Title: Developing Quantum Algorithms for Lattice Boltzmann Method with Nonlinear Collisions: Application to 
Multiphase Flows (QLBM)

Research Environment: The PhD candidate will work at CORIA Lab (CNRS, INSA Rouen, France), a leading 
research center in fluid mechanics and numerical modeling. The laboratory has extensive expertise in CFD, 
multiphase flows, and HPC, with collaborations in quantum computing. The project will also benefit from 
international partnerships, including researchers from TU Delft, University of Sherbrooke, and other quantum 
computing institutions.

Project Overview: Classical computational fluid dynamics (CFD) methods face limitations due to the high 
computational cost of solving nonlinear equations. This PhD project aims to develop a pure quantum 
algorithm for the Lattice Boltzmann Method (LBM), with a focus on efficiently handling nonlinear collision 
terms—a major challenge in quantum computing. The project will explore: (i)Encoding strategies for a fully 
quantum LBM (QLBM) solver. (ii) Quantum algorithms for directly calculating nonlinear terms. (iii) 
Implementation on real quantum hardware with error correction techniques. (iv)Application to multiphase 
flows using the Shan-Chen model. Successful development of this solver could revolutionize CFD by enabling 
high-dimensional simulations that are currently infeasible on classical supercomputers.

Tasks and Responsibilities
The PhD candidate will:
1.	Review state-of-the-art quantum algorithms (QAs) and LBM techniques.
2.	Develop quantum algorithms for LBM, focusing on nonlinear collision terms.
3.	Implement and optimize quantum circuits for LBM on quantum simulators.
4.	Test and validate the solver on real quantum devices, such as IBM Quantum.
5.	Extend the QLBM solver for multiphase flows, incorporating the Shan-Chen model.
6.	Publish results in leading scientific journals and present findings at international conferences.

Candidate Profile
•	Background: Master’s degree (or equivalent) in computational fluid dynamics, applied mathematics, 
quantum computing, physics, or a related field.
•	Skills:
o	Strong foundation in fluid mechanics and numerical methods.
o	Experience with lattice Boltzmann methods (LBM) or computational fluid dynamics (CFD).
o	Familiarity with quantum computing principles, including quantum circuits and algorithms.
o	Proficiency in programming (Python, MATLAB, or C++).
o	Interest in high-performance computing (HPC) and parallel computing.
o	Motivation for interdisciplinary research in fluid mechanics and quantum computing.

Application Procedure
Interested candidates should submit the following documents:
•	CV detailing academic background and relevant experience.
•	Cover letter explaining motivation for the PhD and fit for the project.
•	Transcripts of academic records (Master’s/Bachelor’s).
•	Reference letters (and contact information of referees).
To apply, mention the QLBM project in title of your email and send your complete application files to:
•	Prof. Mostafa Safdari Shadloo (Mostafa.Safdari-Shadloo@insa-rouen.fr)
•	Prof. Abdellah Hadjadj (Abdellah.Hadjadj@coria.fr)

Deadline for applications: Open until filled (early applications are encouraged).
Location: CORIA Lab, CNRS, INSA Rouen, Rouen, Normandy, France.
Start Date: Oct. 2025.
Join us in pushing the boundaries of quantum computing for fluid dynamics!
PS: Only the shortlisted candidates will be contacted.