by Amara Graps
To what extent does an aircraft firm value innovation? To an extent to be a priority. From the Rolls-Royce Holdings company’s history, no one should be surprised that there is a team of quantum experts at this company. When the British government bailed out Rolls-Royce Holdings, after the RB211-22 jet engine project bankrupted the company fifty years ago, it was innovation that enabled this company to recover.
One of the customers I really appreciate is Rolls-Royce. The Rolls-Royce team is built of quantum experts. They are dealing with a very interesting problem, which is CFD. Its really a problem that pushes the boundaries of classical computing to the limit. —-Nir Minerbi (Classiq), QCR transcript on Superposition Guy’s Podcast
A QCFD Use Case with the Harrow-Hassidim-Lloyd (HHL) Algorithm
It also takes courage to maintain innovation as a priority. This Rolls-Royce team did not appear to be daunted by the Harrow-Hassidim-Lloyd algorithm, which is said to be appropriate only for fault-tolerant quantum computers.
The Lapworth, 2022 research: A Hybrid Quantum-Classical CFD Methodology with Benchmark HHL Solutions developed a non-linear, hybrid quantum-classical CFD solver for fully converged solutions using the SIMPLE CFD algorithm and the HHL algorithm. His research investigated the solution accuracy achievable with HHL, using test matrices sampled from the classical CFD solver. The work performed full, non-linear, hybrid CFD calculations for the smallest 5 × 5 and 9 × 9 CFD meshes and considered meshes with up to 65 × 65 nodes. The research estimated the number of logical qubits needed by HHL, which ranged from 15 to 33. The work provided CFD test cases and benchmark solutions for the first generation of fault-tolerant devices. The Appendices introduce the general principles of CFD, which is useful for newcomers.
The work probed the limits of a hybrid CFD solution, analyzing timing results of the hybrid solver compared to the classical solver. For example, the 65 × 65 node test case takes thirty times longer to calculate the Pauli strings in the decomposition than it does for the complete CFD solver. On the other hand, benchmark results from emulating a hybrid CFD solution with HHL on the smallest 5 × 5 mesh, demonstrated that HHL can achieve convergence levels with high accuracy and does not require full 64-bit precision to match the iterative performance of the CFD solver. Lapworth notes that even though the Pauli string approach can be parallelized more easily than a CFD solver, it is likely to require large super-computing expenses to reach the cross-over threshold for those large mesh, industrial scale CFD applications.
Collaborations for QCFD Support
- In October 2022, in an effort that surely built on the Lapworth, 2022 result, the software developer Classiq revealed that they were collaborating with Rolls-Royce, to implement a hybrid classical/quantum implementation of CFD, using the quantum HHL method.
- In January 2023, Xanadu and Rolls-Royce agreed to add new functionality to Xanadu’s Pennylane software with a new quantum algorithm which solves linearized equations, called the Quantum Singular Value Transformation (QSVT).
- In May 2023, NVIDIA, Rolls-Royce, and Classiq announced a collaboration to enhance jet engine efficiency by designing and simulating the world’s largest quantum computing circuit for CFD, which is 10 million layers deep with 39 qubits. The simulation was performed using NVIDIA’s A100 Tensor Core GPUs and cuQuantum software. NVIDIA’s Grace Hopper Superchip was designed for large-scale quantum simulations, combining GPUs and CPUs for optimal performance, and linking to quantum processors. NVIDIA’s CUDA Quantum programming model connected the GPUs and QPUs, which supported the development of hybrid quantum-classical computing systems.
- In December 2023, Riverlane, with Rolls-Royce and National Quantum Computing Centre (NQCC) agreed to explore accelerating materials design using quantum computing. Through the QuaMaD project, they will be simulating complex materials, reducing qubit requirements.
- In March 2024, Rolls-Royce, Riverlane, and Xanadu Teamed Up on a UK and Canadian grants project, to develop quantum computing applications for modeling air flow in jet engines.
A QCFD Use Case with the Finite Method based on Quantum Linear Solver Algorithm (QLSA)
In keeping with the jet engine theme of this article, jet engine simulations using quantum computers also has advanced according to BosonQ Psi. Using QCFD with a hybrid quantum-classical solver on their BQPhy® platform, after conducting ~100000 runs, a jet engine simulation might be achievable with just 30 logical qubits, compared to the present requirement of 19.2 million HPC cores. The research: Bosco et al., 2024, Demonstration of Scalability and Accuracy of Variational Quantum Linear Solver for Computational Fluid Dynamics developed their Hybrid Quantum-Classical Finite Method (HQCFM), based on an existing Quantum Linear Solver Algorithm (QLSA), to demonstrate highly accurate solutions for the 2D, transient, incompressible, viscous, non-linear, coupled, Burgers’ equation, with results comparable to classical solvers for large systems up to 2048 mesh points.
In an earlier QCR Article, I identified the HHL algorithm, as a quantum algorithm primitive, to begin learning how to include quantum computers in solving differential equations. See the GQI Quantum Algorithms Framework in the next Figure for GQI’s approach to quantum algorithms primitives. As we are linearizing the Navier-Stokes equation and appropriately applying quantum primitives, we should add the QLSS Linear Algebra primitives to the QCFD task as well.
We will present an interesting twist to solve CFD without these extra linearization steps in the Part 3 of this series.
(*) If you are interested to learn more, please don’t hesitate to contact [email protected].
October 10, 2024
