In the last few years, quantum computing has evolved as the next big technological breakthrough. Many big companies are actively researching this area and have built open-source frameworks which can be used to develop solutions for problems that connect be solved by classical computers. One such problem is the solution of Navier-Stokes equations which takes exponential time for simulation but using quantum computers, they can be solved in polynomial time. But the current state of quantum computation does not enable everyone to test their implementation on a real quantum computer. In this situation, a simulator enables rapid prototype and testing techniques and algorithms for when the real quantum computer is ready. This paper focuses on simulating fluid flow algorithms using a quantum framework, such as Navier- Stokes equations, with the lattice Boltzmann method (LBM) used to numerically solve the relevant system of equations on both CPU and GPU to speed up the process. The quantum framework used in this paper is Qiskit, an open-source software development kit created by IBM that allows developers to create and test quantum algorithms. NVIDIA cuQuantum is an SDK of optimized libraries and tools for expediting quantum computing operations used in this paper to solve the fundamental problem of modeling large-size quantum circuits using the power of GPU
In the last few years, quantum computing has evolved as the next big technological breakthrough. Many big companies are actively researching this area and have built open-source frameworks which can be used to develop solutions for problems that connect be solved by classical computers. One such problem is the solution of Navier-Stokes equations which takes exponential time for simulation but using quantum computers, they can be solved in polynomial time. But the current state of quantum computation does not enable everyone to test their implementation on a real quantum computer. In this situation, a simulator enables rapid prototype and testing techniques and algorithms for when the real quantum computer is ready. This paper focuses on simulating fluid flow algorithms using a quantum framework, such as Navier- Stokes equations, with the lattice Boltzmann method (LBM) used to numerically solve the relevant system of equations on both CPU and GPU to speed up the process. The quantum framework used in this paper is Qiskit, an open-source software development kit created by IBM that allows developers to create and test quantum algorithms. NVIDIA cuQuantum is an SDK of optimized libraries and tools for expediting quantum computing operations used in this paper to solve the fundamental problem of modeling large-size quantum circuits using the power of GPU
A new algorithm for solving the Navier-Stokes equations (NSE) on a quantum device is presented. The non-linearity of fluid flow equations is managed by using the stream function-vorticity formulation, while the lattice Boltzmann method (LBM) is utilized for solving the corresponding system of equations numerically. Following the nature of the lattice Boltzmann method, the proposed quantum algorithm consists of five major sections: initialization, collision, propagation, boundary condition implementation, and macros calculation. The collision and boundary condition step is quantumly implemented by applying the standard-form encoding approach, while the quantum walk procedure is applied for the propagation step. The algorithm is implemented by using IBM's quantum computing software development framework Qiskit, while for the verification purposes two-dimensional (2D) cavity flow is simulated and compared with classical code.
In this paper, a new algorithm for solving the Navier–Stokes equations (NSE) on a quantum device is presented. For the fluid flow equations, the stream function-vorticity formulation is adopted, while the lattice Boltzmann method (LBM) is utilized for solving the corresponding system of equations numerically for one time step. Following the nature of the lattice Boltzmann method, the proposed quantum algorithm consists of five major sections: initialization, collision, propagation, boundary condition implementation and calculation of macroscopic quantities. The collision and boundary condition step is quantumly implemented by applying the standard-form encoding approach, while the quantum walk procedure is applied for the propagation step. The algorithm is implemented by using IBM’s quantum computing software development framework Qiskit, while for the verification purposes, two-dimensional (2D) cavity flow is simulated and compared with classical code.
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.
This paper explores the application of quantum-inspired algorithms to accelerate the simulation of fluid dynamics. Traditional computational fluid dynamics (CFD) methods, particularly those solving the Navier-Stokes equations, are often computationally expensive, limiting their applicability in real-time simulations and complex scenarios. This research investigates the potential of mimicking quantum phenomena, specifically wave interference and amplitude estimation, through the design and implementation of novel algorithms. The core idea is to leverage techniques inspired by quantum computing to achieve a significant speedup in solving these equations. We present a framework utilizing amplitude estimation to efficiently approximate solutions, offering a potential pathway to overcome the computational bottlenecks inherent in conventional CFD. The presented approach provides a novel methodology for simulating fluid dynamics with reduced computational cost, opening opportunities for advancements in areas such as aerospace, automotive, and weather forecasting.
Abstract There is great interest in using quantum computers to efficiently simulate a quantum system’s dynamics as existing classical computers cannot do this. Little attention, however, has been given to quantum simulation of a classical nonlinear continuum system such as a viscous fluid even though this too is hard for classical computers. Such fluids obey the Navier–Stokes nonlinear partial differential equations, whose solution is essential to the aerospace industry, weather forecasting, plasma magneto-hydrodynamics, and astrophysics. Here we present a quantum algorithm for solving the Navier–Stokes equations. We test the algorithm by using it to find the steady-state inviscid, compressible flow through a convergent-divergent nozzle when a shockwave is (is not) present. We find excellent agreement between numerical simulation results and the exact solution, including shockwave capture when present. Finally, we compare the algorithm’s computational cost to deterministic and random classical algorithms and show that a significant speed-up is possible. Our work points to a large new application area for quantum computing with substantial economic impact, including the trillion-dollar aerospace industry, weather-forecasting, and engineered-plasma technologies.
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.