Nuclear scattering phase shifts with factorized geometric-time RODEO on a quantum processor

Abstract

We reconstruct elastic $s$-wave neutron-proton ($np$) phase shifts from trapped spectra measured on IBM Aachen using a compressed RODEO circuit. For a schematic square-well interaction represented by classically constructed four-dimensional effective Hamiltonians, four positive-energy levels at five trap strengths supply twenty inputs to classical modified effective range expansion (MERE) extrapolation to free space. The six-cycle factorized geometric-time RODEO implementation (FG-R6) combines ancilla reuse, exact query-phase separation, post-compilation binding, and six numerically optimized geometric evolution times. Numerical cycle-count tests support this choice within the adopted local spectral tolerances. At the same three-qubit width and equal shot budgets, FG-R6 reduces median compiled depth and two-qubit-gate count by 33.1% and 37.2% relative to ten-cycle dynamic direct RODEO (direct R10), increases the median fitted amplitude, and lowers median finite-shot energy uncertainty from 0.610 to 0.534 keV. For this dataset's primary fit on the 0.1-30.0 MeV grid, the maximum central phase-shift deviation from exact-energy MERE decreases from $0.842^\circ$ to $0.163^\circ$, despite a larger root-mean-square (RMS) trapped-energy deviation. The full-grid gain arises mainly in the low-energy extrapolation region; direct R10 has slightly smaller residuals relative to the same reference on the 10.0-30.0 MeV common energy-interpolation subset. The FG-R6 central curve differs from the analytical square-well solution by at most $0.156^\circ$. Fit-form sensitivity remains appreciable and is assessed separately from finite-shot uncertainty. This reduced-space benchmark connects RODEO circuit compression to nuclear continuum observables and shows why circuit performance must be assessed through the scattering reconstruction and its energy range, not spectral RMS errors alone.