What problem does it solve? Solving partial differential equations like advection and heat diffusion on quantum hardware is hard because their dynamics are non-unitary, while quantum computers only perform unitary evolution. This Skill routes PDE-solving requests to specialized guides that apply the Schrodingerization technique, converting non-unitary PDE dynamics into unitary Schrodinger-type dynamics suitable for both classical and quantum simulation. ## Core Features & Use Cases - PDE Routing: Directs requests to the correct leaf guide based on PDE type and dimension: 1D advection, 1D heat equation, or 2D heat equation. - Dual Solver Paths: Each leaf guide supports classical matrix-exponentiation solvers and Trotterized quantum simulation with automatic circuit generation. - Boundary and Scheme Handling: Covers periodic, Dirichlet, and Neumann boundary conditions, central and upwind discretization schemes, source terms, and anisotropic 2D diffusion. - Use Case: A researcher wants to simulate the 2D heat equation with anisotropic diffusion coefficients on a quantum simulator. The Skill routes to the 2D heat guide, which provides the Kronecker-product Laplacian construction, Schrodingerized Hamiltonian, Trotter evolution code, and 3D surface visualization. ## Quick Start Ask the assistant to solve the 1D heat equation with Dirichlet boundary conditions using Schrodingerization and compare the classical and Trotter solver results.
