Symmetry-Adapted Quantum Circuits for Many-Body Physics and Modal Sensing

We present a symmetry-adapted quantum framework that targets correlated many-body phenomena with shallow, measurement-efficient circuits and a clear path from chemistry to wave-scattering applications. The key ingredient is a Schur/Clebsch–Gordan (CG) basis change that recouples local spins/orbitals into global (J,M) sectors. This change of basis groups states into well-defined symmetry sectors, where selection rules suppress many off-diagonal couplings. Our workflow begins from a localized reference state and applies symmetry-preserving updates that remain inside the chosen sectors. Energetic diagnostics are obtained from commuting observables requires only Z  and ZZ expectations, and accuracy improves primarily by increasing state quality rather than by inflating measurement budgets. Resource estimates for the qubit count scales as N_q= 2N_atoms(L_max+1)²  with Toffoli complexity Ο(N_atoms(L_max+1)⁴) per step (L_max:maximum multipole order). Although motivated by electronic structure, the same symmetry toolkit extends naturally to wave and field problems governed by the Helmholtz equation, where illumination and scattering decompose into spherical-harmonic channels. Accuracy is controlled by a multipole cutoff, which is only dependent on aperture size and wavenumber, so resources scale exactly as in the electronic case while symmetry keeps depth low. Compared to an N-sensor by M-pixel near-field array needing Ο((NsensorM)²) cross-coupling calibration with classical method, our modal approach uses only Ο((L_max+1)²)  calibration parameters. In summary, we present a “Schur-first” strategy for chemistry and sensing: exploit angular-momentum structure to cut circuit depth, measurements, and classical post-processing, while retaining systematic control via max multipole expansion factor and block-diagonal resource accounting.