Echoed Cross-Resonance Gate Simulator

The cross-resonance gate is the native two-qubit entangling operation used on real superconducting quantum computers: drive a control qubit at the frequency of a qubit it's coupled to, and the coupling turns that drive into a conditional Z⊗X rotation of the target. This simulator integrates the real two-qubit Schrödinger equation for that interaction, letting you prepare the control qubit, dial in the pulse area and an always-on IX crosstalk term, and watch the target's Bloch vector — and its two conditional "ghost" branches — rotate and split apart as entanglement builds. Flip on the echoed pulse sequence to see the exact same trick real hardware uses to cancel the crosstalk while keeping the entangling rotation intact.