Trotterized Quantum Time Evolution

Real quantum computers cannot apply an arbitrary Hamiltonian directly — they build up continuous-time evolution from short bursts of elementary gates, using the Trotter–Suzuki product formula. This simulator evolves a single qubit under H = h_xX + h_zZ two ways at once: exactly, via the closed-form Rabi precession solution (a smooth cyan circle on the Bloch sphere), and digitally, by chaining first- or second-order Trotter gate sequences (a jagged magenta path). Adjust the field strengths and the number of Trotter steps to watch the gate-based approximation converge onto the true trajectory, and read the live infidelity between the two quantum states as the gap closes.