed-loop optimal control on nitrogen-vacancy center ensembles in diamond
• A multiple-circuit approach to quantum resource reduction with application to the quantum lattice Boltzmann method
• Towards Variational Quantum Algorithms for generalized linear and nonlinear transport phenomena
• Quantum circuits for partial differential equations in Fourier space
• An Efficient Decomposition of the Carleman Linearized Burgers' Equation
• Quantum Simulation-Based Optimization for Cooling System Design
• Spectral quantum algorithm for passive scalar transport in shear flows
• Fully Quantum Lattice Gas Automata Building Blocks for Computational Basis State Encodings
• An efficient explicit implementation of a near-optimal quantum algorithm for simulating linear dissipative differential equations