We prove inference-time quantum coordination advantages for specified AI state-tracking tasks. A solver compresses semantic history into a future-accessible boundary state and later answers a query. We count communication $B$, persistent instance-dependent memory $M$, and local work $D$; classical recurrence, caches, tools, and recomputation are allowed and charged. The central result is a boundary-preserving semantic-compilation theorem. It maps a finite one-way, streaming, or adaptive causal task into a semantic AI interface while preserving event order and access to past input. Classical boundary-state lower bounds and quantum-memory upper bounds transfer up to explicit compiler overhead, independently of the finite-precision recurrent architecture. Two applications have classical semantics. Matched-entity synopsis QA inherits the hidden-matching separation between $O(\log N)$ qubits and $Ω(\sqrt{N})$ classical boundary bits. Continual requirements auditing inherits a Max-$k$SAT streaming separation: a recurrent solver uses $O(\log^5 n\log(1/δ))$ qubits and polylogarithmic classical workspace to obtain a $0.7172$-approximation, whereas every classical one-pass finite-information solver attaining that ratio requires $Ω(\sqrt{n})$ coordination width. As a quantum-native compiler test, a stabilizer latent-state dialogue uses $n$ qubits, while every exact finite-state classical causal online realization satisfies $B+M \ge \frac{1}{2}n^2+(\frac{3}{2}-\log_2 3)n+O(1)$. The source protocols, streaming algorithms, and stabilizer witness are imported; the new result is their architecture-independent semantic transfer. These are memory and coordination separations, not runtime or empirical advantages for present-day language models. The stabilizer result assumes exact simulation and ideal noiseless quantum memory.
QAOA training repeatedly queries an objective and all shared gradients, making exact evaluation a feasibility bottleneck even when QUBO terms have bounded causal cones. Building on established causal-cone restriction and adjoint differentiation, LC-Implicit-QAOA profiles cone structure and induced-edge counts before local-amplitude and named-workspace allocation, then jointly selects equal-size microbatches and checkpoint schedules under a named active-evaluator workspace budget. "Implicit" means omitting both global state and global cost table, not implicit differentiation; infeasible requests are rejected before those allocations. An independently implemented complex128/float64 dense adjoint agrees with LC over 1,800 graph-angle comparisons, with a worst relative gradient error of 1.56 x 10^-13. LC completes all 104 target requests in a p=2 bounded-cone grid; under a prespecified n <= 24 validation cap, the matched state-plus-cost reference is executed for 28 requests and deliberately not run on 76. Across 80 budgeted requests, measured allocated evaluator memory stays within budget, reaching at most 0.797 of it. On 3-regular n=512, p=2, the adjoint reaches the same finite-budget endpoint in 101 objective-equivalent calls and 189 s, versus 909 calls and 1,565 s for central differences. LC targets fixed-depth one- and two-local diagonal QUBO costs with a transverse-field mixer; it provides neither global states, sampling, nor a hardware-independent fastest-backend rule.