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

Simulation of quantum computers

Ronald E. Meyers, Keith S. Deacon

Published Feb 3, 2004• 9 citations
Publisher

Abstract

Quantum computers are simulated solving a variety of important physics problems. The numerical solution of the Burgers equation, Dirac’s Equation, Schrodinger’s equation, and other physics equations are solved by simulations of quantum computers. Navier Stokes equation turbulence solutions are produced both over simple and complex structures.

DOI
10.1117/12.503187

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Quantum computers are simulated solving a variety of important physics problems. The numerical solution of the Burgers equation, Dirac’s Equation, Schrodinger’s equation, and other physics equations are solved by simulations of quantum computers. Navier Stokes equation turbulence solutions are produced both over simple and complex structures.
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.
Abstract Computational fluid dynamics (CFD) simulations are a vital part of the design process in the aerospace industry. Although reliable CFD results can be obtained with turbulence models, direct numerical simulation of complex bodies in three spatial dimensions (3D) is impracticable due to the massive amount of computational elements. For instance, a 3D direct numerical simulation of a turbulent boundary-layer over the wing of a commercial jetliner that resolves all relevant length scales using a serial CFD solver on a modern digital computer would take approximately 750 million years or roughly 20% of the earth’s age. Over the past 25 years, quantum computers have become the object of great interest worldwide as powerful quantum algorithms have been constructed for several important, computationally challenging problems that provide enormous speed-up over the best-known classical algorithms. In this paper, we adapt a recently introduced quantum algorithm for partial differential equations to Burgers’ equation and develop a quantum CFD solver that determines its solutions. We used our quantum CFD solver to verify the quantum Burgers’ equation algorithm to find the flow solution when a shockwave is and is not present. The quantum simulation results were compared to: (i) an exact analytical solution for a flow without a shockwave; and (ii) the results of a classical CFD solver for flows with and without a shockwave. Excellent agreement was found in both cases, and the error of the quantum CFD solver was comparable to that of the classical CFD solver.
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.
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.
Quantum computing is based on the exploitation of quantum effects to perform some important computations more efficiently than ever possible on classical computers. Well known quantum algorithms are Shors polynomial time factoring algorithm and Grovers data base search scheme. Their potential is due to the parallelism of a quantum computation increasing exponentially with the size of the computing device. IBM has succeeded in building a first working quantum computing device with up to 7 qubits based on NMR technology, however, the construction of large multi-qubit systems appears to become extremely difficult due to the loss of coherence of the quantum states. Like the design process of modern microprocessors which is carried out by means of sophisticated software, modelling and simulation of the entire QC device is even more relevant. Simulation is required in order to understand the functioning of quantum algorithms, to construct novel quantum algorithms, to write quantum programs, to teach quantum computing, to construct real quantum computers, to understand and fight de-coherence and to understand and control the influence of the environment. Since quantum parallelism increases exponentially with the size of the quantum computer, parallel supercomputers are required for realistic simulations. I intend to give an introduction into the simulation of quantum computers using conventional computers. The simulation is based on a generic physical model of quantum computer hardware. Issues like parallel gate level simulators, modelling of QCs, simulators for physical quantum computers are addressed.
A practical and efficient way to use the power of quantum mechanics (quantum parallelism due to the superposition and entanglement of states) could enormously speed up numerical simulations of interest to computational physicists. The diffusion equation the nonlinear Burgers equations, the turbulent Navier-Stokes equations, and the many-body Schroedinger equation could all be solved much more rapidly if efficient quantum algorithms could be implemented for their solution. The presentations at the conference that are published here review the progress toward these goals.