advection-schrodingerization

You can solve a non-unitary 1D advection equation by applying Schrödingerization, which transforms the discretized system into a Hamiltonian form suitable for unitary time evolution. This allows quantum or hybrid simulation of the PDE.

Schrödingerization is a transformation technique that converts non-unitary discretized PDE systems into a Hamiltonian form. This enables the use of quantum evolution methods to solve classical numerical equations.

You can compare classical and quantum time evolution by running dual execution paths provided by the solver: a classical Schrödingerization-based solver and a quantum Trotterized evolution, evaluating accuracy and performance on the same grid.

Yes, you need numpy and the unitarylab toolkit. These dependencies are required to build derivative operators, construct Hamiltonians, and execute the Schrödingerization and Trotterized solvers.

Yes, the workflow supports customizable boundary conditions on the simulation grid. The PDE parsing and discretization step extracts domain, grid, and boundary conditions to build the appropriate derivative operator.

Trotterized evolution accuracy depends on the time step size and grid resolution. Comparing its results against the classical Schrödingerization solver on the same grid helps identify numerical errors and performance limits.