Quantum Coordination Advantages in AI State-Tracking Tasks: Semantic Compilation and Latent Memory

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-kSAT 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.