Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2409.09736 · Sadhana

Towards simulating fluid flows with quantum computing

Sachin S. Bharadwaj, Katepalli R. Sreenivasan

Published Mar 19, 2025• 20 citations
arXivHTMLPDF
DOI
10.1007/s12046-024-02660-3

Related papers

Challenges of simulating fluid flows on near-term quantum computer

Zhaoyuan Meng, Chao Song, Yue Yang

Science China Physics Mechanics and Astronomy•Jun 16, 2025•13 citations

A quantum computing-based lattice Boltzmann method with a linearized non-equilibrium collision operator and modular circuit for practical flow simulation

Kang-Yang Zeng, Xiaodong Niu, Adnan Khan +2 more

Quantum computing (QC) has emerged as a potential computational tool in fluid dynamics. However, a practical QC protocol with end-to-end practical applications to fluid flow is still in nascent. We here propose a simple and practical hybrid QC algorithm based on lattice Boltzmann methods (LBM), which we term HQLBM, for fluid dynamics simulations. The existing QC-based LBMs are limited to simple low-Reynolds-number flow simulations due to their disability to handle the nonlinear collision term in LBM for QC. In this work, a linearized non-equilibrium collision, derived from kinetic theory, is presented for HQLBM simulating practical flows. The present approach ensures the unitary of quantum algorithms while keeping the collision relaxation parameter adjustable for simulating different Reynolds number flows. Most importantly, the linearized collision keeps the accuracy of the original nonlinear one in the lattice Boltzmann equation when it theoretically recovers its macroscopic counterpart—Navier–Stokes equations. The practicality of the proposed method is demonstrated by simulating two typical flows, including lid-driven and natural convection flows in a square cavity at different Reynolds and Rayleigh numbers, respectively. It is shown that the proposed HQLBM has good numerical accuracy compared to the conventional LBM, and lower complexity on comparisons to the QC-based LBM carried out on single-circuit QC even when it is performed on a Qiskit virtual quantum computer. This work offers a practical application of QC-based LBM for complex fluid dynamics problems.

Physics of Fluids•Aug 1, 2025•6 citations

QFlowS: Quantum simulator for fluid flows

Sachin S. Bharadwaj

Quantum computing presents a possible paradigm shift in computing, given its advantages in memory and speed. However, there is a growing need to demonstrate its utility in solving practical problems that are nonlinear, such as in fluid dynamics, which is the subject of this work. To facilitate this objective, it is essential to have a dedicated toolkit that enables the development, testing, and simulation of new quantum algorithms and flow problems, taken together. To this end, we present here a high performance, quantum computational simulation package called Quantum Flow Simulator (QFlowS), designed for computational fluid dynamics simulations. QFlowS is a versatile tool that can create and simulate quantum circuits using an in-built library of fundamental quantum gates and operations. We outline here all its functionalities with illustrations. Algorithms to solve flow problems can be built using the expanding list of the core functionalities of QFlowS with its hybrid quantum–classical type workflow. This is demonstrated here by solving an example, one-dimensional, diffusion flow problem. These simulations serve as a check on the algorithm's correctness as well as an ideal test-bed for making them more efficient and better suited for near-term quantum computers for addressing flow problems.

Physics of Fluids•Oct 1, 2024•10 citations

Quantum-Ready and Quantum-Inspired Computing for Fluid Dynamics

Peyman Givi

Bulletin of the American Physical Society•Nov 22, 2021•0 citations

Hybrid quantum algorithms for flow problems

Sachin S. Bharadwaj, Katepalli R. Sreenivasan

For quantum computing (QC) to emerge as a practically indispensable computational tool, there is a need for quantum protocols with end-to-end practical applications-in this instance, fluid dynamics. We debut here a high-performance quantum simulator which we term QFlowS (Quantum Flow Simulator), designed for fluid flow simulations using QC. Solving nonlinear flows by QC generally proceeds by solving an equivalent infinite dimensional linear system as a result of linear embedding. Thus, we first choose to simulate two well-known flows using QFlowS and demonstrate a previously unseen, full gate-level implementation of a hybrid and high precision Quantum Linear Systems Algorithms (QLSA) for simulating such flows at low Reynolds numbers. The utility of this simulator is demonstrated by extracting error estimates and power law scaling that relates [Formula: see text] (a parameter crucial to Hamiltonian simulations) to the condition number [Formula: see text] of the simulation matrix and allows the prediction of an optimal scaling parameter for accurate eigenvalue estimation. Further, we include two speedup preserving algorithms for a) the functional form or sparse quantum state preparation and b) in situ quantum postprocessing tool for computing nonlinear functions of the velocity field. We choose the viscous dissipation rate as an example, for which the end-to-end complexity is shown to be [Formula: see text], where [Formula: see text] is the size of the linear system of equations, [Formula: see text] is the solution error, and [Formula: see text] is the error in postprocessing. This work suggests a path toward quantum simulation of fluid flows and highlights the special considerations needed at the gate-level implementation of QC.

arXiv:2307.00391•Proceedings of the National Academy of Sciences•Dec 1, 2023•44 citations

Solving the Navier-Stokes governing equations through quantum computing

Frank Gaitan

Bulletin of the American Physical Society•Nov 26, 2019•0 citations
Quantum computing (QC) has emerged as a potential computational tool in fluid dynamics. However, a practical QC protocol with end-to-end practical applications to fluid flow is still in nascent. We here propose a simple and practical hybrid QC algorithm based on lattice Boltzmann methods (LBM), which we term HQLBM, for fluid dynamics simulations. The existing QC-based LBMs are limited to simple low-Reynolds-number flow simulations due to their disability to handle the nonlinear collision term in LBM for QC. In this work, a linearized non-equilibrium collision, derived from kinetic theory, is presented for HQLBM simulating practical flows. The present approach ensures the unitary of quantum algorithms while keeping the collision relaxation parameter adjustable for simulating different Reynolds number flows. Most importantly, the linearized collision keeps the accuracy of the original nonlinear one in the lattice Boltzmann equation when it theoretically recovers its macroscopic counterpart—Navier–Stokes equations. The practicality of the proposed method is demonstrated by simulating two typical flows, including lid-driven and natural convection flows in a square cavity at different Reynolds and Rayleigh numbers, respectively. It is shown that the proposed HQLBM has good numerical accuracy compared to the conventional LBM, and lower complexity on comparisons to the QC-based LBM carried out on single-circuit QC even when it is performed on a Qiskit virtual quantum computer. This work offers a practical application of QC-based LBM for complex fluid dynamics problems.
Quantum computing presents a possible paradigm shift in computing, given its advantages in memory and speed. However, there is a growing need to demonstrate its utility in solving practical problems that are nonlinear, such as in fluid dynamics, which is the subject of this work. To facilitate this objective, it is essential to have a dedicated toolkit that enables the development, testing, and simulation of new quantum algorithms and flow problems, taken together. To this end, we present here a high performance, quantum computational simulation package called Quantum Flow Simulator (QFlowS), designed for computational fluid dynamics simulations. QFlowS is a versatile tool that can create and simulate quantum circuits using an in-built library of fundamental quantum gates and operations. We outline here all its functionalities with illustrations. Algorithms to solve flow problems can be built using the expanding list of the core functionalities of QFlowS with its hybrid quantum–classical type workflow. This is demonstrated here by solving an example, one-dimensional, diffusion flow problem. These simulations serve as a check on the algorithm's correctness as well as an ideal test-bed for making them more efficient and better suited for near-term quantum computers for addressing flow problems.
For quantum computing (QC) to emerge as a practically indispensable computational tool, there is a need for quantum protocols with end-to-end practical applications-in this instance, fluid dynamics. We debut here a high-performance quantum simulator which we term QFlowS (Quantum Flow Simulator), designed for fluid flow simulations using QC. Solving nonlinear flows by QC generally proceeds by solving an equivalent infinite dimensional linear system as a result of linear embedding. Thus, we first choose to simulate two well-known flows using QFlowS and demonstrate a previously unseen, full gate-level implementation of a hybrid and high precision Quantum Linear Systems Algorithms (QLSA) for simulating such flows at low Reynolds numbers. The utility of this simulator is demonstrated by extracting error estimates and power law scaling that relates [Formula: see text] (a parameter crucial to Hamiltonian simulations) to the condition number [Formula: see text] of the simulation matrix and allows the prediction of an optimal scaling parameter for accurate eigenvalue estimation. Further, we include two speedup preserving algorithms for a) the functional form or sparse quantum state preparation and b) in situ quantum postprocessing tool for computing nonlinear functions of the velocity field. We choose the viscous dissipation rate as an example, for which the end-to-end complexity is shown to be [Formula: see text], where [Formula: see text] is the size of the linear system of equations, [Formula: see text] is the solution error, and [Formula: see text] is the error in postprocessing. This work suggests a path toward quantum simulation of fluid flows and highlights the special considerations needed at the gate-level implementation of QC.