Periodic Reporting for period 1 - QCFD (Quantum Computational Fluid Dynamics)
Reporting period: 2022-11-01 to 2024-04-30
Computational Fluid Dynamics(CFD) is a mature field of research that facilitates scientific findings in physical and life sciences including climate research and technological progress in the energy, chemical and transportation industries. For diagnostic purposes, i.e. for analyzing existing flow configurations, powerful numerical CFD tools are widely available. These tools extensively use approximate physical models to represent unresolved physical phenomena and employ scale-reducing simplifications and constraints to increase the realizability of the computations involved. Difficulties in identifying broadly applicable physical models and approximations severely limit the usage and general reliability of CFD methods for predictive and design purposes.
Direct Numerical Simulation captures all relevant processes directly and does not rely on approximate models for unresolved physics, making it the computational continuum method with the highest fidelity. The wide separation of length and time scales in technical flows, however, makes direct numerical simulation of all but the most simplistic applications computationally intractable. This holds particularly for multi-physics applications such as conjugate heat transfer and chemically reacting flows, where the added physical complexity further compounds the problem. Similarly, methods for computing probability distribution functions of turbulent reactive flows suffer from the high dimensionality of the underlying problem. For complex flows, often only incomplete information about its properties can thus be obtained from numerical simulations.
The ability to fully characterize complex flows by numerical simulations is thus the holy grail of CFD research and would enable the reliable design of much more energy-efficient products and infrastructure. The NASA CFD Vision 2030 study addresses the current state of CFD and concludes that present CFD capabilities must undergo a revolutionary change to meet the future needs of academia and industry.
Quantum CFD (QCFD) promises to fundamentally change this paradigm by stripping away the need for limits, simplification and specialization, through the direct resolution of all relevant physical scales and phenomena. More importantly, it promises to do so for a small fraction of the computational cost required by classical methods. The impact of such technology on the field of CFD and product design, in general, would be nothing short of revolutionary. More generally, it would massively strengthen numerical simulations and data sciences as the third pillar of today’s scientific enterprise next to theory and physical experiments.
The overarching goal of the QCFD is to rise to this challenge by developing a versatile quantum algorithmic framework for efficiently solving a wide range of CFD problems without making the usual compromises on accuracy. We propose and develop QCFD algorithms. We test and benchmark them on classical emulators and on quantum hardware developed in European Quantum Technology Flagship Projects. Our approach demonstrates the feasibility and potential advantages of QCFD compared to standard CFD methods and identifies the requirements on the quantum hardware to successfully run QCFD software. Our project tackles increasingly complex flow examples and utilizes them to iteratively benchmark, verify and improve the employed quantum algorithms. The resulting software framework shall enable users to run QCFD algorithms on suitable quantum flagship hardware when this becomes available.
Direct Numerical Simulation captures all relevant processes directly and does not rely on approximate models for unresolved physics, making it the computational continuum method with the highest fidelity. The wide separation of length and time scales in technical flows, however, makes direct numerical simulation of all but the most simplistic applications computationally intractable. This holds particularly for multi-physics applications such as conjugate heat transfer and chemically reacting flows, where the added physical complexity further compounds the problem. Similarly, methods for computing probability distribution functions of turbulent reactive flows suffer from the high dimensionality of the underlying problem. For complex flows, often only incomplete information about its properties can thus be obtained from numerical simulations.
The ability to fully characterize complex flows by numerical simulations is thus the holy grail of CFD research and would enable the reliable design of much more energy-efficient products and infrastructure. The NASA CFD Vision 2030 study addresses the current state of CFD and concludes that present CFD capabilities must undergo a revolutionary change to meet the future needs of academia and industry.
Quantum CFD (QCFD) promises to fundamentally change this paradigm by stripping away the need for limits, simplification and specialization, through the direct resolution of all relevant physical scales and phenomena. More importantly, it promises to do so for a small fraction of the computational cost required by classical methods. The impact of such technology on the field of CFD and product design, in general, would be nothing short of revolutionary. More generally, it would massively strengthen numerical simulations and data sciences as the third pillar of today’s scientific enterprise next to theory and physical experiments.
The overarching goal of the QCFD is to rise to this challenge by developing a versatile quantum algorithmic framework for efficiently solving a wide range of CFD problems without making the usual compromises on accuracy. We propose and develop QCFD algorithms. We test and benchmark them on classical emulators and on quantum hardware developed in European Quantum Technology Flagship Projects. Our approach demonstrates the feasibility and potential advantages of QCFD compared to standard CFD methods and identifies the requirements on the quantum hardware to successfully run QCFD software. Our project tackles increasingly complex flow examples and utilizes them to iteratively benchmark, verify and improve the employed quantum algorithms. The resulting software framework shall enable users to run QCFD algorithms on suitable quantum flagship hardware when this becomes available.
One important part of the initial phase of the project was to increase the level of complexity of flows amenable to QCFD algorithms starting from basic examples that demonstrated the in-principal feasibility of QCFD. To move to the next level, we developed tensor network methods for describing boundary conditions, curvilinear coordinates, improved variational ansatzes for flow fields and high dimensional flow functions. We have also investigated a range of variational ansatzes for quantum circuits to encode flow fields and studied the efficacy of classical optimizers working together with the quantum algorithms. We have developed hardware-optimized quantum circuits and studied the scaling of the depth of the quantum circuits required to compute the relevant cost functions. Furthermore, we have analyzed a range of different quantum hardware platforms for their strength and expect several of them to become available to run QCFD algorithms in the future.
The project has successfully created datasets that contain solutions to a core set of simple CFD problems for benchmarking and validation. A similar set of CFD data resulting from tensor network simulations has also been computed. We have demonstrated that complex boundary conditions can be handled efficiently in tensor networks and quantum algorithms. Importantly, we found that quantum algorithms can provide an exponential compression of discrete representations of flow fields and at least a quadratic speed-up compared to tensor network algorithms. We have raised the interest and awareness of additional industry partners and have attracted intense attention from researchers around the world.
The project has successfully created datasets that contain solutions to a core set of simple CFD problems for benchmarking and validation. A similar set of CFD data resulting from tensor network simulations has also been computed. We have demonstrated that complex boundary conditions can be handled efficiently in tensor networks and quantum algorithms. Importantly, we found that quantum algorithms can provide an exponential compression of discrete representations of flow fields and at least a quadratic speed-up compared to tensor network algorithms. We have raised the interest and awareness of additional industry partners and have attracted intense attention from researchers around the world.
We showed that classical tensor network methods scale more favorably than standard DNS methods for the paradigm example of a lid driven cavity. In our example calculations this crossover happened at Re ≈10^4 (Fig. 1). We have performed direct simulations of 5-dimensional probability distributions that can usually only be sampled to obtain moments of the relevant physical quantities (Fig. 2).
From these classical simulations we also give a lower bound of the potential quantum advantage based on the required bond dimension. We showed that the resulting tensor networks can be translated efficiently into quantum networks to run on quantum hardware and that, while all tensor networks scale logarithmically with the problem size, the detailed scaling does depend heavily on the native capabilities of the quantum hardware (Fig. 3).
We have studied the implementation of basic QCFD examples on quantum hardware and compared gate-level simulations with runs on actual IBM quantum hardware. In Fig. 4 we show that current quantum hardware is in principle capable of accurately representing simple superfluid flows, but current noise levels diminish the quality of the reachable accuracy thus providing valuable feedback to hardware developers.
From these classical simulations we also give a lower bound of the potential quantum advantage based on the required bond dimension. We showed that the resulting tensor networks can be translated efficiently into quantum networks to run on quantum hardware and that, while all tensor networks scale logarithmically with the problem size, the detailed scaling does depend heavily on the native capabilities of the quantum hardware (Fig. 3).
We have studied the implementation of basic QCFD examples on quantum hardware and compared gate-level simulations with runs on actual IBM quantum hardware. In Fig. 4 we show that current quantum hardware is in principle capable of accurately representing simple superfluid flows, but current noise levels diminish the quality of the reachable accuracy thus providing valuable feedback to hardware developers.