Mitigating Macroscopic Decoupling in Quantum Neural Networks: Geometric Bounds of π and Open Dissipative Stabilizations

Abstract

We specify a design constraint for quantum neural networks (QNNs) that must operate next to a macroscopic control plane (hybrid training, satellite/telemetry loops, or a chaotic prior). Closed unitary evolution and the second law are treated as operationally incompatible demands on one undivided register: Schrödinger evolution preserves the von Neumann entropy of a pure state, while thermodynamic scrambling is statistical and open. Embedding scramble in a training loss, or copying control-plane statistics into core weights, returns the queried chaos rather than a coherent computation. The Hilbert space is split into a core register, a control-plane factor, and an interface. A Lindblad generator is supported so that (i) scramble unitaries act only on the control plane as a convex random-unitary channel, (ii) dissipators at the wall dump heat (Landauer), and (iii) write-back into the core Hamiltonian is identically zero. A monitor on the wall may report scrambling diagnostics (rate, scrambling time, phase drift toward pi) without updating core parameters. Protection against slow gravitational Lyapunov chaos is a timescale inequality and is not the operational problem. Protection against control-plane scramble is architectural. The register returns the statistics of the queried observable and does not inject an encoding the queried channel cannot support. Geometric pi-inversion, open-system dissipation, and driven subharmonic substrates are recast as containment of the control plane, not as native integration of macroscopic chaos into the QNN. This is a design paper. No measured coherence time, paramagnetic density, or out-of-time-order correlator is reported. No host-material synthesis is open.