Projects

QA4SDE: Quantum Algorithms for the solution of differential equations

The potential of quantum computers for solving partial differential equations

Funding: ICSC Innovation Funds

Enabling technology: High Performance Computing, Quantum computing

Sustainable Development Goals

In principle, quantum computers could achieve polynomial time in operations on vectors within exponentially large vector spaces. However, there are not many known problems in which such exponential speedups have been demonstrated (Shor’s algorithm is one example). This project aims to analyze the potential advantage of using quantum computers to solve linear and nonlinear partial differential equations. Quantum algorithms capable of solving even just a subset of the problems modeled through differential equations on current supercomputers would be of considerable interest and value.

National Centre for HPC, Big Data and Quantum Computing (ICSC), a project funded by the European Union – NextGenerationEU – and by Italy’s National Recovery and Resilience Plan (PNRR) – Mission 4, Component 2.

Objectives

The main goal of this project is to gain a better understanding of the potential advantage quantum computing could bring to the problem of solving partial differential equations, which are needed to model a wide range of problems.

This will be pursued through two industrial applications: fluid dynamics modeling and electromagnetic wave propagation modeling via Maxwell’s equations.

Initial challenge

For certain problems, quantum computers have been shown to provide an exponential speedup over their classical counterparts. However, there are not many known problems in which such uses and potential have been demonstrated.

Solution

The solution proposed by the project involves exploring the application of quantum computing to solve PDEs in scenarios of scientific and industrial relevance, identifying the appropriate quantum algorithms and assessing their potential advantage over classical methods. For example, cases being studied include simulating fluid propagation through porous media, air flow behavior for aerodynamic profile design, and radar electromagnetic wave backscattering from complex targets.

Benefits

Differential equations are needed to model a wide variety of problems, including industrial design and weather forecasting, and their numerical solution lies at the heart of many applications run in supercomputing centers. For this reason, quantum algorithms capable of solving even just a subset of the problems modeled through differential equations on current supercomputers would be of considerable interest and value.

IFAB’s role

IFAB contributed to the development and implementation of the algorithmic solutions and benchmarking tools needed to assess the potential of quantum computing in solving partial differential equations (PDEs) — computationally intensive problems with direct applications in industrial fields such as fluid dynamics and electromagnetic simulation.

IFAB’s technical contribution was organized along three main lines:

Analyzing and evaluating the most promising quantum theoretical frameworks for the identified application areas;
Developing classical algorithms to support quantum techniques, translating theoretical models into implementations executable on industrial use cases;
Running the solutions and conducting comparative benchmarking against classical computational methods, to measure their performance, accuracy, and efficiency.

Participation in QA4SDE allowed Fondazione IFAB to develop specialized expertise in applied quantum computing, consolidated through interaction with a partnership of excellence involving ENI, IIT, Leonardo, Thales Alenia Space, University of Bari, and University of Padua.