Vortex Detection from Quantum Data

Abstract

Quantum solutions to differential equations represent quantum data -- states that contain relevant information about the system's behavior, yet are difficult to analyze. We propose a toolbox for reading out information from such data, where customized quantum circuits enable efficient extraction of flow properties. We concentrate on the process referred to as quantum vortex detection (QVD), where specialized operators are developed for pooling relevant features related to vorticity. Specifically, we propose approaches based on sliding windows and quantum Fourier analysis that provide a separation between patches of the flow field with vortex-type profiles. First, we show how contour-shaped windows can be applied, trained, and analyzed sequentially, providing a clear signal to flag the location of vortices in the flow. Second, we develop a parallel window extraction technique, such that signals from different contour positions are coherently processed to avoid looping over the entire solution mesh. We show that Fourier features can be extracted from the flow field, leading to classification of datasets with vortex-free solutions against those exhibiting Lamb-Oseen vortices. Our work exemplifies a successful case of efficiently extracting value from quantum data and points to the need for developing appropriate quantum data analysis tools that can be trained on them.

10 pages, 8 figures

References in corpus (62)

• Quantum Machine Learning
• Quantum algorithm for solving linear systems of equations
• Machine Learning for Fluid Mechanics
• Control of star formation by supersonic turbulence
• Turbulence Modeling in the Age of Data
• Quantum Convolutional Neural Networks
• Direct numerical simulation of turbulent channel flow up to $R{e}_{\tau }\approx 5200$
• Quantum algorithm for systems of linear equations with exponentially improved dependence on precision
• Quantum advantage in learning from experiments
• Generalization in quantum machine learning from few training data
• Quantum convolutional neural network for classical data classification
• Variational quantum algorithms for nonlinear problems
• 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
• Quantum algorithms and the finite element method
• Quantum algorithm and circuit design solving the Poisson equation
• Quantum algorithms for systems of linear equations inspired by adiabatic quantum computing
• A Quantum Inspired Approach to Exploit Turbulence Structures
• Realizing Quantum Convolutional Neural Networks on a Superconducting Quantum Processor to Recognize Quantum Phases
• Hamiltonian Simulation Using Linear Combinations of Unitary Operations
• Optimal polynomial based quantum eigenstate filtering with application to solving quantum linear systems
• Improved quantum algorithms for linear and nonlinear differential equations
• Variational Quantum Algorithms for Computational Fluid Dynamics
• Quantum simulation of partial differential equations via Schrodingerisation: technical details
• A Quantum Algorithm for Solving Linear Differential Equations: Theory and Experiment
• Does provable absence of barren plateaus imply classical simulability?
• Understanding quantum machine learning also requires rethinking generalization
• Data-Driven, Physics-Based Feature Extraction from Fluid Flow Fields
• Quantum Kernel Methods for Solving Differential Equations
• Quantum algorithms: A survey of applications and end-to-end complexities
• Towards quantum advantage via topological data analysis
• Block-encoding structured matrices for data input in quantum computing
• Simulating all quantum measurements using only projective measurements and postselection
• Analyzing Prospects for Quantum Advantage in Topological Data Analysis
• Three Carleman routes to the quantum simulation of classical fluids
• Two quantum algorithms for solving the one-dimensional advection-diffusion equation
• On Physics-Informed Neural Networks for Quantum Computers
• Interpretable Quantum Advantage in Neural Sequence Learning
• Nonlinear dynamics as a ground-state solution on quantum computers
• Analog quantum simulation of partial differential equations
• Towards Quantum Computational Mechanics
• Quantum Circuits for partial differential equations via Schrödingerisation
• An innovative and automated method for vortex identification. I. Description of the SWIRL algorithm
• Let Quantum Neural Networks Choose Their Own Frequencies
• Lie-algebraic classical simulations for quantum computing
• Quantum Quantile Mechanics: Solving Stochastic Differential Equations for Generating Time-Series
• What can we learn from quantum convolutional neural networks?
• Efficient parallelization of quantum basis state shift
• Further improving quantum algorithms for nonlinear differential equations via higher-order methods and rescaling
• Protocols for classically training quantum generative models on probability distributions
• Self-Adaptive Physics-Informed Quantum Machine Learning for Solving Differential Equations
• Digital-analog co-design of the Harrow-Hassidim-Lloyd algorithm
• Shape and size of large-scale vortices: A generic fluid pattern in geophysical fluid dynamics
• Error-tolerant quantum convolutional neural networks for symmetry-protected topological phases
• Quantum Carleman linearisation efficiency in nonlinear fluid dynamics
• Protocols for Trainable and Differentiable Quantum Generative Modelling
• Quantum simulation of discrete linear dynamical systems and simple iterative methods in linear algebra via Schrodingerisation
• The topology of data hides in quantum thermal states
• Quantum topological data analysis via the estimation of the density of states
• Quantum Iterative Methods for Solving Differential Equations with Application to Computational Fluid Dynamics
• Quantum algorithms for solving a drift-diffusion equation: A complexity analysis