QA4SDE: Quantum Algorithms for the solution of differential equations

Quantum computing's potential to solve partial differential equations
Thematic area: Projects, Tech
Financing: ICSC Innovation Grants
Enabling Technology: High Performance Computing, Quantum computing

Quantum Computers could in principle achieve polynomial times in operations dealing with vectors in exponentially large vector spaces. However, there are not many known problems where such exponential speedups have been demonstrated (Shor algorithm is an example). This project plans to analyze the potential advantage of using quantum computers for the solution of linear and non-linear partial differential equations. Quantum algorithms able to solve even a subset of the problems modeled through differential equations on current supercomputers would be of considerable interest and value. 

Italian Research Center on High Performance Computing Big Data and Quantum Computing (ICSC), project funded by European Union – NextGenerationEU – and National Recovery and Resilience Plan (NRRP) – Mission 4 Component 2. 

The goal

The main objective of this project is to better understand the potential advantage that Quantum Computing could bring to the problem of solving partial differential equations, which are needed for modeling a vast variety of problems.  

This will be implemented having in mind two industrial applications: the modelling of fluid dynamics and the modelling of electromagnetic waves propagation via Maxwell equations. 

The initial challenge

For some problems, quantum computers have been shown to provide exponential speed compared to their classical counterparts. However, there are not many demonstrations of such uses and the potential beyond it has not yet been studied.  

The solution

The solution proposed by the project is to explore the application of Quantum Computing to solve PDEs in scenarios of scientific and industrial relevance, identifying the appropriate quantum algorithms and evaluating their potential advantage over classical methods. For example, cases such as the simulation of fluid propagation in porous media, the behavior of airflows for airfoil design, and the backscattering of radar electromagnetic waves from complex targets are studied. 


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


Participating Spoke

Spoke 10


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