Quantum Algorithms for Geologic Fracture Networks

TL;DR

This paper introduces two quantum algorithms for modeling fractured flow in geologic systems, addressing the limitations of classical methods and demonstrating feasibility on current noisy quantum hardware for small to medium-sized problems.

Contribution

The paper presents two novel quantum algorithms tailored for fractured flow modeling, with one designed for future error-free quantum computers and the other for current noisy hardware.

Findings

The noise-resilient algorithm performs well on small to medium-sized problems.

Current hardware is too noisy for the error-free quantum algorithm to be effective.

Further improvements are possible with quantum error mitigation and preconditioning.

Abstract

Solving large systems of equations is a challenge for modeling natural phenomena, such as simulating subsurface flow. To avoid systems that are intractable on current computers, it is often necessary to neglect information at small scales, an approach known as coarse-graining. For many practical applications, such as flow in porous, homogenous materials, coarse-graining offers a sufficiently-accurate approximation of the solution. Unfortunately, fractured systems cannot be accurately coarse-grained, as critical network topology exists at the smallest scales, including topology that can push the network across a percolation threshold. Therefore, new techniques are necessary to accurately model important fracture systems. Quantum algorithms for solving linear systems offer a theoretically-exponential improvement over their classical counterparts, and in this work we introduce two quantum algorithms for fractured flow. The first algorithm, designed for future quantum computers which operate without error, has enormous potential, but we demonstrate that current hardware is too noisy for adequate performance. The second algorithm, designed to be noise resilient, already performs well for problems of small to medium size (order 10 to 1000 nodes), which we demonstrate experimentally and explain theoretically. We expect further improvements by leveraging quantum error mitigation and preconditioning.