Quantum Process Tomography 2D: The Bloch Ellipsoid

Every real quantum gate is noisy, and the standard way engineers characterize that noise is quantum process tomography: send a handful of known probe states through the device, measure where they land, and reconstruct the underlying affine map R·r + t on the Bloch ball. This 2D simulator applies a chosen ideal single-qubit gate followed by adjustable depolarizing, dephasing and amplitude-damping noise, reconstructs the 3×3 transfer matrix and offset vector from exactly four probe measurements the way a real lab would, and renders the result as a deformed, drag-to-rotate point cloud projected onto the canvas — the image of the Bloch sphere under the channel is an ellipsoid whose size and shift directly encode how much quantum information the process destroys. Live readouts track average gate fidelity, the Bloch-volume shrink ratio |det R|, and mean output purity as you turn the noise up.