Innovative Applications of FEM and Physics-Informed Neural Networks in Thermal Management of Superconducting Qubits

This project combines the Finite Element Method (FEM) with Physics-Informed Neural Networks (PINN) to develop a complete MATLAB-based simulation framework, offering solutions to the ballistic-diffusive heat transfer and quasiparticle poisoning problems in superconducting qubit structures, which represents a significant advancement in thermal management research for quantum computing hardware.

The performance of superconducting qubits is severely affected by thermal noise and quasiparticle poisoning. At extremely low temperatures, heat transfer exhibits a mixed ballistic-diffusive characteristic, making the traditional Fourier's law of heat conduction no longer applicable. Quasiparticle poisoning reduces the coherence time of qubits, which is a key bottleneck for large-scale development. Traditional numerical methods have high accuracy but enormous computational costs, making them difficult to meet the needs of design iterations. Thus, developing efficient and accurate simulation tools has become an urgent requirement.

The FEM_BallisticDiffusion_PINN project provides a MATLAB-based simulation framework that combines FEM and PINN, with the core goal of maintaining physical accuracy while improving computational efficiency. It includes key components such as a physical derivation module, 3D geometric modeling, a cryogenic material physics database, trap and heat sink design tools, and a PINN acceleration engine.

At low temperatures, the mean free path of phonons is comparable to the device size, so heat transfer exhibits ballistic characteristics. The project uses the Phonon Boltzmann Transport Equation (BTE) for description, distinguishing between ballistic phonons (propagating directly without scattering) and diffusive phonons (transferring energy through scattering). Parameters can be adjusted to observe the transition from pure ballistic to pure diffusive. Accurate modeling helps optimize heat dissipation channels and maintain the Josephson junction at low temperatures to preserve coherence time.

Quasiparticle poisoning is the main cause of decoherence. Cooper pairs are broken by high-energy photons to generate quasiparticles, which diffuse and are captured by Josephson junctions, leading to decoherence. The project models the quasiparticle generation mechanism (external excitation sources), diffusion and recombination processes, and trap design optimization (low-energy gap regions attract quasiparticles). The optimal trap configuration is found through parameter scanning.

Traditional FEM has high computational costs. PINN encodes physical laws into loss functions, so its outputs naturally satisfy constraints. In the project, PINN learns the mapping from parameters to temperature distribution and quasiparticle concentration, using residual loss, boundary condition loss, data-driven loss, and transfer learning strategies. The hybrid method enables rapid parameter exploration and optimization.

The framework has direct engineering value for quantum computing hardware development, as improving coherence time helps achieve quantum advantage. Application scenarios include new qubit design, packaging and heat sink optimization, radiation shielding design, and process improvement guidance. The PINN method can be transferred to multi-physics problems such as superconducting resonator design and single-photon detector optimization.

The project is implemented in MATLAB, utilizing matrix operations and the Partial Differential Equation Toolbox, with modular code. Learning path: Physical derivation documents → Example scripts → Mesh generation → PINN training. The documentation contains a large number of references covering basic cryogenic physics to the latest PINN advancements.