Bulletin of the American Physical Society
77th Annual Meeting of the Division of Fluid Dynamics
Sunday–Tuesday, November 24–26, 2024; Salt Lake City, Utah
Session A16: Quantum Computing for Fluids |
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Chair: Alexander Alexeev, Georgia Institute of Technology Room: 155 F |
Sunday, November 24, 2024 8:00AM - 8:13AM |
A16.00001: Simulating unsteady flows on near-term quantum computers Sachin Satish Bharadwaj, Katepalli R Sreenivasan Quantum computers are favored to overtake classical devices in solving certain tasks, with substantial gains in speed and memory. Despite fervent efforts on theoretical and experimental fronts, the gap between them precludes utilitarian quantum algorithms to solve practical problems. In particular, we are interested in solving nonlinear fluid flow problems. To this end, we propose here a quantum algorithm based on Linear combination of Unitaries, consisting of Time Marching Compact Quantum Circuits to solve unsteady PDEs. The present algorithm has a time complexity that is near-optimal (logarithmic) compared to existing proposals, along with a qubit complexity that is logarithmic in the problem size. We outline specific solutions to bottlenecks such as the quantum state preparation, quantum measurements, as well as noise and decoherence from real quantum devices, which tend to diminish quantum advantage. In that sense, our algorithm is end-to-end, preserving potential quantum advantage. To assess its performance, we simulate the well-known one-dimensional, linear advection-diffusion problem by implementing the algorithm on QFlowS (an in-house quantum simulator) and by performing experiments on an actual quantum computer (IBM Cairo). Our results show that the proposed quantum algorithm successfully captures the flow physics qualitatively and quantitatively. We make a case that the present approach is amenable for near-term devices, and highlight that the proposed algorithm offers an efficient way for performing iterative matrix operations such as inversions and matrix-vector products, thus broadening its applicability well beyond fluid dynamics. |
Sunday, November 24, 2024 8:13AM - 8:26AM |
A16.00002: Quantum annealing computation methods to obtain a converged flow solution Yuichi Kuya, Takahito Asaga In this study, we propose quantum annealing computation methods to obtain converged flow solutions, utilizing quantum superposition states. In conventional numerical simulations, converged solutions are obtained from a given initial state using time advancement or iterative methods. In contrast, the proposed methods extract a converged solution from all the possible solutions under quantum superposition states by quantum annealing. The proposed quantum annealing methods are developed for LGA and finite difference methods. |
Sunday, November 24, 2024 8:26AM - 8:39AM |
A16.00003: Quantum-Inspired High-Fidelity Solver for Simulating Incompressible Two-Phase Turbulence Han Liu, Lian Shen In Computational Fluid Dynamics (CFD), accurately computing two-phase incompressible turbulent flows is essential for many problems. Traditionally, the flow is solved using methods like finite difference and finite volume, coupled with a linear solver for pressure and velocity fields. However, these methods face limitations due to the curse of dimensionality: the ratio of the largest eddy to the Kolmogorov scale eddy is proportional to the Reynolds number raised to the power of 9/4, leading to a formidable increase in the grid number and computing resources required to fully resolve turbulence. |
Sunday, November 24, 2024 8:39AM - 8:52AM |
A16.00004: Forecasting chaotic dynamics on a quantum computer: A hardware-efficient recurrence-free quantum reservoir computer Osama Ahmed, Felix Tennie, Luca Magri Quantum reservoir computing (QRC) has recently emerged as a promising framework in quantum computing to predict chaotic dynamics and extreme events. The main objective of this work is to propose a hardware-efficient quantum reservoir network to predict chaotic dynamics and its stability properties from data only. First, we propose a recurrence-free quantum reservoir computing (RF-QRC) architecture, which avoids exponential circuit depth, scales with higher dimensional chaotic systems, and does not have an additional feedback loop, making it suitable for hardware implementation. Second, we develop a method for optimal training of finitely sampled quantum reservoir computers. The methods are employed for a turbulent shear flow model with extreme events (MFE) on IBM Quantum backends. We demonstrate the feasibility of our methods by training the RF-QRC on multiple parallel QPUs, coupled with denoising techniques. Third, we derive the analytic Jacobian of quantum reservoir computers to infer the stability property of the chaotic system from data only. We correctly infer the Lyapunov spectrum in both the Lorenz-63 and MFE turbulence models. This work opens opportunities for using quantum reservoir computing for time series forecasting of chaotic flows in near- and mid-term quantum hardware. |
Sunday, November 24, 2024 8:52AM - 9:05AM |
A16.00005: Quantum Computing of Fluid Dynamics Via Hamiltonian Simulation Zhaoyuan Meng, Zhen Lu, Yue Yang It is anticipated that quantum computing will be able to tackle hard real-world problems. Fluid dynamics, a highly challenging problem in classical physics and various applications, emerges as a good candidate for showing quantum utility. We report our recent progress on quantum computing of fluid dynamics. In theory, we propose a quantum spin representation of fluid dynamics, which transforms the Navier-Stokes equation into the Schrödinger-Pauli equation through the generalized Madelung transformation. In this way, the fluid flow can be regarded as a special quantum system, which is feasible for flow simulation on a quantum computer. In terms of algorithm, we propose a quantum Hamiltonian simulation algorithm, which is able to simulate compressible or incompressible flows and scalar convection-reaction-diffusion problems with quantum acceleration. In terms of hardware implementation, we have realized the quantum simulation of two-dimensional unsteady flow on a quantum processor. These results demonstrate the potential of quantum computing to simulate complex flows, including turbulence, in future endeavors. |
Sunday, November 24, 2024 9:05AM - 9:18AM |
A16.00006: Quantum time evolution for solving the advection-diffusion equation. Hirad Alipanah, A. Baris Ozguler, Peyman Givi, Juan José Mendoza Arenas, Brian J McDermott, Feng Zhang, Yongxin Yao, Richard Joel Thompson, Nam Nguyen Time evolution algorithms are an effective and gate-efficient tool for implementing quantum simulations on contemporary NISQ hardware. Simulating Hamiltonians in quantum chemistry and condensed matter physics is one example of their efficiency. With Trotterization or variational (real or imaginary) time evolution algorithms, the dynamics of a quantum system can be properly implemented using quantum gates and physical qubits. Here, an approach is presented to utilize these tools for solving the linear convection-diffusion equation, which is a type of non-unitary evolution. The results show the variational solution obtained with these methods follows the accurate classical direct numerical simulation (DNS). The two-local ansatz has also been implemented on the IBM Torino quantum computer, showing that the circuit depth is suitable for present-day hardware. In general, variational time evolution algorithms can be a valid option for solving PDEs, expanding the applicability of quantum hardware to this class of problems. |
Sunday, November 24, 2024 9:18AM - 9:31AM |
A16.00007: Quantum advantage for probability-density-function-based sub-grid scale and wall modeling Xiang Yang, Mahdi Abkar Recent advancements in quantum computing have shown limited advantages over classical computing for direct numerical simulation of turbulent flows. This talk explores a novel application of quantum computing for large-eddy simulation (LES), specifically focusing on sub-grid scale and wall modeling. We investigate the use of probability-density-function (PDF) based methods, which solve for the PDFs of unresolved eddies. While these methods provide realistic sub-grid information, they are often considered too computationally expensive due to the additional dimensions of the PDFs. However, quantum computing overcomes this challenge by encoding PDF information into qubits, thus achieving quantum advantage. As a proof of concept, we present results from Burgers turbulence and turbulent channel flow simulations. |
Sunday, November 24, 2024 9:31AM - 9:44AM |
A16.00008: A Quantum Lattice Boltzmann Algorithm For Simulating Heat Transfer With Phase Change Christopher Jawetz, Spencer H. Bryngelson, Alexander Alexeev Accurate solutions of heat transfer problems require large amounts of computational resources even employing simplifying assumptions. One promising new avenue to drastically accelerate numerical solutions is the use of quantum computing, which promises to speed up these computations exponentially. Here, we develop the quantum lattice-Boltzmann method (QLBM) to solve the unsteady heat transfer equations with phase change. To solve these nonlinear equations, we use a strategy where the temperature readings are delayed allowing a significant reduction in the number of reinitializations of the quantum circuit. We show that the delayed measurements can be performed without a meaningful impact on the overall solution accuracy. The quantum algorithm is validated by comparison with an LBM solution and an analytical solution.
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Sunday, November 24, 2024 9:44AM - 9:57AM |
A16.00009: Linearization-based quantum algorithms for the statistical description of chaotic systems Brad W Roberts, Adrian Lozano-Duran One of the primary challenges in quantum computing is developing algorithms that can efficiently encode the nonlinear terms of underlying equations. Much of the previous work has focused on linearization techniques combined with quantum linear systems algorithms (QLSA). However, these linearization-based algorithms are only efficient for flows with weak nonlinearity. Our objective is to create a fully quantum algorithm capable of efficiently obtaining the statistical description of chaotic systems, with potential applications to turbulent flows. To this end, we explore a linearization approach for chaotic dynamical systems that encodes solutions for multiple time steps within a single linear system. The success of this algorithm hinges on balancing two competing effects. On one hand, the efficiency of solving the linear systems via a QLSA-based quantum algorithm improves with the number of time steps encoded. On the other hand, the accuracy of the statistical descriptions derived from this method decreases as the size of the linear system increases. In this talk, we will discuss the conditions under which this quantum algorithm can accurately perform its task while providing a speedup over the best classical techniques. |
Sunday, November 24, 2024 9:57AM - 10:10AM |
A16.00010: QPDE: Quantum Neural Network Based Stabilization Parameter Prediction for Numerical Solvers for Partial Differential Equations Sangeeta Yadav We propose a Quantum Neural Network (QNN) for predicting stabilization parameter for solving Singularly Perturbed Partial Differential Equations (SPDE) using the Streamline Upwind Petrov Galerkin (SUPG) stabilization technique. SPDE-Q-Net, a QNN, is proposed for approximating an optimal value of the stabilization parameter for SUPG for 2-dimensional convection-diffusion problems. Our motivation for this work stems from the recent progress made in quantum computing and the striking similarities observed between neural networks and quantum circuits. Just like how weight parameters are adjusted in traditional neural networks, the parameters of the quantum circuit, specifically the qubits' degrees of freedom, can be fine-tuned to learn a nonlinear function. The performance of SPDE-Q-Net is found to be at par with SPDE-Net, a traditional neural network-based technique for stabilization parameter prediction in terms of the numerical error in the solution. Also, SPDE-Q-Net is found to be faster than SPDE-Net, which projects the future benefits which can be earned from the speed-up capabilities of quantum computing. |
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