Quantum Lattice Boltzmann Algorithm Simulates Heat Transfer with Phase Change, Achieving Results with 0.005 Accuracy

Simulating heat transfer involving phase change, such as melting or boiling, presents a significant computational challenge for engineers and scientists, demanding substantial processing power and time. Christopher L. Jawetz, Zhixin Song, and Spencer H. Bryngelson, alongside Alexander Alexeev and colleagues at the George W. Woodruff School of Mechanical Engineering and the School of Physics at Georgia Institute of Technology, have developed a novel approach to overcome these limitations. Their research introduces a quantum lattice Boltzmann method, which harnesses the power of quantum computing to model heat transfer with phase change more efficiently than classical methods. This innovative technique accurately tracks the movement of interfaces between solid and liquid phases, and initial simulations, utilising a small quantum system, demonstrate a high degree of accuracy when compared with established analytical solutions and classical lattice Boltzmann simulations, paving the way for detailed analysis of complex thermal systems.

This new method leverages the principles of quantum computation to accelerate key calculations, representing the thermal field on a lattice and evolving it using quantum gates. The algorithm accurately predicts temperature distributions and phase transition dynamics in systems undergoing solidification and melting processes. The quantum lattice Boltzmann method employs a sharp interface approach to accurately capture the distinct phases and their boundaries, correctly representing the latent heat associated with phase change. Performance analysis reveals significant speedups compared to classical lattice Boltzmann simulations, particularly for large-scale problems, demonstrating the potential of quantum computing to address complex thermal-fluid transport phenomena. This advancement offers a promising pathway towards more efficient and accurate simulations for applications in materials processing, energy storage, and thermal management.

Quantum Lattice Boltzmann Simulations Advance Fluid Dynamics

This research presents a comprehensive framework for simulating fluid dynamics using the quantum lattice Boltzmann method (QLBM), combining computational fluid dynamics, quantum computing, and numerical analysis. The central goal is to translate the established lattice Boltzmann method into quantum circuits, exploring how quantum computers can accelerate simulations and address limitations of classical approaches. The work focuses on developing algorithms suitable for near-term quantum hardware, acknowledging the constraints of limited qubit counts and noise. The research encompasses several key areas, beginning with a detailed explanation of the lattice Boltzmann method and fundamental quantum computing concepts.

The team then developed a quantum lattice Boltzmann algorithm by mapping the classical method’s collision and streaming steps into quantum circuits, encoding fluid density and velocity into quantum states. They investigated various quantum implementations of the collision operator and addressed the challenges of implementing boundary conditions in a quantum setting. To optimise performance on near-term hardware, the team focused on reducing circuit depth and qubit count, and explored error mitigation techniques. The research extends to modelling phase change, incorporating latent heat and tracking the interface between liquid and solid phases while maintaining thermodynamic consistency. The team also considered the potential of more powerful future quantum computers and explored hybrid quantum-classical approaches. The team successfully implemented an interface-tracking strategy that separates solid and liquid domains, allowing accurate modelling of the discontinuity in the enthalpy-temperature relationship during phase change. Results demonstrate that the QLBM accurately replicates temperature distribution and liquid fraction evolution, aligning closely with both classical lattice Boltzmann simulations and analytical solutions. The method achieves this accuracy using a relatively small quantum circuit, comprising 17 lattice nodes and 51 qubits, while maintaining root-mean-square errors below 0.

005 when compared to classical methods. Importantly, the researchers explored postponing circuit reinitialization, a common bottleneck in quantum computations, and found that delaying reinitialization to every 12 time steps did not significantly impact accuracy. While designed for large-scale, fault-tolerant quantum computers, the team acknowledges that recent advances in quantum algorithm optimisation and circuit design may enable implementation on near-term quantum hardware. Future research will likely focus on reducing the frequency of circuit reinitialization, potentially through further algorithmic optimisation, and scaling the method to more complex geometries and physical scenarios relevant to applications such as thermal management, energy storage, and additive manufacturing.