Resonant Touchdown of Fisher Zeros and Super-Kink Dynamical Quantum Phase Transitions via Lagrangian-Engineered Riemann Potentials

Dynamical quantum phase transitions (DQPT) provide a non-equilibrium framework for probing quantum criticality, where the non-analytic kinks in the Loschmidt echo rate function λ(t) signal the crossing of Fisher zeros across the real-time axis. In disordered many-body localized (MBL) systems, spatial inhomogeneity typically induces multi-frequency dephasing that melts these non-analytic signatures into diffuse crossovers. Here, we demonstrate that deterministic on-site potential landscapes derived from the unfolded non-trivial zeros of the Riemann zeta function prevent the thermalized melting of DQPT signatures through Gaussian Unitary Ensemble (GUE) level repulsion. While strong unengineered Riemann potentials (W = 2.0J) induce multi-frequency spectral beating resulting in dense multi-kink profiles, we formulate an augmented Lagrangian variational framework that directly targets the trade-off between isochronous periodicity and singular non-analyticity. By minimizing a multi-objective functional encompassing Fisher zero proximity, high-frequency beating penalties, and GUE level-repulsion kernels, the optimization converges to a dual-champion configuration h*. Under quantum quench dynamics of a one-dimensional transverse-field Ising chain (L=10, 1024-dimensional Hilbert space), this engineered landscape drives the Loschmidt echo down to the numerical machine-precision floor (L_min = 2.03e-13), generating an ultra-sharp super-kink with peak amplitude λ_max = 2.9219, nearly three times the baseline transition height. These results reveal a direct route for engineering singular non-equilibrium criticality in digital quantum processors.