arXiv subjects

Nis-Luca van Hülst

Publications and source records attributed to Nis-Luca van Hülst.

6 recordsLinked to original sources

arXiv2026

Quantum Algorithms for Computational Fluid Dynamics

We present a comprehensive review of quantum approaches for solving partial differential equations (PDEs) arising in computational fluid dynamics (CFD). We examine fully quantum approaches, including quantum linear system algorithms (QLSAs), ranging from the Harrow--Hassidim--Lloyd (HHL) algorithm to quantum singular value transformation (QSVT), Hamiltonian simulation, and quantum lattice Boltzmann methods (QLBMs), while emphasizing hybrid quantum--classical approaches, including quantum physics-informed neural networks (QPINNs) and amplitude-encoded variational PDE solvers. We focus on hardware-agnostic algorithms compatible with present noisy processors and emerging fault-tolerant architectures. For each framework, we analyze the mathematical formulation, algorithmic structure, and principal limitations. We also examine tensor-network (TN) representations, since CFD fields, differential operators, and geometrical information can often be encoded efficiently in low-rank form. The TN formalism bridges CFD discretizations and quantum states, operators, and circuits, enabling compact representations to be translated into tensor-programmable variational quantum algorithms (TP-VQAs). We further review benchmark problems, including Poisson, reaction, diffusion, and nonlinear model equations, and assess how well quantum algorithms capture key features of fluid dynamics. Our analysis highlights that potential quantum advantage is highly problem dependent and governed by condition number, representational complexity, state preparation, and measurement constraints. We outline capabilities, limitations, and challenges toward scalable quantum algorithms for CFD.

quant-ph↗

arXiv2026

Efficient Treatment of Non-Linearity in Quantum Computational Fluid Dynamics Using Hybrid Tensor Networks

Nonlinear terms present a fundamental challenge for quantum computational fluid dynamics, as their implementation on inherently linear quantum hardware typically requires resource-intensive workarounds that limit scalability to large-scale simulations. We present a hybrid quantum-classical tensor network algorithm that addresses this bottleneck by combining variational time-stepping with quantum tensor programming to efficiently compile operators and time-dependent fields into quantum circuits. Within a probabilistic framework, we replace prior state-based nonlinear implementations with tensor-based block encodings, stabilizing success probabilities that otherwise decay exponentially with system size. Benchmarking on turbulent flow fields demonstrates that the algorithm maintains high success probabilities and moderate measurement overhead across increasing Reynolds numbers and grid resolutions. Compared to fully classical tensor network solvers, our hybrid approach yields substantial reductions in both memory footprint and computational cost, establishing a scalable pathway toward practical quantum advantage in scale-resolving CFD simulations.

quant-ph↗

arXiv2026

Quantum-Inspired Simulation of 2D Turbulent Rayleigh-Bénard Convection

Turbulent thermal convection governs heat transport in systems ranging from stellar interiors to industrial heat exchangers. Two-dimensional Rayleigh-Bénard convection serves as a paradigm for these flows, reproducing key features such as thin boundary layers, large-scale circulation, and sustained plume dynamics. While Matrix Product State (MPS) methods have demonstrated significant compression of isothermal turbulent fields, their application to buoyancy-driven flows with active thermal coupling has remained unexplored. We apply MPS to two-dimensional Rayleigh-Bénard convection with dynamical simulations up to $\mathrm{Ra} = 10^{10}$. An a priori decomposition of DNS snapshots up to $\mathrm{Ra} = 10^{11}$ shows that the bond dimension $χ$ required to represent the flow fields grows without saturation, in contrast to the plateauing of $χ$ reported for velocity fields in isothermal 2D turbulence. Crucially, however, dynamical simulations solving the governing equations directly in the compressed MPS format at fixed $χ$ show that the $χ$ required to recover statistical observables, such as the Nusselt number, scales significantly more favorably with $\mathrm{Ra}$ than the a priori complexity suggests. At $\mathrm{Ra} = 10^{10}$, a relative error of $1.8\%$ in the mean Nusselt number is achieved with a nearly 9-fold reduction in degrees of freedom, using a $χ$ comparable to that required at $\mathrm{Ra} = 10^{9}$. Spectral analysis confirms the progressive recovery of spatial and temporal scales with increasing $χ$. These findings establish MPS as a scalable tool for simulating thermally driven turbulence, suggesting the method may remain viable for investigations of the ultimate regime at substantially higher $\mathrm{Ra}$.

physics.flu-dyn↗

arXiv2025

Tensor-Programmable Quantum Circuits for Solving Differential Equations

We present a quantum solver for partial differential equations based on a flexible matrix product operator representation. Utilizing mid-circuit measurements and a state-dependent norm correction, this scheme overcomes the restriction of unitary operators. Hence, it allows for the direct implementation of a broad class of differential equations governing the dynamics of classical and quantum systems. The capabilities of the framework are demonstrated for linear and non-linear partial differential equations using the example of the linearized Euler equations with absorbing boundaries and the nonlinear Burgers' equation. For a turbulence data set, we demonstrate potential advantages of the quantum tensor scheme over its classical counterparts.

quant-ph↗

arXiv2025

Quantum Solvers: Predictive Aeroacoustic & Aerodynamic modeling

This technical report presents our winning contribution to the 2024 Airbus and BMW Group Quantum Computing Challenge under the category 'Quantum Solvers'. This submission addresses efficient simulation in industrial CFD using (i) quantum-inspired algorithms and (ii) hybrid quantum-classical algorithms. We reproduce the submitted materials exactly as handed in, providing an archival record, with the sole addition of a note citing the publication that resulted from this challenge.

quant-ph↗

arXiv2025

Quantum-Inspired Tensor-Network Fractional-Step Method for Incompressible Flow in Curvilinear Coordinates

We introduce an algorithmic framework based on tensor networks for computing fluid flows around immersed objects in curvilinear coordinates. We show that the tensor network simulations can be carried out solely using highly compressed tensor representations of the flow fields and the differential operators and discuss the numerical implementation of the tensor operations required for computing fluid flows in detail. The applicability of our method is demonstrated by applying it to the paradigm example of steady and transient flows around stationary and rotating cylinders. We find excellent quantitative agreement in comparison to finite difference simulations for Strouhal numbers, forces and velocity fields. The properties of our approach are discussed in terms of reduced order models. We estimate the memory saving and potential runtime advantages in comparison to standard finite difference simulations. We find accurate results with errors of less than 0.3% for flow-field compressions by a factor of up to 20 and differential operators compressed by factors of up to 1000 compared to sparse matrix representations. We provide strong numerical evidence that the runtime scaling advantages of the tensor network approach with system size will provide substantial resource savings when simulating larger systems. Finally, we note that, like other tensor network-based fluid flow simulations, our algorithmic framework is directly portable to a quantum computer leading to further scaling advantages.

physics.flu-dyn↗