Researchers Simulate Fluid Dynamics on Quantum Processor

Scientists José Diogo da Costa Jesus and colleagues at the Hamburg Centre for Ultrafast Imaging, Luruper Chaussee 149, Hamburg D-22761, Germany, and the University of Oxford, have demonstrated a new method realising the time evolution of nonlinear fluid dynamics on a quantum processor. Numerical simulation of nonlinear partial differential equations underpins modern scientific computing, spanning areas from fluid flow and transport to collective dynamics. Extending this capability to quantum computers represents a longstanding challenge because nonlinear and non-Hermitian evolution is fundamentally incompatible with conventional Hamiltonian-based quantum simulation. The difficulty arises because quantum mechanics, at its core, describes systems evolving according to the Schrödinger equation, which is linear and governed by Hermitian operators; representing dissipative or nonlinear forces requires fundamentally different approaches. Quantum simulation accurately models high Reynolds number fluid convection Error rates in reconstructing the time evolution of fluid dynamics dropped to 0.3 per cent for the first timestep, a substantial improvement over previous methods limited by shallower circuits and susceptibility to hardware noise. This reduction in error is critical, as quantum systems are inherently prone to decoherence and gate errors, which rapidly degrade the accuracy of computations.

The team achieved this by implementing a hybrid quantum-classical variational framework, directly encoding nonlinear dynamics and circumventing the need for complex linear approximations. Traditional quantum algorithms often rely on mapping the problem onto a Hamiltonian and then evolving it using unitary transformations; however, this approach struggles with nonlinear terms. The variational framework instead uses a parameterised quantum circuit, where the parameters are optimised classically to minimise the difference between the quantum simulation and the desired solution. This allows for the direct representation of nonlinearities without requiring approximations like small-angle approximations or linearization. A breakthrough enables the simulation of convection-dominated dynamics at Reynolds numbers of order 102, a regime previously inaccessible on quantum processors due to the depth of circuits required; this represents a step towards modelling realistic fluid behaviours. The Reynolds number is a dimensionless quantity that characterizes the ratio of inertial forces to viscous forces within a fluid. Higher Reynolds numbers indicate more turbulent and chaotic flow, which are notoriously difficult to simulate classically due to the computational resources required to resolve the smallest scales of motion.

The team’s work demonstrates a substantial leap forward in the field of quantum fluid dynamics. The circuits employed contained up to 60 controlled-Z layers, a measure of circuit depth, on IBM superconducting quantum hardware. Circuit depth is a crucial factor in quantum computation, as each gate operation introduces a potential source of error. Deeper circuits are more susceptible to decoherence and require more robust error mitigation techniques. The use of 60 controlled-Z layers signifies a significant advancement in the ability to perform complex computations on current quantum hardware. This was enabled by a novel error mitigation technique that avoids the need to duplicate circuit components. Error mitigation is essential for extracting meaningful results from noisy quantum computers. Techniques like circuit duplication, while effective, increase the resource requirements substantially.

The team’s approach offers a more efficient way to reduce the impact of errors without significantly increasing the circuit size. COBYLA and Sequential Grid-based Explicit Optimisation were used to benchmark the approach, with the latter proving more robust against hardware imperfections. These are both classical optimisation algorithms used to find the optimal parameters for the quantum circuit. Sequential Grid-based Explicit Optimisation demonstrated superior performance in the presence of noise, suggesting its suitability for near-term quantum devices. A reconstruction fidelity of 99.7 per cent for the initial field demonstrates the accuracy of the encoding and optimisation procedures. This high fidelity indicates that the quantum processor is accurately representing the initial conditions of the fluid simulation. While previous quantum processors have implemented linear simulations, including Poiseuille flow and vortex dynamics, this advancement extends beyond those limitations. Poiseuille flow describes the laminar flow of a viscous fluid through a pipe, while vortex dynamics focuses on the evolution of swirling flows. These simulations, while important, are limited to linear regimes. This new work demonstrates the ability to simulate nonlinear interactions, which are crucial for understanding more complex fluid phenomena. However, current simulations remain limited to relatively small grid sizes and short timescales, and scaling to realistically complex scenarios and longer durations remains a substantial hurdle. The computational cost of simulating larger grids and longer times increases rapidly, requiring more qubits and more complex optimisation procedures.

The team are now focusing on improving the scalability of the method and exploring techniques to reduce the computational cost of the classical optimisation loop. Quantum simulation unlocks potential for modelling complex fluid behaviours For a long time, scientists have sought to extend the power of quantum computers to simulate the complex, nonlinear systems governing much of the physical world. The demonstration of nonlinear fluid dynamics, achieved through a hybrid quantum-classical approach, represents a step towards this goal, sidestepping the limitations of methods reliant on linear approximations. The ability to simulate nonlinear systems is crucial for modelling a wide range of physical phenomena, including turbulence, weather patterns, and chemical reactions. Successfully modelling even simplified fluid dynamics on a quantum processor proves that these machines can move beyond simulating simple, static systems and offers a pathway to tackling more complex problems as quantum hardware improves and allows for higher fidelity calculations with greater numbers of qubits. The current generation of quantum computers is limited by the number of qubits and their coherence times. As these parameters improve, the complexity of the simulations that can be performed will increase dramatically. This experimental realisation of nonlinear fluid dynamics marks an advance, successfully demonstrating time propagation on a quantum processor where previous methods struggled with the complexities of nonlinear systems. Direct encoding of the dynamics of the viscous and inviscid Burgers equations bypassed the need for linear approximations inherent in conventional quantum simulation techniques, opening possibilities for modelling a wider range of physical phenomena and establishing a foundation for quantum computation applied to continuum dynamics. The Burgers equation is a fundamental equation in fluid dynamics that describes the evolution of fluid velocity. It is often used as a model for studying turbulence and shock waves. By directly encoding the dynamics of this equation, the team avoided the need to simplify the problem, allowing for a more accurate simulation. Despite this progress, the current implementation is limited to relatively low Reynolds numbers, hindering the modelling of truly realistic and chaotic fluid behaviours. The limitations in Reynolds number are due to the computational resources required to resolve the small-scale features of turbulent flow. Further research will focus on overcoming these limitations and expanding the scope of quantum fluid simulations. This includes developing more efficient algorithms, improving the coherence times of qubits, and exploring new methods for encoding and optimising quantum circuits. The researchers experimentally demonstrated the time evolution of nonlinear fluid dynamics on a quantum processor, successfully modelling the viscous and inviscid Burgers equations. This achievement means quantum computers are now capable of simulating systems that change over time, moving beyond static calculations and opening avenues for more complex modelling.

The team directly encoded the equations into quantum circuits and reconstructed the field using quantum-classical optimisation, achieving convection-dominated dynamics at Reynolds numbers of order 102. They suggest future work will focus on improving algorithms, qubit coherence, and encoding methods to expand the scope of these quantum fluid simulations. 👉 More information 🗞 Time evolution of nonlinear dynamics on a quantum processor ✍️ José Diogo da Costa Jesus, Abhishek Setty, Tommaso Calarco, Dieter Jaksch, Francisco Cárdenas López and Felix Motzoi 🧠 ArXiv: https://arxiv.org/abs/2608.13041 Stay currentSee today’s quantum computing news on Quantum Zeitgeist for the latest breakthroughs in qubits, hardware, algorithms, and industry deals. Tags: