Quantum Simulation Accurately Models Complex Vortex Interactions in Fluids.

Researchers simulated interactions between multiple vortices using a quantum computer. Reformulating the Navier-Stokes equations within a mechanical framework and employing eight superconducting qubits with high gate fidelities enabled reproduction of natural vortex behaviour. This approach links classical fluid dynamics with quantum computation, offering a new method for studying complex fluid behaviours.

The behaviour of interacting vortices – swirling flows present in phenomena ranging from atmospheric turbulence to biological systems – poses a significant computational challenge for classical simulations. Capturing the intricate dynamics at fine scales over extended periods demands substantial resources. Researchers from Zhejiang University and Peking University have now demonstrated a novel approach, utilising a superconducting quantum processor to model the interactions of multiple vortices. By reformulating the governing Navier–Stokes equations within a mechanical framework, the team, led by Ziteng Wang, Jiarun Zhong, and Yaomin Zhao, mapped the problem onto a quantum system. Their work, detailed in a paper entitled ‘Simulating fluid vortex interactions on a superconducting quantum processor’, leverages eight qubits with high gate fidelities to simulate vortex dynamics, offering a potential pathway to address longstanding challenges in fluid dynamics and expand applications across diverse scientific and engineering disciplines.

Quantum Simulation Advances Understanding of Vortex Dynamics

Researchers have demonstrated a quantum simulation of interacting vortices, offering a potential pathway to overcome limitations inherent in classical computational fluid dynamics (CFD). The study successfully models the behaviour of multiple vortices by translating the governing equations of fluid motion – the Navier-Stokes equations – into a mechanical framework amenable to quantum computation.

Classical CFD struggles with the complex, multi-scale nature of vortex interactions. This new approach constructs an effective Hamiltonian – a mathematical description of the total energy of the system – to govern the vortex dynamics. This Hamiltonian then drives a spatiotemporal evolution circuit implemented on a superconducting processor. The circuit accurately simulates vortex behaviour over extended periods, utilising eight qubits. Qubits are the fundamental units of quantum information, analogous to bits in classical computing. Maintaining high gate fidelities – a measure of the accuracy of quantum operations – is critical for preserving the integrity of the simulation and ensuring a faithful representation of the physical system.

Detailed characterisation of the transmon qubits – a specific type of superconducting qubit – was undertaken. Measurements of frequency, relaxation time (how quickly the qubit loses its quantum state), dephasing time (how long the qubit maintains phase coherence), and gate errors provide essential data for reproducibility and validation by the wider research community. Supplementary materials detail the methodology employed.

Circuit optimisation leveraged a neural network to refine the structure, while the Adam algorithm, coupled with a CosineAnnealingLR learning rate scheduler, was used to fine-tune circuit parameters, ensuring both convergence and accuracy. This combination of techniques allowed for efficient exploration of the parameter space.

The simulation employed a hardware-efficient ansatz (HEA) within a variational quantum eigensolver (VQE) framework. A VQE is a hybrid quantum-classical algorithm used to find the ground state energy of a quantum system. The HEA is a specific structure of quantum circuits designed to be efficiently implemented on available quantum hardware. Parameters were optimised using the COBYLA algorithm, and gradients – which indicate the rate of change of a function – were calculated efficiently using the parameter-shift rule. This technique avoids the need for direct measurement of gradients, enhancing computational efficiency.

The successful reproduction of natural vortex interactions validates the potential of quantum computing to address longstanding challenges in fluid dynamics. This opens possibilities for applications in diverse fields, including aerodynamics, oceanography, and weather forecasting.

Future research will focus on scaling up the number of qubits and extending coherence times – the duration for which qubits maintain their quantum state – to enable simulations of more complex fluid dynamics problems. Exploration of alternative quantum algorithms and further optimisation of circuit design could further enhance both the efficiency and accuracy of these simulations. Applying this approach to other areas of computational fluid dynamics, such as turbulence modelling and multi-phase flow, may yield new insights and advancements in the field.