Measurement-based (one-way) quantum computation turns the measurement "ground" of quantum mechanics into the engine of computation: first you build a fixed, highly entangled cluster state, then you compute purely by measuring its qudits one at a time and feeding outcomes forward. Here it is generalized from qubits to qudits (d-level systems) for d = 2, 3, 5. No φ: this is measurement × entanglement physics.

The upper chart is the resource state. On a 2×M grid the entanglement across the left/right cut is exactly the number of edges crossing it times ln d (two edges, so 2·ln d) and that stays flat as the lattice grows wider: an area law, quantized in ln d. Entanglement lives in the crossings, the loom made exact. The lower chart is the computation: a chain of measured J_d = F_d·D(θ⃗) gadgets realizes an arbitrary single-qudit unitary, and the byproduct-corrected output matches the directly applied unitary with fidelity 1 at every depth and every d.

The cards verify the rest: the generalized graph-state stabilizers fix the state (defect ≈ 0); the measured cut entropy matches rank·ln d to machine precision; and the entangling gadget produces entanglement only with its vertical link (≈ ln d) and a product state without it (entropy 0): the control that proves the link is doing the work. Computed live in your browser via WebAssembly.