BB [[144,12,12]] on QCCD — every design, ranked

a real direct machine: grid13x13 with control.model 'direct', so a cycle may play several waveforms. It does in most: 930 of 1,319 transport cycles move ions in two to eight directions at once (up to 10 distinct motions, 11 waveforms with the hold), and the round takes 405.6 ms at 4.8 ions per instruction -- against 866.1 ms for the same lattice told to play one waveform a cycle (12). Every site has channels of its own: no select bits, and 12,480 DACs, over the task's 128.

the fastest lattice, as a direct machine: 376.7 ms at 4.95 ions per instruction, 883 of 1,208 cycles moving ions in two to eight directions at once. And a die with zero control electrodes: every trap is 112.5 um from two junctions whose keep-outs reach 180 um. 8,800 DACs.

node-for-node the same graph as 10, pulled apart so its traps clear the keep-outs: the same programme (compiling it here gives the identical instruction list), the same 376.7 ms and 25 rules, 35.6 mm2 instead of 9.4. Still not buildable by today's DRC: 110 traps get no control-electrode pair and the other 110 get 2 of the 3 required.

compiles, then fails R2: a coupled ancilla site is degree 3, and a junction may hold one ion. It cannot both house an ancilla and receive a rider.

the cheapest transport in the study, unusable: rigid rotation preserves cyclic order so two riders never meet, and a loop has one route.

free space is not the constraint: a lattice routes at 76% occupancy, this loop cannot at 35%.

a line has no closed loop for rotation and one route for the router.

genuinely too small -- the one lattice verdict that was right.

a periodic lattice, every row and column a closed loop, with one ancilla per check pair: 516.4 ms at 3.79 ions per instruction, against the planar grid's 648.1 at 72 ancillas (22) and 869.9 at 24 (23). The wrap is worth 1.25x, the ancillas 1.34x. It runs under the one-waveform model (control.model simd_classes: one motion a cycle, the R22 split) on direct wiring, so its time is an upper bound for a direct machine. The study's 97 ms was this programme before the R22 split, several motions a cycle.

the code's cell (i, j) laid at columns i, rows 2j and 2j+1 via --init-placement: 462.8 ms at 4.54 ions per instruction, 1.12x the compiler's own placement (20, 516.4 ms). It runs under the one-waveform model (control.model simd_classes: one motion a cycle, the R22 split) on direct wiring, so its time is an upper bound for a direct machine. Before the R22 split the two placements tied (the study's 99 and 97 ms).

the same planar grid as q06h's lattices with 72 ancillas instead of 24: 648.1 ms instead of 869.9 (23), 1.34x. The lattice family's 24-ancilla numbers were ancilla-starved. It runs under the one-waveform model (control.model simd_classes: one motion a cycle, the R22 split) on direct wiring, so its time is an upper bound for a direct machine.

the control for the ancilla count: the q06h tier, 869.9 ms at 2.62 ions per instruction -- level with grid13x13 under the same model (12, 866.1 ms). It runs under the one-waveform model (control.model simd_classes: one motion a cycle, the R22 split) on direct wiring, so its time is an upper bound for a direct machine.

the torus drawn as a chip with no crossings: each row a closed ring, the columns radial spokes. Under one waveform a cycle it is the slowest of the lattices that pass every rule: 1,254.2 ms at 1.08 ions per instruction, against the torus's 516.4 and the planar grid's 648.1. It runs under the one-waveform model (control.model simd_classes: one motion a cycle, the R22 split) on direct wiring, so its time is an upper bound for a direct machine. The study's 106 ms, which kept most of the torus's speed, was the programme before the R22 split.

a true torus on a plane needs 120 crossings, and every one lands on a ring wire, so the x-hops pay for the y-wrap: 1,489.5 ms, the slowest compiled lattice on the board. The wrap is not worth its crossings. It runs under the one-waveform model (control.model simd_classes: one motion a cycle, the R22 split) on direct wiring, so its time is an upper bound for a direct machine.

28 random swaps take the torus from diameter 12 to 8, and under one waveform a cycle the shorter distances do not pay: the round goes from 516.4 to 1,125.5 ms, one ion per transport instruction. Not drawable: every shortcut would be crossings on a chip. It runs under the one-waveform model (control.model simd_classes: one motion a cycle, the R22 split) on direct wiring, so its time is an upper bound for a direct machine. Before the R22 split it was 82 ms.

the torus's degrees with none of its geometry: diameter 6, 1,036.1 ms at one ion per transport instruction. An expander beats every lattice on distance and has hundreds of crossings in practice. It runs under the one-waveform model (control.model simd_classes: one motion a cycle, the R22 split) on direct wiring, so its time is an upper bound for a direct machine.

a hub per check and per data qubit, a contact trap on each of the 864 Tanner edges: no device makes the contacts shorter. 856.5 ms at one ion per transport instruction -- under the random graphs (1,036 and 1,126 ms), over the torus (516.4). It runs under the one-waveform model (control.model simd_classes: one motion a cycle, the R22 split) on direct wiring, so its time is an upper bound for a direct machine. Before the R22 split it was 79.5 ms.

random AND local, the way a die is: the worst of both. Locality without structure does not route.