Parallel evaluation of quantum algorithms for computational fluid dynamics

Steijl, R.; Barakos, George N.

doi:10.1016/j.compfluid.2018.03.080

Cited by 44 publications

(36 citation statements)

References 11 publications

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“…The Poisson equation is a widely used linear differential equation, which plays a key role across many areas of physics and engineering. For instance, when you simulate the dynamic process of ocean current, the Navier-Stokes equations are a good start to calculate the velocity field of the current, but notoriously hard to solve; while using the well-studied vortex-in-cell method, the velocity field can be evaluated rather easily from a vector potential which satisfies the Poisson equation [12,13]. So solving the Poisson equation constitutes the most computationally intensive part of the current simulation.…”

Section: Introductionmentioning

confidence: 99%

Quantum fast Poisson solver: the algorithm and complete and modular circuit design

Wang

et al. 2020

Quantum Inf Process

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The Poisson equation has applications across many areas of physics and engineering, such as the dynamic process simulation of ocean current. Here we present a quantum Fast Poisson Solver, including the algorithm and the complete and modular circuit design. The algorithm takes the HHL algorithm as the template. The controlled rotation is performed based on the arc cotangent function which is evaluated by the Plouffe's binary expansion method. And the same method is used to compute the cosine function for the eigenvalue approximation in phase estimation. Quantum algorithms for solving square root and reciprocal functions are developed based on the non-restoring digitrecurrence method. These advances make the algorithm's complexity lower and the circuit-design more modular. The number of the qubits and operations used by the circuit are O(dlog 2 (ε -1 )) and O(dlog 3 (ε -1 )), respectively. We demonstrate our circuits on a quantum virtual computing system installed on the Sunway TaihuLight supercomputer. This is an important step toward practical applications of quantum Fast Poisson Solver in the near-term hybrid classical/quantum devices.

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Section: Introductionmentioning

confidence: 99%

Quantum fast Poisson solver: the algorithm and complete and modular circuit design

Wang

et al. 2020

Quantum Inf Process

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“…More recently, significant progress has been made in the area of quantum chemistry and quantum physics. Beyond those two fields, only recently have quantum computing applications appeared in other areas of science and engineering, e.g., work in computational electromagnetics [2,3], mixing in turbulent flow [4], and computational fluid dynamics [5]. More general applications have been developed which take advantage of the unique capabilities of quantum computing platforms, e.g., methods for the solution of linear systems of equations [6] and Poisson equation [7].…”

Section: Introductionmentioning

confidence: 99%

“…In the absence of the required quantum hardware, large-scale parallel simulations on parallel classical computers are required in developing such algorithms. In this work the recently developed quantum simulator [5] included in the MΦC multi-physics CFD framework is used [8,9].…”

Section: Introductionmentioning

confidence: 99%

“…As an example of this hybrid classical/quantum approach, the author introduced a quantum computing application in which the vortex-in-cell method was used to solve the incompressible-flow Navier-Stokes equations in a regular domain [5]. In this algorithm, the Poisson solvers dominating CPU time requirements are based on the quantum computing equivalent of the fast Fourier transform, i.e., the quantum Fourier transform.…”

Section: Introductionmentioning

confidence: 99%

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Quantum Algorithms for Fluid Simulations

Steijl¹

2020

Advances in Quantum Communication and Information

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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.

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“…3 l=1 ( J n ) kl q i k q j l . When the labeling is chosen appropriately (each node has two '-1' and one '+1' label), this energy equals to the value of functional for corresponding state, a, as shown in Eq (12). This relation can be used to estimate J n by solving a set of nine inde-pendent linear equations presented.…”

Section: Element Graphmentioning

confidence: 99%

Box algorithm for the solution of differential equations on a quantum annealer

Srivastava

Sundararaghavan

2019

Phys. Rev. A

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Differential equations are ubiquitous in models of physical phenomena. Applications like steadystate analysis of heat flow and deflection in elastic bars often admit to a second order differential equation. In this paper, we discuss the use of a quantum annealer to solve such differential equations by recasting a finite element model in the form of an Ising hamiltonian. The discrete variables involved in the Ising model introduce complications when defining differential quantities, for instance, gradients involved in scientific computations of solid and fluid mechanics. To address this issue, a graph coloring based methodology is proposed which searches iteratively for solutions in a subspace of weak solutions defined over a graph, hereafter called as the 'box algorithm.' The box algorithm is demonstrated by solving a truss mechanics problem on the D-Wave quantum computer. J n 11 J n 12 J n 13 J n 21 J n 22 J n 23 J n 31 J n 32 J n 33

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Parallel evaluation of quantum algorithms for computational fluid dynamics

Cited by 44 publications

References 11 publications

Quantum fast Poisson solver: the algorithm and complete and modular circuit design

Quantum fast Poisson solver: the algorithm and complete and modular circuit design

Quantum Algorithms for Fluid Simulations

Box algorithm for the solution of differential equations on a quantum annealer

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