Reducing quantum resources for the quantum lattice Boltzmann method
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Kocherla, Sriharsha Vardhan
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Abstract
Computational fluid dynamics is a field that employs numerical analysis and algorithms to simulate and study fluid and gas behavior in defined systems.
These simulations typically tackle the Navier--Stokes equations and necessitate a large number of GPUs and computational resources to run effectively.
To enhance computational efficiency, researchers have explored quantum computing, which has demonstrated significant complexity benefits over classical algorithms for some problems. In this work, a two-circuit approach for solving the Navier--Stokes equations to model fluid flows is proposed, which exhibits quantum resource efficiency gains over the existing quantum lattice Boltzmann method. The streamfunction--vorticity formulation of the 2D Navier--Stokes equations is used, and we show that using separate circuits to evolve streamfunction and vorticity leads to an reduction in CNOT gates in the collision and streaming steps. In addition, a technique is shown to eliminate CNOT gates entirely from the macro step of the simulation. This reduces the amount of quantum resources necessary for the simulation, and the circuits can be run concurrently. In addition, the gate depth of the circuits are lower than the current single-circuit QLBM variant. This algorithm is validated on the two-dimensional lid-driven cavity flow, and shows good agreement with the classical lattice Boltzmann simulations.
The research presents simulation results of a quantum algorithm and quantum resource estimations for the method, indicating considerable advantages over the current method.
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Undergraduate Research Option Thesis