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Project 3
Quantum Algorithm as a PDE Solver for Computational Fluid Dynamics (CFD)

Computational Fluid Dynamics

This open challenge tasks participants with designing and prototyping resource‑lean quantum‑enhanced PDE solvers.
 

We’re excited to have BQP as a key project partner this year. During the Project Orientation session, Dr. Abhishek Chopra (BQP) provided an overview of the project. You can watch the recording below.

About BQP

BQP is a simulation company for mission-critical applications. Their mission is to solve complex, unsolvable simulations with advanced algorithms and next-gen computing through an innovative simulation platform

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Classical high‑fidelity Computational Fluid Dynamics (CFD) solvers struggle with ever‑increasing resolution requirements and stiff nonlinear Partial Differential Equations (PDEs). Quantum algorithms, when carefully co‑designed with classical components, have the potential to unlock exponential state‑space compression and polynomial speed‑ups for CFD analysis in aeronautics, energy, and climate science.

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This open challenge tasks participants with designing and prototyping resource‑lean quantum‑enhanced PDE solvers based on two recently proposed frameworks:

 

Participants should utilize either the QTN or HSE algorithm (hybrid QTN-HSE approaches are also welcome) to solve the important partial differential equation (PDE) in CFD of the Burgers’ Equation for 1D Shock Tube:

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The Burgers’ equation is a canonical nonlinear PDE that blends convective nonlinearity with viscous diffusion in a single scalar (1‑D) field. By stripping away the pressure term and incompressibility constraint of the full Navier–Stokes (NS) system, it retains the hardest parts of fluid motion, non‑linear steepening and viscous smoothing, while remaining analytically tractable. This makes Burgers an ideal entry‑level CFD benchmark and a low‑resource proving ground for quantum solvers. Because Burgers keeps the hard nonlinear/viscous core of NS, but omits pressure projection, any quantum‑classical splitting, Trotterisation, or tensor‑compression validated here will transfer directly to NS once a pressure solver is added. Resource counts obtained on Burgers therefore provide a lower‑bound estimate for full‑scale Navier–Stokes workloads.

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Participants must demonstrate that their approach can be executed on error‑mitigated or early error‑corrected hardware expected within 3–5 years by meeting the following design goals:

  • Low circuit depth.

  • Low qubit footprint.

  • Minimal classical pre/post‑processing overhead.

  • Robustness to realistic gate and readout noise.

  • Clear scalability path to higher grid resolutions and 3‑D flows.

01.

Challenge Duration & Key Dates

  1. 5 weeks

  2. Teams start working on July 1, 2025

  3. Teams submit their challenge solutions on August 10, 2025

02.

Team guidelines

  1. Max. Team size - 3

  2. All team participants must be enrolled in Womanium & WISER 2025 Quantum Program.

  3. Everyone is eligible to participate in this challenge and win awards.

  4. Best participants get selected for QSL fellowships

  5. We strongly encourage interdisciplinary collaborations pairing mathematically inclined researchers and practical developers familiar with diverse quantum SDKs and tooling.

03.

Quantum hardware & platform

  1. Participants may use any quantum SDK or platform of their choice.

  2. Participants may use any quantum hardware for noise-model simulations.

04.

Challenge deliverables

The submission github repo must include the following:
 

  1. Algorithm Design Brief - ≤ 5page PDF describing the chosen framework (QTN, HSE, or hybrid), mapping of PDE (1D Burgers’ Equation), gate decomposition, and resource estimates

  2. Prototype Code - Open‑source implementation runnable on a noiseless simulator and at least one real QPU backend (IBM, IonQ, Rigetti, Quantinuum, etc.).

  3. Validation & Benchmark - Perform a quantitative comparison of the quantum solver against a classical solver reference for the 1-D viscous Burgers shock tube; report L₂-error, wall-clock time, and noisy-simulator metrics (e.g., effective error rates) for ≥ 3 time steps.

  4. Resource & Noise Analysis - Table of qubits, two‑qubit‑gate depth, T‑count (if relevant), and mitigation strategy (e.g. ZNE, Clifford data regression).

  5. Quantum Hardware Run - Execute at least one time step of the 1‑D Burgers benchmark on a physical QPU and present raw and error‑mitigated results, with runtime and noise diagnostics

  6. Scalability Study - Show how resources scale with grid size.

  7. Algorithm Comparison - Discuss trade‑offs between QTN and HSE. 

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Hints: Start with a coarse grid (16 × 16) and short‑time integration to keep depth low.

05.

Judging Criteria

  1. The submissions must be in an easy-to-access, and well-structured format.
    All participants must complete the first four Tasks 1), 2) , 3) and 4) to be eligible for project certificates.

  2. The best attempt at Tasks 5), 6) and 7) would be given the most weight. Finalists for QSL fellowships will be decided on the basis of highest cumulative scores from all the tasks, technical merit, novelty, communication and presentation skills.

  • 20 % - Clear explanation & novelty: rationale for chosen algorithm, theoretical insight, originality of approach.

  • 20 % - Prototype implementation & successful run: clean, well‑documented code that runs end‑to‑end on noisy simulators; reproducible results.

  • 20 % - Quantum resource efficiency: low qubit count and circuit depth for a given accuracy; efficient gate synthesis.

  • 20 % - Noise robustness: effectiveness of error‑mitigation and resilience demonstrated via noisy simulations.

  • 10 % - Hardware results: quality of real‑hardware execution, mitigation applied, insight from raw vs. corrected data.

  • 5 % - Scalability road‑map: evidence of systematic scaling to finer grids or higher dimensions; resource trends.

  • 5 % - Algorithm comparison: critical analysis of trade‑offs between QTN and HSE (or hybrids); reasoned conclusions.

06.

Recommended reading list

  1. Peddinti, R.D., Pisoni, S., Marini, A. et al. Quantum-inspired framework for computational fluid dynamics. Commun Phys 7, 135 (2024). https://doi.org/10.1038/s42005-024-01623-8

  2. Zhaoyuan Meng and Yue Yang. Quantum computing of fluid dynamics using the hydrodynamic Schrödinger equation. Phys. Rev. Research 5, 033182 https://doi.org/10.1103/PhysRevResearch.5.033182

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