| # Trotter (real-time Hamiltonian evolution as gates) | |
| Real-time Hamiltonian evolution as an actual gate circuit | |
| (Trotterization) — did not exist anywhere in this package before. Every | |
| existing piece of "evolution" machinery elsewhere is either | |
| gate-based-and-fixed (a hand-written or VQE-optimized circuit template) | |
| or exact-and-not-a-circuit (`dashboard_core.hamiltonians.ground_state_energy`'s | |
| dense diagonalization). Nothing composed `exp(-i*H*t)` for an arbitrary | |
| Hamiltonian into gates a real quantum computer could run. | |
| `pauli_rotation_ops` is exact for a single Pauli-string term (fidelity | |
| 1.0 against `scipy.linalg.expm`, verified for 1-4 qubit mixed X/Y/Z | |
| strings, not just Z-strings); `trotter_evolve_ops` composes many such | |
| terms via the first-order product formula, an *approximation* whose | |
| error shrinks as `n_steps` grows — verified: infidelity drops roughly 4x | |
| per doubling of steps against a real, non-trivial multi-qubit | |
| Hamiltonian, consistent with the expected quadratic convergence of | |
| first-order Trotter error in state overlap. | |
| ::: dense_evolution.circuits.trotter | |
| --- | |
| **See also**: [`fermions`](fermions.md) and [`entropy`](entropy.md), the | |
| other two modules promoted alongside this one from a real traversable- | |
| wormhole-inspired quantum teleportation reproduction (arXiv:2604.10090). | |
| `dashboard_core.wormhole.run_wormhole_protocol_trotter` uses this | |
| module's Trotterized circuit as the "closer to real hardware" backend, | |
| cross-verified against the exact-evolution backend — see | |
| [Dense-Evolution-Discovery](https://tatopenn-cell.github.io/Dense-Evolution-Discovery/wormhole_syk_teleportation/) | |
| for the real experiments (run with the exact backend, for scan speed). | |