Integrating Quantum Algorithms Into Classical Frameworks: A Predictor-corrector Approach Using HHL

Abstract

The application of quantum algorithms to classical problems is generally accompanied by significant bottlenecks when transferring data between quantum and classical states, often negating any intrinsic quantum advantage. Here we address this challenge for a well-known algorithm for linear systems of equations, originally proposed by Harrow, Hassidim and Lloyd (HHL), by adapting it into a predictor-corrector instead of a direct solver. Rather than seeking the solution at the next time step, the goal now becomes determining the change between time steps. This strategy enables the intelligent omission of computationally costly steps commonly found in many classical algorithms, while simultaneously mitigating the notorious readout problems associated with extracting solutions from a quantum state. Random or regularly performed skips instead lead to simulation failure. We demonstrate that our methodology secures a useful polynomial advantage over a conventional application of the HHL algorithm. The practicality and versatility of the approach are illustrated through applications in various fields such as smoothed particle hydrodynamics, plasma simulations, and reactive flow configurations. Moreover, the proposed algorithm is well suited to run asynchronously on future heterogeneous hardware infrastructures and can effectively leverage the synergistic strengths of classical as well as quantum compute resources.

References in corpus (18)

• Quantum algorithm for solving linear systems of equations
• Quantum Amplitude Amplification and Estimation
• Quantum fingerprinting
• Quantum computing for finance: overview and prospects
• Quantum algorithm for systems of linear equations with exponentially improved dependence on precision
• Is there evidence for exponential quantum advantage in quantum chemistry?
• A quantum linear system algorithm for dense matrices
• The prospects of quantum computing in computational molecular biology
• Quantum Algorithm for Linear Regression
• Quantum computers as universal quantum simulators: state-of-art and perspectives
• Hybrid quantum-classical algorithms in the noisy intermediate-scale quantum era and beyond
• Variational Quantum Algorithms for Computational Fluid Dynamics
• Quantum Computers for Weather and Climate Prediction: The Good, the Bad and the Noisy
• Quantum algorithm for the Navier Stokes equations by using the streamfunction vorticity formulation and the lattice Boltzmann method
• NP-hard but no longer hard to solve? Using quantum computing to tackle optimization problems
• Stability issues in the quasineutral limit of the one-dimensional Vlasov-Poisson equation
• Quantum Algorithms for Solving Ordinary Differential Equations via Classical Integration Methods
• Time complexity analysis of quantum difference methods for linear high dimensional and multiscale partial differential equations