In this paper, we explore the suitability of upcoming novel computing technologies, in particular adiabatic annealing based quantum computers, to solve fluid dynamics problems that form a critical component of several science and engineering applications. We start with simple flows with well-studied flow properties, and provide a framework to convert such systems to a form amenable for deployment on such quantum annealers. We analyze the solutions obtained both qualitatively and quantitatively as well as the sensitivities of the various solution selection schemes on the obtained solution.
In this paper, we explore the suitability of upcoming novel computing technologies, in particular adiabatic annealing based quantum computers, to solve fluid dynamics problems that form a critical component of several science and engineering applications. We start with simple flows with well-studied flow properties, and provide a framework to convert such systems to a form amenable for deployment on such quantum annealers. We analyze the solutions obtained both qualitatively and quantitatively as well as the sensitivities of the various solution selection schemes on the obtained solution.
This paper explores the suitability of upcoming novel computing technologies, particularly adiabatic annealing based quantum computers, to solve fluid dynamics problems that form a critical component of several science and engineering applications. For our experiments, we start with a well-studied one-dimensional simple flow problem, and provide a framework to convert such problems in continuum to a form amenable for deployment on such quantum annealers. Since the DWave annealer returns multiple states sampling the energy landscape of the problem, we explore multiple solution selection strategies to approximate the solution of the problem. We analyze the continuum solutions obtained both qualitatively and quantitatively as well as their sensitivities to the particular solution selection scheme.
Partial differential equations (PDEs) present important computational challenges in several scientific disciplines. Classical numerical methods, while effective, often encounter scalability issues and high computational costs, particularly for complex problems. Quantum computing seems to address these challenges, offering a potential exponential speedup over classical methods. The presented work studies the application of quantum computing, specifically Quantum Annealing, to the computational complexities inherent in solving the Navier-Stokes equations within Computational Fluid Dynamics (CFD). Our study examines the quantum annealing methodology, conducting two different experiments and analyzing the error between the simulation and the analytical solution. The results obtained demonstrate that quantum annealing paradigm can solve this problems and the errors obtained are acceptable in comparison with other methods in the state of the art. By combining theoretical insights with practical implementation, this research clarifies the potential of quantum annealing, providing a comprehensive overview of the simulation framework, analyzing the obtained results, and suggesting future research avenues.
This document is meant to review and discuss the possible applications of Quantum computing to computational fluid dynamics (CFD) problems.A review of the current state-of-the-art of quantum computing applied to computational fluid dynamics has been carried out, highlining how the technology is still in an early stage of development but very promising.Quantum computing is a type of computation that harnesses the collective properties of quantum states, such as superposition, interference, and entanglement, to perform calculations.The devices that perform quantum computations are known as quantum computers.Quantum Computing is currently a very active field of study and development, with expected applications in various fields, including engineering problems.Indeed, several approaches have been proposed for the solutions of CFD problems with the use of quantum algorithms and / or quantum computers.Possible approaches, applicable to compact heat exchangers used in aeronautics, include the development of quantum algorithms, e.g., based on the solutions of Navier Stokes equations or the Lattice Boltzmann Method., the design of an "analog" quantum computer able to mimic the thermal fluid system under investigation, and, finally, the implementation of a scientific machine learning approach.
Abstract This paper explores possible implementations of quantum computing technologies, namely the quantum annealing and the quantum walk search algorithm, to solve fluid dynamics problems related to the design and assessment of compact heat exchangers for aeronautical environmental control and thermal management systems, as well as several other science and engineering applications, e.g. oil and gas refinery process. The purpose of this paper is to introduce two alternative implementations to the already assessed numerical resolution of Navier–Stokes equations or the resolution of analog quantum mechanical problem, highlighting how the use of quantum annealing and a classification algorithm (quantum walk search algorithm) can be implemented for the resolution of a lumped-characteristic analytical model of the heat transfer inside a compact heat exchanger, also in case of two-phase refrigerant fluid, for the use during design phase of environmental control system, e.g. provide the design engineers with a relatively simple and quick to use tool, which provides a reasonable result with an easily interpretable physical meaning. We start with a simple two-phase flow within a single-pass mini-channel heat exchanger, describing the mathematical formulation of the problem followed by a simplified implementation of the proposed quantum approaches, highlighting the main procedures of the calculation as well as the practical implications, advantages and disadvantages of the proposed method, e.g. a limited number of CFD simulations are required to evaluate air side heat transfer coefficient and pressure drop for particular designs within the defined design space, and the specific hardware required to implement the quantum process.
Abstract Efficient simulation of a quantum system's dynamics is expected to be an important application area for quantum computers as existing classical computers cannot do this. However, quantum systems are not unique in being hard to simulate. For example, classical nonlinear continuum systems and fields are governed by nonlinear partial differential equations whose solution is also hard for classical computers. Solving such equations is essential for many economically important industries/applications such as the aerospace industry, weather‐forecasting, fiber‐optics communication, and plasma magneto‐hydrodynamics. This raises the question: can a quantum computer speed‐up solving these equations? In this Review, a new quantum algorithm is described for solving nonlinear partial differential equations for which the answer is yes. First, a new quantum algorithm is discussed for solving the Navier‐Stokes nonlinear partial differential equations which govern the flow of a viscous fluid. Its construction, verification, and computational cost are described, and it is shown that a significant quantum speed‐up is possible. Its generalization to a quantum algorithm for solving nonlinear partial differential equations is described. The Review closes with a discussion of next steps forward. These new quantum algorithms open up a large new application area for quantum computing with substantial economic impact, including the trillion‐dollar aerospace industry.
Abstract There is great interest in using quantum computers to efficiently simulate a quantum system’s dynamics as existing classical computers cannot do this. Little attention, however, has been given to quantum simulation of a classical nonlinear continuum system such as a viscous fluid even though this too is hard for classical computers. Such fluids obey the Navier–Stokes nonlinear partial differential equations, whose solution is essential to the aerospace industry, weather forecasting, plasma magneto-hydrodynamics, and astrophysics. Here we present a quantum algorithm for solving the Navier–Stokes equations. We test the algorithm by using it to find the steady-state inviscid, compressible flow through a convergent-divergent nozzle when a shockwave is (is not) present. We find excellent agreement between numerical simulation results and the exact solution, including shockwave capture when present. Finally, we compare the algorithm’s computational cost to deterministic and random classical algorithms and show that a significant speed-up is possible. Our work points to a large new application area for quantum computing with substantial economic impact, including the trillion-dollar aerospace industry, weather-forecasting, and engineered-plasma technologies.