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Abstract
We present a quantum computing algorithm for the smoothed particle hydrodynamics (SPH) method. We use a normalization procedure to encode the SPH operators and domain discretization in a quantum register. We then perform the SPH summation via an inner product of quantum registers. Using a onedimensional function, we test the approach in a classical sense for the kernel sum and first and second derivatives of a onedimensional function, using both the Gaussian and Wendland kernel functions, and compare various register sizes against analytical results. Error convergence is exponentially fast in the number of qubits. We extend the method to solve the onedimensional advection and diffusion partial differential equations, which are commonly encountered in fluids simulations. This work provides a foundation for a more general SPH algorithm, eventually leading to highly efficient simulations of complex engineering problems on gatebased quantum computers.
Original language  English 

Article number  108909 
Number of pages  12 
Journal  Computer Physics Communications 
Volume  294 
Early online date  4 Sept 2023 
DOIs  
Publication status  Epub ahead of print  4 Sept 2023 
Keywords
 quantum computing
 smoothed particle hydrodynamics
 partial differential equations
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Dive into the research topics of 'Quantum algorithm for smoothed particle hydrodynamics'. Together they form a unique fingerprint.Projects
 3 Active

Quantum Algorithms for Nonlinear Differential Equations  QuANDiE
EPSRC (Engineering and Physical Sciences Research Council)
1/06/23 → 31/03/25
Project: Research

Quantum Enhanced and Verified Exascale Computing  QEVEC (Transfer)
EPSRC (Engineering and Physical Sciences Research Council)
1/11/21 → 31/07/24
Project: Research