Bulletin of the American Physical Society
76th Annual Meeting of the Division of Fluid Dynamics
Sunday–Tuesday, November 19–21, 2023; Washington, DC
Session ZC17: Quantum Computing |
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Chair: Xinfeng Gao, University of Virginia Room: 145B |
Tuesday, November 21, 2023 12:50PM - 1:03PM |
ZC17.00001: Quantum Computing for CFD Hirad Alipanah, Robert Pinkston, Peyman Givi, Nikita Gourianov, Juan José Mendoza Arenas, Brian J McDermott, Dieter Jaksch Quantum computing (QC) is experiencing rapid developments and is widely expected to provide algorithmic scaling performance with polynomial, or even exponential advantages over what is currently possible on classical computers. Work is in progress to assess the performance of numerical methods that will enable the use of QC for computational fluid dynamics (CFD). As a step toward achieving this capability, a demonstration is made of the use of matrix product states (MPS), a subset of tensor network methods borrowed from many-body physics, to provide a low-rank approximation of the discretized Burger's equation. The corresponding MPS structure is solved on IBM's cloud computing platforms. Simulations are conducted on IBM's quantum simulators and noisy intermediate-scale quantum (NISQ) computers. The results are assessed via comparison with those obtained via classical simulations of the full-ranked equation. |
Tuesday, November 21, 2023 1:03PM - 1:16PM |
ZC17.00002: Quantum computing of nonlinear flow problems with a homotopy analysis algorithm Sachin Satish Bharadwaj, Balu Nadiga, Stephan Eidenbenz, K.R. Sreenivasan Quantum Computing (QC) has many nominal advantages over classical computing, but has yet to solve important practical problems efficiently. Simulating nonlinear flow physics is an excellent candidate in the latter class, given its computational onerosity and the wide range of applications. However, the linear underpinnings of quantum mechanics itself and the unitarity of fundamental QC operations blockade tractability of nonlinear PDEs. In this work we develop a hybrid quantum algorithm based on an integral formulation of a Homotopy Analysis Algorithm (HAA) to solve the 1D Burgers equation. We do so in an end-to-end manner by addressing the challenges of data encoding and also measurements in QC by outlining a quantum post-processing algorithm to compute the mean viscous dissipation rate. The method involves bespoke linearization of the problem with HAA, followed by a Quantum Linear System Algorithm (QLSA) to solve the system of equations. All the simulations are performed on an in-house high performance quantum simulator which we term QFlowS, designed specifically to simulate fluid flows with QC. We elucidate the performance of the algorithm and prescribe the algorithmic criteria for physically accurate simulations. |
Tuesday, November 21, 2023 1:16PM - 1:29PM |
ZC17.00003: Quantum Kernels for Data Assimilation of Turbulent Flows Xinfeng Gao Co-processing has played an important role for accelerating computations in the history of supercomputing. Over time, many co-processors become integral parts of modern architectures (floating-point units) or dominate a computation even more than the central processor (distributed GPU-only processing). The quantum co-processor presents unique capabilities with unknown potential for general-purpose high-performance computing. In this study, we explore the potential of quantum co-processing for two different algorithmic kernels within an overall data-assimilation algorithm applied to turbulent flow. A potential hybrid classical-quantum computing algorithm will be designed and experimented to test its feasibility. Specifically, quantum-co-processing kernels are designed to a) find the optimal state for data-assimilation analysis, and b) estimate turbulent subgrid stresses by approximately resolving turbulent subscales. |
Tuesday, November 21, 2023 1:29PM - 1:42PM |
ZC17.00004: Quantum linear solvers for potential flow problems: assessing efficiency and challenges Muralikrishnan Gopalakrishnan Meena, Kalyana C Gottiparthi, Antigoni Georgiadou, Matthew R Norman, Justin G Lietz We leverage quantum algorithms to solve linear equations that govern canonical potential flow problems. Although the development of quantum processors with continuous quantum error correction and high-fidelity (number of qubits) capable of handling practical fluid flow problems may be distant, recent advancements in quantum algorithms, particularly linear solvers, have paved the way for quantum counterparts to classical fluid flow solvers. Assessing the capability of quantum linear systems algorithms (QLSA) in solving ideal flow equations on real hardware is crucial for their future development in practical fluid flow applications. In this study, we test the capability of various QLSA for accurately solving the system of linear equations. Our ongoing preliminary efforts are focused on analyzing the accuracy and computational cost of these solvers. We also evaluate the stability and convergence of the solvers using shots-based simulations of quantum simulators. We employ different state-of-the-art techniques to model and mitigate the effect of noise from quantum hardware. We will also share our experiences with running the algorithms on different quantum hardware. |
Tuesday, November 21, 2023 1:42PM - 1:55PM |
ZC17.00005: Exploring Quantum-Inspired Fluid Dynamics Simulations for Real-World Applications Leonhard W Hölscher, Pooja Rao, Lukas Müller, Carlos A Riofrío, Johannes Klepsch, Andre Luckow, Jin-Sung Kim The direct numerical simulation of complex fluid flows is computationally expensive and quickly becomes infeasible with increasing turbulence, requiring alternate approaches. This is particularly relevant for the automotive industry since the accurate simulation of fluid flow around a car is crucial for efficient vehicle design. Recently, tensor network algorithms, such as Matrix Product State (MPS) algorithms, typically used to study complex quantum many-body systems, have shown promise in fluid dynamics. By treating the interscale correlations in the velocity field like local correlations between quantum states, these quantum-inspired methods offer a way to efficiently capture the underlying structure of turbulence by reducing the bond dimension in MPS using the Schmidt decomposition. We investigate applying these novel methods to real-world scenarios by extending the existing techniques to flows at higher Reynolds no. with more realistic boundaries and analyzing the computational complexity. We benchmark this algorithm using a 2D turbulent jet and the flow around a 2D cylinder. Our findings provide valuable insights into the scalability and suitability of these quantum-inspired approaches for solving fluid dynamics problems, and identify scenarios that can potentially benefit from computation on quantum computers. This work uses cuTensorNet, a high-performance library for tensor network computations in NVIDIA's cuQuantum SDK. |
Tuesday, November 21, 2023 1:55PM - 2:08PM |
ZC17.00006: Quantum algorithms for one-dimensional advection-diffusion equation Julia Ingelmann, Sachin Satish Bharadwaj, Philipp Pfeffer, Katepalli R Sreenivasan, Jörg Schumacher We demonstrate the application of two hybrid quantum-classical algorithms, the Quantum Linear System Algorithm (QLSA) and the Variational Quantum Algorithm (VQA), for the numerical solution of a one-dimensional advection-diffusion problem. The QLSA solves the system of linear equations which follows from the discretization of the flow problem, where the input matrices are prepared classically and the solution to the matrix equation is computed on a quantum simulator. The VQA evaluates a cost function by parameterized quantum circuits, while a classical optimization is performed to find the cost minimum that corresponds to the solution at the next time step. For both methods, the first-order Euler scheme is used to advance in time. We show that both algorithms can successfully solve the given problem and compare the accuracy of the results and their dependence on the number of qubits. |
Tuesday, November 21, 2023 2:08PM - 2:21PM |
ZC17.00007: Reducing quantum resources for the quantum lattice Boltzmann method Sriharsha Kocherla, Spencer H Bryngelson We present a two-circuit approach for solving the Navier-Stokes equations to model fluid flows, which exhibits quantum resource efficiency gains over the existing quantum lattice Boltzmann method. The streamfunction-vorticity formulation of the Navier-Stokes equations is used, and we show that using separate circuits to evolve streamfunction and vorticity leads to a reduction in CNOT gates in the collision and streaming steps. In addition, a technique is shown to eliminate CNOT gates entirely from the macro step of the simulation. This reduces the quantum resources necessary for the simulation, and the circuits can be run concurrently. In addition, the gate depths of the circuits are lower than present single-circuit QLBM variants. This algorithm is validated on the two-dimensional lid-driven cavity flow and shows good agreement with the classical lattice Boltzmann simulations. The research presents simulation results of a quantum algorithm and quantum resource estimations, indicating considerable advantages over current methods. |
Tuesday, November 21, 2023 2:21PM - 2:34PM |
ZC17.00008: Reduced-order modeling of two-dimensional turbulent Rayleigh-B'{e}nard flow by hybrid quantum-classical reservoir computing Philipp Pfeffer, Florian Heyder, Jörg Schumacher Two hybrid quantum-classical reservoir computing models are presented to reproduce low-order statistical properties of a two-dimensional turbulent Rayleigh-B'{e}nard convection flow at a Rayleigh number Ra = 105 and a Prandtl number Pr = 10. The models have to learn the nonlinear and chaotic dynamics of the flow in a lower-dimensional latent data space which is spanned by the time series of the 16 most energetic Proper Orthogonal Decomposition (POD) modes. The reservoir computing models are operated in the reconstruction or open-loop mode, i.e., they receive 3 POD modes as an input at each step and reconstruct the missing 13 ones. We analyse the reconstruction error in dependence on the hyperparameters which are specific for the quantum cases or shared with the classical counterpart, such as the reservoir size and the leaking rate. We show that both quantum algorithms are able to reconstruct essential statistical properties of the turbulent convection flow successfully with a small number of qubits of n ≤ 9. |
Tuesday, November 21, 2023 2:34PM - 2:47PM |
ZC17.00009: Hybrid classical-quantum algorithm for solving the incompressible Navier-Stokes equations on quantum hardware Zhixin Song, Bryan Gard, Spencer H Bryngelson Efficient PDE solvers for Navier-Stokes-like problems are critical to solving many science and engineering problems. Quantum algorithms have been proposed to solve PDEs and verified on small-scale simulators. In the (very) long term, PDEs can be solved via method-of-lines-like approaches and a Harrow-Hassidim-Lloyd (HHL) algorithm, bringing an exponential speedup over classical methods. For near-term quantum hardware (NISQ-era), variational quantum algorithms such as the Variational Quantum Eigensolver (VQE) are more appropriate, entailing fewer quantum gates and are thus more robust to noise. Here, we solve the incompressible Navier-Stokes equation via a classical-hybrid solution strategy. Variational methods are used to solve the Poisson equation and enforce incompressibility, while nonlinear inertial effects inappropriate for a quantum algorithm are computed classically. Both methods leverage the advantages of their respective compute substrates and exchange requisite information at each time step. Benchmarks for canonical flow problems on simulators and quantum hardware determine the required and realized solution fidelity on noisy quantum hardware. |
Tuesday, November 21, 2023 2:47PM - 3:00PM |
ZC17.00010: Simulation of nonlinear partial differential equations with quantum algorithms: A Fokker-Planck approach Felix Tennie, Luca Magri As manufacturing of classical computing chips has reached the scale of a few nanometers, i.e. a few dozen atoms, the progress of enhancements of classical computing resources is slowing down and, possibly, coming to an end. Quantum Algorithms represent a new paradigm of information processing that have theoretically been shown to outperform their classical counterparts on a number of specific tasks such as sparse matrix inversion, Fourier transformation and Singular Value Decomposition to only name a few. All these tasks being linear, the important question arises whether Quantum Computers can be successfully deployed to integrate non-linear dynamics. After two decades of research, a number of conceptually different algorithms have been proposed recently. Unfortunately, these algorithms have either no proven Quantum Advantage or cannot yet be run on currently available quantum hardware. |
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