Graph-Theoretic Scaling and Fault-Tolerant Resource Trade-offs of a Deterministic Modular Qubit Interconnect: A Black-Box Study with Local, Expander, and Edge-Budget-Matched Controls

Deterministic, modular qubit-interconnect topologies are attractive forfault-tolerant quantum computing (FTQC) because they may offer structuredlong-range connectivity without the geometric disorder of an unconstrainedrandom graph. We study one such topology (FPN-Hub; pending patentPCT/IB2026/053138) with an IP-preserving black-box methodology: every analysisstarts from an exported coupling map, and no construction rule is used ordisclosed. The central controlled result is a trade-off measured against exactly matchedrandomization. Across 20 rewires preserving the complete per-vertex degreesequence and the edge budget at N=512, FPN-Hub trades higher communicationcost (1.70x mean path length, 1.78x scheduled corridor layers) forlower geometric interconnect complexity. Evaluated under three independentplacement methods with exactly counted crossings, FPN-Hub uses about 27% lesstotal wire and about 2.8x fewer crossings than these matched controls, anddoes so in every placement run. A deterministic circulantsmall-world control with the same degree sequence and edge budget is weaker thanFPN-Hub on both axes, so the result is not a simple random-versus-deterministicdichotomy. Against a random 4-regular expander (RR4)--a deliberately strongcommunication baseline carrying 12.1% more edges--FPN-Hub loses about2x on certified communication while using 30--45% less wire andabout 2.5x fewer crossings under non-overlapping placement. An executedN=4096, 64-factory corridor schedule favours FPN-Hub over a local torus by1.57--2.01x across four workload seeds; under the point surface-codecalibration only, the corresponding point-model space--time-volume ratios equalthe executed layer ratios, while the absolute code distance remainsmodel-sensitive. Over N=64--4096, mean logical distance grows log-like whereas a 2D torusfollows sqrt(N); predictions frozen at N<=1024 gave held-out errors of-4.2% and -6.0%, the latter a formal miss of the predeclared +/-5%interval on the favourable side. A harmonized, fixed-frame population search(240 deduplicated graphs per control per size) shows that FPN-Hub is not astrict low-dimensional optimum: matched alternatives beat it on distance andwire together, and--under a pre-specified, out-of-sample-confirmed rule--onscheduled layers as well, at N<=2048. Such dominators are common at N=512,rare at N=1024--2048 with frame-dependent counts, and absent at N=4096 inthree of three independently frozen frames (1440 sampled graphs). FPN-Hub is therefore not a global metric optimum, but occupies a reproducible,baseline-dependent multidimensional trade-off across communication, wiring,and scheduling. This is an interconnect evaluation, not afull circuit-level FTQC demonstration.