heat-2d-schrodingerization

Schrödingerization transforms the non-unitary 2D heat diffusion process into unitary evolution, enabling quantum simulation of anisotropic diffusion with Dirichlet or periodic boundaries. This allows classical and Trotter quantum routines to solve the heat equation.

Yes, you can simulate anisotropic heat diffusion with periodic and Dirichlet boundaries. The Skill supports both classical and Trotter-based quantum evolution, automatically generating 2D quantum circuits and 3D visualizations for the temperature field.

You need a Python environment with NumPy and the unitarylab library. Running python ./scripts/algorithm.py compares classical Schrödingerization with a Trotter quantum circuit for the 2D heat equation.

The Skill assembles Kronecker-based Laplacians to form the Schrödingerized Hamiltonian, handling initial conditions and source terms to produce a 2D temperature field suitable for analysis and benchmarking.

Classical evolution solves the Schrödingerized 2D heat equation directly, while Trotter quantum evolution approximates the unitary operator using quantum circuits. Both methods support anisotropic diffusion and produce comparable 3D visualizations.

Schrödingerization applies to anisotropic diffusion with Dirichlet or periodic boundaries, requiring NumPy and unitarylab. It transforms non-unitary heat diffusion into unitary evolution but is constrained to 2D temperature fields and Trotter-based quantum circuit approximations.