Ensemble‑Based Pauli Channel Tomography with Gate Tolerances

This laboratory exercise introduces ensemble-based tomography of single-qubit Pauli channels with gate tolerances. Students use Quirk to construct an ensemble of quasi-noise gates whose rotation angles vary within a prescribed tolerance interval and determine their Bloch-sphere contraction coefficients from three canonical test states. Maple is then used to reconstruct the corresponding Pauli-probability vectors simultaneously through a matrix transformation, calculate the average channel and parameter spreads, analyze their dependence on the rotation angle, and visualize the average contraction ellipsoid. The exercise provides an accessible engineering-oriented model of how gate-implementation tolerances generate a family of nearby quantum channels.