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 and entropy, 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
for the real experiments (run with the exact backend, for scan speed).