Distributed Quantum Computing: Amplitude-Plane Gate Teleportation

This is a 2D companion to the 3D Bloch-sphere gate-teleportation simulator, built around a genuinely different representation of the same physics: instead of a rotating 3D arrow, each qubit's state is drawn as two vectors in a 2D complex (Argand) plane — one for each basis amplitude. A live histogram of the four possible Bell-measurement outcomes is recomputed directly from the exact 2×2 complex-matrix quantum mechanics every time you move a slider, before you even run the protocol. Pressing Run Protocol samples a real outcome from that distribution, animates two classical correction bits crossing a channel strip between Node A and Node B, and then reveals Node B's corrected amplitude vectors — exactly U|ψ⟩ — confirmed by a live fidelity readout. The underlying math (complex 2×2 unitaries, the Bell basis, and the runtime-derived correction operator) is identical to the 3D version; only the visual representation is 2D-native.