Quantum Computing for Heat Transfer Simulation

Solving partial differential equations is fundamental to industries that work with complex physical systems. In aerospace, these equations describe how heat moves through a spacecraft during reentry or how air flows around an aircraft surface. As designs become more advanced, the mathematical problems behind them increase in size and complexity, often pushing classical numerical methods to their limits.

One example is the design of thermal protection systems for hypersonic reentry vehicles. Engineers must simulate how heat propagates through micro heat exchangers under extreme temperatures and pressure. Traditional approaches, such as finite element and finite volume methods, can become difficult to scale while maintaining accuracy. This makes heat transfer a compelling candidate for studying how quantum computing could support large, sparse systems of equations and complement existing tools.

The AQEDP (Advancing Quantum Exploration for Discretized Physics) project was created to explore this opportunity. Its goal is to understand how quantum algorithms could accelerate the resolution of discretized physical problems and to determine what is required to bring these methods closer to industrial use.

A consortium built for quantum innovation

AQEDP brings together expertise from industry, research, and quantum technology:

C12 contributes its quantum hardware architecture based on carbon nanotube spin qubits and Callisto, a noisy quantum emulator that models realistic quantum behavior.
Dassault Aviation provides the industrial use case. The company brings deep aerospace experience and defines the heat transfer problems that guide the project, focusing on micro heat exchangers for reentry applications.
The Île-de-France Region (IDF) finances the project and supports its development, strengthening the regional quantum and HPC ecosystem.
IRT SystemX hosts the PhD researcher who develops the algorithmic backbone of the project and contributes systems engineering capabilities.
LMF/Inria supervises the scientific work and provides expertise in quantum algorithms and compilation.
Systematic Paris-Region supports the project within the regional innovation framework.

Together, the partners aim to create quantum techniques that are grounded in physical reality and that deliver insights useful for future industrial design workflows.

From physical models to quantum-ready workflows

The project focuses on building a hybrid quantum–classical approach for solving discretized PDEs. The workflow develops across three connected layers.

Co-design from the physics upward

Instead of inserting quantum algorithms into an existing classical pipeline, the team works from the physical model outward. Starting with a simplified 2D heat transfer system, the consortium evaluates:

how different discretization strategies affect sparsity and matrix structure
which quantum algorithms, such as QSVT, HHL or VQLS, are appropriate for the resulting system
how both the numerical and quantum steps can be co-optimized to reduce circuit depth and resource requirements

This approach ensures that quantum methods are matched to the physics of the problem rather than applied in isolation.

Quantum circuit emulation and dequantization

Since near-term hardware remains limited in scale, Callisto plays an essential role. The emulator allows the team to simulate candidate quantum circuits both in ideal and noise-aware configurations and to estimate expected performance on future hardware.

The project also studies dequantization, which examines how ideas from quantum algorithms can inspire classical solvers. This helps define the boundary between what is uniquely quantum and what can be achieved classically with quantum-inspired tools.

Industrial testing and benchmarking

Algorithms developed in AQEDP are evaluated on aerospace test cases provided by Dassault Aviation. These include steady-state heat equations with controlled boundary conditions and progressively more complex geometries.

Performance is compared with classical solvers across accuracy, computational cost and scalability. The objective is to identify where quantum methods could offer a meaningful advantage and to quantify the resources needed for real applications.

Moving forward

AQEDP is a three-year effort designed to build both theoretical understanding and practical workflows. By its conclusion, the consortium aims to deliver a validated prototype that demonstrates how quantum computing, supported by realistic emulation on Callisto, can contribute to next-generation industrial simulation.

Full report available soon.

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23 january 2026