Solving the Hele-Shaw flow using the Harrow-Hassidim-Lloyd algorithm on superconducting devices: A study of efficiency and challenges

TL;DR

This paper evaluates the effectiveness of the Harrow-Hassidim-Lloyd quantum linear solver in simulating ideal fluid flow problems, analyzing accuracy, computational costs, and challenges on superconducting quantum hardware.

Contribution

It provides the first practical assessment of the HHL algorithm for fluid flow simulations on real quantum devices, including error mitigation strategies.

Findings

HHL can solve ideal flow equations with measurable accuracy

Quantum hardware introduces significant errors requiring mitigation

Preliminary results highlight challenges and potential of quantum fluid simulations

Abstract

The development of quantum processors capable of handling practical fluid flow problems represents a distant yet promising frontier. Recent strides in quantum algorithms, particularly linear solvers, have illuminated the path toward quantum solutions for classical fluid flow solvers. However, assessing the capability of these quantum linear systems algorithms (QLSAs) in solving ideal flow equations on real hardware is crucial for their future development in practical fluid flow applications. In this study, we examine the capability of a canonical QLSA, the Harrow-Hassidim-Lloyd (HHL) algorithm, in accurately solving the system of linear equations governing an idealized fluid flow problem, specifically the Hele-Shaw flow. Our investigation focuses on analyzing the accuracy and computational cost of the HHL solver. To gauge the stability and convergence of the solver, we conduct shots-based simulations on quantum simulators. Furthermore, we share insights gained from executing the HHL solver on superconducting quantum devices. To mitigate errors arising from qubit measurement, gate operations, and qubit decoherence inherent in quantum devices, we employ various error suppression and mitigation techniques. Our preliminary assessments serve as a foundational step towards enabling more complex quantum utility scale evaluation of using QLSA for solving fluid flow problems.