Quantum Process Tomography: 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 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 point cloud — 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 Monte-Carlo average gate fidelity, the Bloch-volume shrink ratio |det R|, and mean output purity as you turn the noise up.