Simulating fluid flows with quantum computing
arXiv:2409.09736 · doi:10.1007/s12046-024-02660-3
Abstract
The applications and impact of high fidelity simulation of fluid flows are far-reaching. They include settling some long-standing and fundamental questions in turbulence. However, the computational resources required for such efforts are extensive. Here, we explore the possibility of employing the recent computing paradigm of quantum computing to simulate fluid flows. The lure of this new paradigm is the potentially exponential advantage in memory and speed, in comparison with classical computing. This field has recently witnessed a considerable uptick in excitement and contributions. In this work, we give a succinct discussion of the progress made so far, with focus on fluid flows, accompanied by an enumeration of challenges that require sustained efforts for progress. Quantum computing of fluid flows has a promising future, but the inherently nonlinear nature of flows requires serious efforts on resolving various bottlenecks, and on synthesising progress on theoretical, numerical and experimental fronts. We present certain critical details that have not yet attracted adequate attention.
arXiv comment17 pages, 12 figures
References in corpus (47)
- Quantum algorithm for solving linear systems of equations
- Variational Quantum Algorithms
- Error mitigation for short-depth quantum circuits
- Predicting Many Properties of a Quantum System from Very Few Measurements
- An adaptive variational algorithm for exact molecular simulations on a quantum computer
- Simulating Hamiltonian dynamics with a truncated Taylor series
- Challenges and Opportunities in Quantum Machine Learning
- Quantum error correction below the surface code threshold
- Quantum algorithm for systems of linear equations with exponentially improved dependence on precision
- Connecting ansatz expressibility to gradient magnitudes and barren plateaus
- Quantum Decoherence
- Variational quantum algorithms for nonlinear problems
- Efficient quantum algorithm for dissipative nonlinear differential equations
- Exponential improvement in precision for simulating sparse Hamiltonians
- Variational Quantum Linear Solver
- Solving nonlinear differential equations with differentiable quantum circuits
- Quantum algorithms for systems of linear equations inspired by adiabatic quantum computing
- High-precision quantum algorithms for partial differential equations
- A Quantum Inspired Approach to Exploit Turbulence Structures
- A comprehensive review of Quantum Machine Learning: from NISQ to Fault Tolerance
- Quantum simulation of partial differential equations via Schrodingerisation: technical details
- Quantum Analog-Digital Conversion
- Linear combination of Hamiltonian simulation for nonunitary dynamics with optimal state preparation cost
- Quantum computing of fluid dynamics using the hydrodynamic Schrödinger equation
- Quantum algorithm for the Navier Stokes equations by using the streamfunction vorticity formulation and the lattice Boltzmann method
- Enhancing the Quantum Linear Systems Algorithm using Richardson Extrapolation
- The area rule for circulation in three-dimensional turbulence
- Hybrid quantum algorithms for flow problems
- Forecasting small scale dynamics of fluid turbulence using deep neural networks
- Linear embedding of nonlinear dynamical systems and prospects for efficient quantum algorithms
- Efficient quantum amplitude encoding of polynomial functions
- Lattice Boltzmann-Carleman quantum algorithm and circuit for fluid flows at moderate Reynolds number
- The Efficient Preparation of Normal Distributions in Quantum Registers
- Quantum State Preparation of Normal Distributions using Matrix Product States
- Three Carleman routes to the quantum simulation of classical fluids
- Two quantum algorithms for solving the one-dimensional advection-diffusion equation
- Nonlinear dynamics as a ground-state solution on quantum computers
- Noisy intermediate-scale quantum simulation of the one-dimensional wave equation
- Quantum algorithm for time-dependent differential equations using Dyson series
- Quantum Circuits for partial differential equations via Schrödingerisation
- Efficient Deterministic Preparation of Quantum States Using Decision Diagrams
- Reduced-order modeling of two-dimensional turbulent Rayleigh-Bénard flow by hybrid quantum-classical reservoir computing
- Quantum computing of reacting flows via Hamiltonian simulation
- Efficient and fail-safe quantum algorithm for the transport equation
- Fully quantum algorithm for lattice Boltzmann methods with application to partial differential equations
- Quantum Algorithm for Solving a Quadratic Nonlinear System of Equations
- Physics of the Majorana-superconducting qubit hybrids
Cited by in corpus (7)
- Compact quantum algorithms for time-dependent differential equations
- Numerical solution of nonlinear Schrödinger equation by a hybrid pseudospectral-variational quantum algorithm
- Quantum Carleman linearisation efficiency in nonlinear fluid dynamics
- Quantum circuits for partial differential equations in Fourier space
- Quantum implicit representation of vortex filaments in turbulence
- Quantum State Preparation for Probability Distributions with Reflection Symmetry Using Matrix Product States
- Schrödinger-Navier-Stokes equation for capillary fluids