Quantum lattice Boltzmann algorithm for heat transfer with phase change

Abstract: Heat transfer involving phase change is computationally intensive due to moving phase boundaries, nonlinear computations, and time step restrictions. This paper presents a quantum lattice Boltzmann method (QLBM) for simulating heat transfer with phase change. The approach leverages the statistical nature of the lattice Boltzmann method (LBM) while addressing the challenges of nonlinear phase transitions in quantum computing. The method implements an interface-tracking strategy that partitions the problem into separate solid and liquid domains, enabling the algorithm to handle the discontinuity in the enthalpy-temperature relationship. We store phase change information in the quantum circuit to avoid frequent information exchange between classical and quantum hardware, a bottleneck in many quantum applications. Results from the implementation agree with both classical LBM and analytical solutions, demonstrating QLBM as an effective approach for analyzing thermal systems with phase transitions. Simulations using 17 lattice nodes with 51 qubits demonstrate root-mean-square (RMS) errors below 0.005 when compared against classical solutions. The method accurately tracks interface movement during phase transition.