Propelling aerospace applications with Rolls-Royce, AMD, and PennyLane

PennyLane loves AMD, and we have demonstrated how our Lightning quantum simulator can unlock the full power of AMD GPUs (whether on your laptop, supercomputers, or the cloud). Today, we are taking that foundation and applying it to a practical challenge that sits at the very heart of aerospace engineering: simulating computational fluid dynamics (CFD).

Collaborating with Rolls-Royce and AMD, we have successfully scaled up compilation and simulation of a key component of Rolls-Royce’s CFD workflow — the Quantum Singular Value Transformation (QSVT) — on AMD GPUs. This allows us to utilize complex models in our quantum workflows that are truly representative of the industrial problems found in jet engine design; resulting in compiling and executing a 256 x 256 CFD mesh model on 20 qubits with 35 million gates in under two hours.

Separately, we have demonstrated simulation speedups of 25x on AMD GPUs, and that PennyLane is capable of dynamic compilation of QSVT workflows with over 60 qubits and millions of hardware-native gates.

Read on to learn more about bridging the gap between quantum computing and jet engine design, and how you can get started using AMD hardware and PennyLane.

Contents

• Why Rolls-Royce needs quantum
• QSVT for fluid dynamics
• Scaling QSVT with Lightning, Catalyst, and AMD GPUs
• Large scale compilation
• Tackling computational fluid dynamics
• What’s next?
• How to get started

Why Rolls-Royce needs quantum

Quantum computing often faces the question: what is it actually useful for? Every day, incredible advances are being made in a host of advanced industries — from drug design to engineering — yet underlying these advances are increasingly expensive large-scale simulations. The challenge we face in the quantum computing community is understanding these advances and techniques, and determining ways to map these problems to things that quantum computers are good at, to avoid bottlenecks and reduce costs.

Modelling and simulation using high performance computers are essential design tools in many industries, including aerospace engineering. In particular, CFD is one of the preeminent tools used to model the air-flow and related phenomena through jet engines, with millions of CFD calculations, which solve massive systems of linear equations, being run annually to design new low-emission engines.

However, as Rolls-Royce moves towards whole engine simulations, this classical supercomputing time is becoming increasingly prohibitive. Luckily, QSVT is a leading candidate for solving these linear systems faster on fault-tolerant quantum computers (FTQC).

QSVT for fluid dynamics

QSVT is often called the "grand unification" of quantum algorithms, as it allows for the arbitrary transformation of matrices embedded in the quantum computer via some specified polynomial, without performing actual singular value decompositions. Assuming that you can efficiently encode your input matrix using only a polynomial depth quantum circuit, the entire computation will run in polynomial time.

Another advantage of the QSVT algorithm is that, while it generates deep circuits (and thus will require fault-tolerant quantum computers with logical, error corrected qubits), it requires relatively narrow circuits, making it a leading candidate for early-FTQC (that is, consisting of 100-500 error corrected qubits).

All of this makes QSVT a leading candidate for solving linear systems of equations found in many practical applications — such as Rolls-Royce’s CFD workflow — on early fault-tolerant quantum hardware.

Scaling QSVT with Lightning, Catalyst, and AMD GPUs

To battletest PennyLane’s built-in QSVT functionality, we first created a simple QSVT program with block encoded Toeplitz matrices, and a fixed set of phase angles. Then, we just-in-time compiled the quantum program using the Catalyst compiler (a scalable MLIR/LLVM compiler for hybrid quantum-classical PennyLane programs), and executed it using lightning.amdgpu on a MI300X GPU on the AMD Dev Cloud.

We can see that compiling and executing the program on a single GPU results in an approximate 20x speedup compared to multithreaded CPU execution with 16 OpenMP threads.

Since Catalyst supports compilation of structured parametric programs (that is, we can compile the program once and feed the optimized binary input parameter values at runtime), we can isolate and time solely the execution time. Looking at just the execution time, we achieve an almost 25x speedup for QSVT simulation on the MI300X GPU compared to multithreaded CPU execution ✈️

Large scale compilation

Simulation is only part of the story — in parallel, we are developing the PennyLane software stack to efficiently compile and optimize large-scale workflows (with hundreds of logical qubits and billions of gates) to ensure that when the hardware arrives, the code is ready to fly. This is critically important — without the ability to compile the program down to classical and quantum instructions, we will not be able to execute even if the FTQC hardware is available.

Our Catalyst LLVM infrastructure is currently able to support compiling the QSVT algorithm on logical qubits to an executable workload with up to 68 qubits. In addition, we also need to ensure we are optimizing the circuit, and generating low-level quantum instructions that are quantum hardware compatible. Decomposing the circuit to Clifford+T gates, we are able to generate a hardware-optimized workload with over 15 million gates.

In addition, we can parametrically compile this workflow for arbitrary parameters, then execute it with thousands of different QSVT phase angles — avoiding re-compilation and only incurring the execution cost on the simulator or future hardware device.

Tackling computational fluid dynamics

Working with Rolls-Royce, the next step was to utilize PennyLane’s QSVT infrastructure to solve realistic CFD problems. To do so, we needed to make sure that we are both embedding the matrix-representation of the CFD system, and the parameters specifying how to solve the system, into the quantum computer.

• For that first ingredient, the Rolls-Royce team generated various meshes representing a 2-dimensional lid driven cavity test case. These meshes are represented as square matrices, of increasing size depending on the accuracy of the model. From here, the non-linear fluid equations for laminar flow on this mesh are linearized — resulting in a large sparse matrix with structure, but typically non-Hermitian (and often ill-conditioned). Taking advantage of this structure allows for efficient block-encoding techniques for embedding.

• Secondly, we need to provide parameters to the QSVT algorithm to perform the correct polynomial transformation of the matrix. Since we wish to solve a system of linear equations, we needed to encode a polynomial that will approximate inverting this matrix, with the quality of the approximation determined by accuracy considerations. The larger the size of the encoded matrix, the more terms are needed in the polynomial to give the same level of accuracy.

To this end, we have implemented a GPU compatible version of the Non-linear Fast Fourier Transform in PennyLane, which allows us to quickly convert our inverse polynomial approximation into quantum operations. With these two pieces in place, and leveraging the scalable infrastructure of Catalyst and Lightning, we executed a 256 x 256 CFD matrix on 20 qubits with 35 million gates in under two hours — a problem size that has never before been executed in a quantum setting.

Contours of velocity magnitude for the 256 x 256 CFD mesh.

While the power of quantum computing will be truly unlocked when FTQC hardware is here, for now quantum simulation still plays an important role in validating quantum algorithm research. The results we shared here utilized a single GPU, but there is potential for scaling to even larger system sizes by distributing across multiple GPUs.

What’s next?

Building on this momentum, we will continue to scale up PennyLane’s infrastructure — enabling meaningful quantum algorithm development with industry, and pushing the limits of compilation and simulation. To do so, there is work ahead to optimize the generation of hardware-native gates, and ensure that program structure is preserved throughout the stack.

As we continue building out the quantum software stack, it’s important to ensure we aren't just running random circuits, but are guided by practical applications (that could one day help design jet engines!). However, the path to quantum advantage is not a solo journey. It requires the industrial context of partners like Rolls-Royce, the hardware leadership of AMD, and the software ecosystem of PennyLane to connect the two — providing the software stack that allows researchers to express complex algorithms like QSVT and compile them for high-performance execution.

How to get started

Whether you are interested in industrial applications like CFD or fundamental research, the combination of PennyLane and high-performance hardware is ready for you.

• Read more: Check out more details over on the AMD blog, and learn how to get started with Lightning on the AMD Dev Cloud.

• Explore the science: Read about the Rolls-Royce and Xanadu partnership.

• Get hands-on: Learn how to implement QSVT in PennyLane with our step-by-step demos, and analyze it with our resource estimation tooling.

Take Lightning for a spin wherever you have AMD GPUs — from laptops, to supercomputing centers, to the cloud—and scale your quantum simulations even further.

Interested in getting in touch with us? Simply head over to our GitHub repository and check out the ongoing work and join in on the development. Or pop over to the PennyLane discussion forum to let us know how you are using PennyLane, Lightning, and Catalyst in your workflows.

And if you are as excited as we are, make sure to keep an eye on the PennyLane blog and follow us on social media for the latest PennyLane features and updates!