Trotterized Ising Chain — Digital Quantum Simulation

Quantum simulation, as a field, means using a controllable quantum system — often a gate-based quantum computer — to compute the time evolution of another quantum system that is otherwise intractable to simulate classically. This page runs a genuine digital quantum-simulation circuit: a chain of N spins under the transverse-field Ising Hamiltonian, evolved with a first-order Trotter-Suzuki decomposition that alternates the non-commuting coupling and field terms as a sequence of gates applied to the full statevector. You can tune the coupling J, the transverse field h, and — most importantly — the Trotter step size, watching the simulated state's fidelity against a much finer continuum reference degrade as steps get coarser, exactly the tradeoff that limits real digital quantum simulators today. Each spin's exact reduced Bloch vector is rendered live along the chain, visibly shrinking as nearest-neighbor entanglement builds from the quench.