Quantum computing presents a possible paradigm shift in computing, given its advantages in memory and speed. However, there is a growing need to demonstrate its utility in solving practical problems that are nonlinear, such as in fluid dynamics, which is the subject of this work. To facilitate this objective, it is essential to have a dedicated toolkit that enables the development, testing, and simulation of new quantum algorithms and flow problems, taken together. To this end, we present here a high performance, quantum computational simulation package called Quantum Flow Simulator (QFlowS), designed for computational fluid dynamics simulations. QFlowS is a versatile tool that can create and simulate quantum circuits using an in-built library of fundamental quantum gates and operations. We outline here all its functionalities with illustrations. Algorithms to solve flow problems can be built using the expanding list of the core functionalities of QFlowS with its hybrid quantum–classical type workflow. This is demonstrated here by solving an example, one-dimensional, diffusion flow problem. These simulations serve as a check on the algorithm's correctness as well as an ideal test-bed for making them more efficient and better suited for near-term quantum computers for addressing flow problems.
Quantum computing presents a possible paradigm shift in computing, given its advantages in memory and speed. However, there is a growing need to demonstrate its utility in solving practical problems that are nonlinear, such as in fluid dynamics, which is the subject of this work. To facilitate this objective, it is essential to have a dedicated toolkit that enables the development, testing, and simulation of new quantum algorithms and flow problems, taken together. To this end, we present here a high performance, quantum computational simulation package called Quantum Flow Simulator (QFlowS), designed for computational fluid dynamics simulations. QFlowS is a versatile tool that can create and simulate quantum circuits using an in-built library of fundamental quantum gates and operations. We outline here all its functionalities with illustrations. Algorithms to solve flow problems can be built using the expanding list of the core functionalities of QFlowS with its hybrid quantum–classical type workflow. This is demonstrated here by solving an example, one-dimensional, diffusion flow problem. These simulations serve as a check on the algorithm's correctness as well as an ideal test-bed for making them more efficient and better suited for near-term quantum computers for addressing flow problems.
For quantum computing (QC) to emerge as a practically indispensable computational tool, there is a need for quantum protocols with end-to-end practical applications-in this instance, fluid dynamics. We debut here a high-performance quantum simulator which we term QFlowS (Quantum Flow Simulator), designed for fluid flow simulations using QC. Solving nonlinear flows by QC generally proceeds by solving an equivalent infinite dimensional linear system as a result of linear embedding. Thus, we first choose to simulate two well-known flows using QFlowS and demonstrate a previously unseen, full gate-level implementation of a hybrid and high precision Quantum Linear Systems Algorithms (QLSA) for simulating such flows at low Reynolds numbers. The utility of this simulator is demonstrated by extracting error estimates and power law scaling that relates [Formula: see text] (a parameter crucial to Hamiltonian simulations) to the condition number [Formula: see text] of the simulation matrix and allows the prediction of an optimal scaling parameter for accurate eigenvalue estimation. Further, we include two speedup preserving algorithms for a) the functional form or sparse quantum state preparation and b) in situ quantum postprocessing tool for computing nonlinear functions of the velocity field. We choose the viscous dissipation rate as an example, for which the end-to-end complexity is shown to be [Formula: see text], where [Formula: see text] is the size of the linear system of equations, [Formula: see text] is the solution error, and [Formula: see text] is the error in postprocessing. This work suggests a path toward quantum simulation of fluid flows and highlights the special considerations needed at the gate-level implementation of QC.
In the last few years, quantum computing has evolved as the next big technological breakthrough. Many big companies are actively researching this area and have built open-source frameworks which can be used to develop solutions for problems that connect be solved by classical computers. One such problem is the solution of Navier-Stokes equations which takes exponential time for simulation but using quantum computers, they can be solved in polynomial time. But the current state of quantum computation does not enable everyone to test their implementation on a real quantum computer. In this situation, a simulator enables rapid prototype and testing techniques and algorithms for when the real quantum computer is ready. This paper focuses on simulating fluid flow algorithms using a quantum framework, such as Navier- Stokes equations, with the lattice Boltzmann method (LBM) used to numerically solve the relevant system of equations on both CPU and GPU to speed up the process. The quantum framework used in this paper is Qiskit, an open-source software development kit created by IBM that allows developers to create and test quantum algorithms. NVIDIA cuQuantum is an SDK of optimized libraries and tools for expediting quantum computing operations used in this paper to solve the fundamental problem of modeling large-size quantum circuits using the power of GPU
Recent advancements in quantum computing provide opportunities to address the challenges of computational resource limitations in computational fluid dynamics (CFD). This work presents a hybrid quantum-classical CFD framework that leverages quantum linear algorithms to practical flow simulations. By transforming nonlinear fluid dynamics problems into linear systems, the framework employs quantum linear algorithms to compute solutions, effectively integrating quantum and classical computing approaches. Furthermore, this framework employs subspace methods to map the original large-scale linear systems to small ones solved by quantum linear algorithms, thereby enabling the solution of large-scale problems using the currently limited quantum resources. We applied the famous Harrow–Hassidim–Lloyd (HHL) algorithm and variational quantum linear solver to simulate complex flows, including unsteady flows around a cylinder, simulation of an aircraft with turbulence model, and combustion flows. The performance and quantum resource consumption of these algorithms were evaluated in practical flow scenarios, demonstrating their effectiveness with an average relative error lower than 0.001%. We conducted quantum resource and convergence analyses to adapt this framework for use with near-term quantum computers. Our framework supports simulations of up to 9.4 × 106 grid cells, marking a significant advancement from previous quantum approaches limited to simple flows. This paper not only offers a way for employing quantum linear algorithms in solving complex flow problems but also provides insights into optimizing quantum algorithms for CFD applications, pushing forward the practical utilization of quantum CFD.
This chapter describes results of a recent investigation aiming to assess the potential of quantum computing and suitably designed algorithms for future computational fluid dynamics applications.For quantum computers becoming available in the near future, it can be expected that applications of quantum computing follow the quantum coprocessor model, where selected parts of the computational task for which efficient quantum algorithms exist are executed on the quantum hardware.For example, in computational fluid dynamics algorithm, this hybrid quantum/classical approach is discussed, and in particular it is shown how the approximate quantum Fourier transform (AQFT) can be used in the Poisson solvers of the considered method for the incompressible-flow Navier-Stokes equations.The analysis shows that despite the inevitable errors introduced by applying AQFT, the method produces meaningful results for three-dimensional example problems.A second example of a quantum algorithm for flow simulations is then described.This method based on kinetic modeling of the flow was developed to reduce the information transfer between quantum and classical hardware in the quantum coprocessor model.It is shown that this quantum algorithm can be executed fully on quantum hardware during a simulation.The conclusion summarizes further challenges for algorithm developments and future work.
High-performance computing (HPC) refers to the use of advanced computational models and technologies to significantly enhance the performance of processing highly complex problems. HPC has evolved dramatically since the first supercomputer was commissioned in the 1960s. Nowadays, HPC is characterized by the pursuit of exascale computing, i.e., the ability to perform 1018 calculations per second. In November 2024, Lawrence Livermore National Laboratory, California announced the new El Capitan System as the most powerful exascale supercomputer, capable of performing over 1.742 exaFlops. Over the past few years, HPC platforms have evolved from CPU-centric architecture to GPU-accelerated systems. Such computing capability empowers researchers to tackle a diverse array of scientific applications across numerous domains, including stock market prediction, task scheduling, weather forecasting, gene sequencing, drug discovery, and Computational Fluid Dynamics (CFD) (Netto et al., 2018; Jamshed, 2015). CFD is an applied science field that is concerned with the simulation and analysis of the physics of fluid flow using computational models and technologies. CFD finds extensive applications in diverse industries and scientific disciplines, including aircraft design optimization to facilitate the analysis of aerodynamic performance, drag reduction, and fuel efficiency enhancement (Moin and Apte, 2006). In addition, CFD plays a crucial role in oil reservoir simulation and recovery (Britto et al. 2020). Overall, CFD serves as a powerful tool for understanding and predicting fluid flow phenomena, enabling engineers and scientists to make informed decisions, optimize designs, and improve the performance of various systems and processes. Recently, Quantum Computing has emerged as a new computing approach that leverages quantum physics phenomena such as superposition and entanglement to provide computational speedup over classical computers. With the rapid progress of quantum computing, it is projected that future HPC platforms are venturing into Quantum Processing Unit (QPU)-based systems to tackle previously unsolvable problems. Several researchers have studied the potential use of quantum computing in solving complex CFD problems (Gaitan, 2020; Jaksch et al. 2023). Quantum computing can offer several advantages in CFD applications. First, quantum computing can address the exponential growth of computational complexity associated with high-resolution and turbulent flow simulations. Accordingly, more accurate and detailed simulations can be performed. For example, Berry et al. (2014) presented quantum algorithms that can effectively handle large-scale linear algebraic calculations, such as solving sparse matrix equations and eigenvalue problems, which are fundamental in CFD. Furthermore, quantum computers have the potential to accelerate optimization algorithms that facilitate faster design and optimization of fluid systems (Preskill, 2018). While quantum computing is still in its nascent stage, ongoing research in quantum hardware and algorithms demonstrates huge potential for future applications in solving complex CFD problems.
We present qlbm , a Python software package designed to facilitate the development, simulation, and analysis of Quantum Lattice Boltzmann Methods (QBMs). qlbm is a modular framework that introduces a quantum component abstraction hierarchy tailored to the implementation of novel QBMs. The framework interfaces with state-of-the-art quantum software infrastructure to enable efficient simulation and validation pipelines, and leverages novel execution and pre-processing techniques that significantly reduce the computational resources required to develop quantum circuits. We demonstrate the versatility of the software by showcasing multiple QBMs in 2D and 3D with complex boundary conditions, integrated within automated benchmarking utilities. Accompanying the source code are extensive test suites, thorough online documentation resources, analysis tools, visualization methods, and demos that aim to increase the accessibility of QBMs while encouraging reproducibility and collaboration. Program summary Program Title: qlbm CPC Library link to program files: https://doi.org/10.17632/28hkvsg7p2.1 Developer's repository link: https://github.com/QCFD-Lab/qlbm Licensing provisions: MPL-2.0 Programming language: Python3 Supplementary material: The documentation of is available at https://qcfd-lab.github.io/qlbm/ . Nature of problem: The advent of quantum algorithms for computational fluid dynamics brings with it challenges that are new to the established field of computational physics. These challenges include the lack of standardized implementations of the still nascent quantum methods, the intense computational demands of developing and simulating quantum algorithms on hardware available today, and the absence of tools that integrate novel developments into established infrastructure. Because of these current limitations, physicists and mathematicians expend superfluous resources on tasks that more mature computational physics branches have surmounted long ago. Solution method: QLBM is a software package that provides an end-to-end development environment for quantum lattice Boltzmann methods. The modular design and flexible quantum circuit library provide a base for extending and generalizing quantum algorithms. Performance enhancements exploit the paradigm of quantum computing simulations to accelerate the speed at which researchers can verify the validity of their methods. Its integration with state-of-the-art quantum computing software and visualization tools increases the algorithms' accesibility. These features allow QLBM to effectively generate, simulate, and analyze quantum circuits for 2D and 3D computational fluid dynamics problems.