A multiple-circuit approach to quantum resource reduction with application to the quantum lattice Boltzmann method

2024-01-20

AI Summary

To address the high resource overhead of fluid dynamics simulation on noisy intermediate-scale quantum (NISQ) devices, this work proposes QLBM-frugal—a multi-circuit quantum lattice Boltzmann method tailored for incompressible Navier–Stokes equations. Unlike conventional single-circuit QLBM, QLBM-frugal innovatively decomposes the quantum algorithm into lightweight, parallelizable subcircuits. It integrates quantum circuit decomposition, CNOT gate optimization, and parallel scheduling to drastically reduce hardware requirements while preserving physical fidelity. Evaluated on the 2D lid-driven cavity flow benchmark with 64 lattice sites, QLBM-frugal reduces the total CNOT count by 35%, lowers individual circuit depth by 16%, and halves the effective observable circuit depth via concurrent execution. This work establishes a scalable, resource-efficient paradigm for quantum algorithms solving partial differential equations.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Sampling/Simulation-based Search
• Intelligent Robots: Learning & Optimization for ROB

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

This work proposes a multi-circuit quantum lattice Boltzmann method (QLBM) algorithm that leverages parallel quantum computing to reduce quantum resource requirements. Computational fluid dynamics (CFD) simulations often entail a large computational burden on classical computers. At present, these simulations can require up to trillions of grid points and millions of time steps. To reduce costs, novel architectures like quantum computers may be intrinsically more efficient for these computations. Current quantum algorithms for solving CFD problems are based on single quantum circuits and, in many cases, use lattice-based methods. Current quantum devices are adorned with sufficient noise to make large and deep circuits untenable. We introduce a multiple-circuit algorithm for a quantum lattice Boltzmann method (QLBM) solve of the incompressible Navier--Stokes equations. The method, called QLBM-frugal, aims to create more practical quantum circuits and strategies for differential equation-based problems. The presented method is validated and demonstrated for 2D lid-driven cavity flow. The two-circuit algorithm shows a marked reduction in CNOT gates, which consume the majority of the runtime on quantum devices. Compared to the baseline QLBM technique, a two-circuit strategy shows increasingly large improvements in gate counts as the qubit size, or problem size, increases. For 64 lattice sites, the CNOT count was reduced by 35%, and the gate depth decreased by 16%. This strategy also enables concurrent circuit execution, further halving the seen gate depth.

Problem

• Quantum Computing
• Fluid Dynamics Simulation
• Efficiency

Innovation

• Quantum Computing
• Parallel Processing
• Fluid Dynamics