Polynomial Quantum Recurrent Channels for Matrix Inverse Actions: Deferred-Reset Dynamics and Chebyshev Filtering

arXiv:2611.13778v1 Announce Type: new Abstract: We develop completely positive, trace-preserving polynomial recurrent channels for quantum solution-state preparation and derive fixed-point and time-varying tracking bounds. Across 2,880 synthetic configurations, resident Chebyshev recurrence improves accuracy-passing snapshot counts in 608 cases, ties in 2,271, and loses in one. A separate 360-scenario cost study shows that fresh recurrence is cheaper in all 184 jointly feasible scenarios (median resident-to-fresh cost ratio: 3.12), while resident recurrence uniquely satisfies accuracy requirements in 74 cases. At a logical noise rate of $10^-4$, neither recurrent method qualifies.