Towards quantum computing of turbulence

Shervin Sammak, Arash G. Nouri, Naseem Ansari +1 more

Felix Tennie, Sylvain Laizet, Seth Lloyd +1 more

Zhaoyuan Meng, Leyu Chen, Jin-Peng Liu +1 more

We propose an end-to-end quantum algorithm to simulate rapidly distorted turbulence via linear combination of Hamiltonian (LCHS). The algorithm comprises three primary stages: the efficient preparation of an initial turbulent state with a prescribed energy spectrum, its subsequent time evolution via LCHS, and the direct measurement of key turbulence statistics. Our analysis indicates that the algorithm can offer a practical quantum speedup over the classical simulation methods for a sufficiently large computational grid. We evaluate the quantum resource requirements for simulating a minimal instance of non-trivial turbulence with classical validation. The numerical results show excellent agreement with ground-truth solutions, capturing both the qualitative evolution of turbulent fields and the quantitative behavior of statistics, including the Reynolds stresses and the fluctuating velocity spectrum. Despite its linearity, rapidly distorted turbulence captures essential turbulence mechanisms and may inform the development of quantum algorithms for the Navier-Stokes equations. Our work establishes a foundation for addressing more complex turbulent phenomena on future fault-tolerant quantum computers.

Felix Tennie, Sylvain Laizet, Seth Lloyd +1 more

A large spectrum of problems in classical physics and engineering, such as turbulence, is governed by nonlinear differential equations, which typically require high-performance computing to be solved. Over the past decade, however, the growth of classical computing power has slowed down because the miniaturisation of chips has been approaching the atomic scale. This is marking an end to Moore's law, which calls for a new computing paradigm: Quantum computing is a prime candidate. In this paper, we offer a perspective on the current challenges that need to be overcome in order to use quantum computing for the simulation of nonlinear dynamics. We review and discuss progress in the development of both quantum algorithms for nonlinear equations and quantum hardware. We propose pairings between quantum algorithms for nonlinear equations and quantum hardware concepts. These avenues open new opportunities for the simulation of nonlinear systems and turbulence.

Mukta Nivelkar, Sunil G. Bhirud, Manmeet Singh +2 more

The analysis and investigation of the data obtained from Direct Numerical (DNS) simulation of droplet dynamics in cloud turbulence is a complex and time-consuming task when performaed on traditional computers. The DNS data generally have, a high spatial resolution ≈ 1mmand require considerable space to store. It is tedious to find specific features of this data, such as locating high and low vortex areas in cloud turbulence using machine learning algorithms. In this research, we employ quantum computing to examine and analyze cloud droplet dynamics data and present a quantum supervised machine learning algorithm, namely, a support vector machine (SVM) to segregate low and high vortex regions and investigate the droplet characteristics in those regions. The result show that use of quantum computers can accelerate the entire process, and quantum mechanics tools, such as quantum kernels and quantum circuits can better manage the complex nature of data than traditional methods.

Han Li, Yutong Lou, Dunhui Xiao

Accurately predicting turbulent flows remains a central challenge in fluid dynamics due to their high dimensionality and intrinsic nonlinearity. Recent developments in quantum algorithms and machine learning offer new opportunities for overcoming the computational barriers inherent in turbulence modeling. Here we present a new hybrid quantum-classical framework that enables faster-than-real-time turbulence prediction by integrating machine learning, quantum computation, and fluid dynamics modeling, in particular, the reduced-order modeling. The novel framework combines quantum proper orthogonal decomposition (QPOD) with a quantum-enhanced deep kernel learning (QDKL) approach. QPOD employs quantum circuits to perform efficient eigenvalue decomposition for low-rank flow reconstruction, while QDKL exploits quantum entanglement and nonlinear mappings to enhance kernel expressivity and dynamic prediction accuracy. The new method is demonstrated on three benchmark turbulent flows, our architecture achieves significantly improved predictive accuracy at reduced model ranks, with training speeds up to 10 times faster and parameter counts reduced by a factor of 1/N compared to classical counterparts, where N is the input dimensionality. Although constrained by current noisy intermediate-scale quantum (NISQ) hardware, our results demonstrate the potential of quantum machine learning to transform turbulence simulation and lay a solid foundation for scalable, real-time quantum fluid modeling in future quantum computers.