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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Simulation of applications in quantum computing

Ronald E. Meyers, Keith S. Deacon

Published Oct 19, 2004• 1 citation
Publisher

Abstract

This paper discusses simulation of quantum computing applications solving important physics and engineering problems. Methodologies are developed for quantum computing solutions of the Navier Stokes Equation, Dirac's Equation, and Schrodinger's Equation in complex domains. Turbulent Navier Stokes solutions were generated in complex geometries including urban domains. A quantum computing algorithm is also developed for the processing of sound which has a greater than classical efficiency in compression when run on a quantum computer. The algorithm also has interesting and useful properties on a classical computer, but without the superior speed and storage properties realized on a quantum computer.

DOI
10.1117/12.564279

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This paper discusses simulation of quantum computing applications solving important physics and engineering problems. Methodologies are developed for quantum computing solutions of the Navier Stokes Equation, Dirac's Equation, and Schrodinger's Equation in complex domains. Turbulent Navier Stokes solutions were generated in complex geometries including urban domains. A quantum computing algorithm is also developed for the processing of sound which has a greater than classical efficiency in compression when run on a quantum computer. The algorithm also has interesting and useful properties on a classical computer, but without the superior speed and storage properties realized on a quantum computer.
This article is meant to review and discuss the possible applications of Quantum computing in the area of computational fluid dynamics (CFD), with a focus on the application to the aerospace compact heat exchangers. Quantum computing is a type of computation that harnesses the collective properties of quantum states, such as superposition, interference, and entanglement, to perform calculations. Several approaches have been proposed for the solutions of CFD problems with the use of quantum algorithms, being the rationale of the development the estimated scalability of quantum computing and the analogy between Navier Stokes equations with the hydrodynamic Schrödinger equation or between the Lattice Boltzmann equation with the quantum Dirac equation. A review of the current state-of-the-art of quantum computing applied to CFD will be carried out, with the description of some practical applications, highlining how the technology is promising but still in an early stage of development.
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.
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.
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.
Simulating fluid dynamics on a quantum computer is intrinsically difficult due to the nonlinear and non-Hamiltonian nature of the Navier-Stokes equation (NSE). We propose a framework for quantum computing of fluid dynamics based on the hydrodynamic Schr\"odinger equation (HSE), which can be promising in simulating three-dimensional turbulent flows in various engineering applications. The HSE is derived by generalizing the Madelung transform to compressible or incompressible flows with finite vorticity and dissipation. Since the HSE is expressed as a unitary operator on a two-component wave function, it is more suitable than the NSE for quantum computing. The flow governed by the HSE can resemble a turbulent flow consisting of tangled vortex tubes with the five-thirds scaling of energy spectrum. We develop a prediction-correction quantum algorithm to solve the HSE. This algorithm is implemented for simple flows on the quantum simulator Qiskit with partial exponential speedup.