Rational quantum spectral filtering by repeat-until-success protocol

arXiv:2611.13154v1 Announce Type: new Abstract: We introduce a finite-memory repeat-until-success (RUS) framework for implementing rational spectral filters on a quantum computer, extending spectral filtering beyond the polynomial transformations implemented by quantum signal processing (QSP) and quantum singular value transformation (QSVT). Our approach interleaves queries to a block encoding of a Hermitian operator $X$, whose spectrum lies in $[-1,1]$, and mid-circuit measurements that either accept, reject, or continue the computation without resetting the quantum state. Although the protocol may run for arbitrarily many rounds, its terminal statistics are determined by a finite-dimensional Lyapunov equation.