The 14-gate per-channel quantum circuit that encodes EEG connectivity into a 2-qubit state.
The A-Gate is a fixed quantum circuit. It is not trained, optimized, or adapted to the data. Each of the 28 channel pairs in the 8-channel configuration passes through the same 14-gate sequence independently. The three encoding parameters (a, b, c) are derived directly from the PLV connectivity matrix. This page shows what happens inside that circuit, gate by gate, on a single 2-qubit register.
The first ten gates act on each qubit independently. Each gate is a rotation on that qubit's Bloch sphere: Hadamard, phase, Rx, Ry. The arrows trace specific paths across the sphere surface but stay at unit length. The small wireframe spheres at each arrow tip remain point-sized. The four amplitude bars show probability redistributing across basis states, but the joint state remains a product of two independent qubit states. Concurrence stays at exactly zero.
Gates 11 through 14 are controlled rotations that couple the two qubits. When qubit E's gate fires conditional on qubit I's state, neither qubit alone fully describes the system. The Bloch arrows shrink. Gold lines and wireframe spheres appear at each arrow tip, showing the information that now lives in correlations between the qubits rather than in either qubit alone.
The wireframe sphere at each arrow tip is the locus of conditional states: positions the qubit could collapse to depending on how its partner is measured. As entanglement grows, this set expands from a single point (no entanglement, the qubit has a definite pure state) to a larger sphere (stronger entanglement, more possible conditional outcomes). For a maximally entangled state the wireframe would fill the entire Bloch sphere, meaning every direction is equally possible conditional on the partner's measurement outcome.
The A-Gate's fixedness is what makes polarity measurable. Because the measurement basis does not adapt to the data, patients whose covariance shifts in opposite directions produce opposite signs in the expectation value. A trained circuit would learn to compensate, erasing exactly the signal that distinguishes the two populations.