A Symmetry-Enabled Direct Quantum Protocol for Many-Body Green's Functions

We present a symmetry-enabled direct quantum protocol for computing many-body Green's functions, a central tool for studying strongly correlated quantum systems. Our protocol relies only on native time evolution and straightforward measurements available on current hardware platforms. By exploiting parity symmetry -- satisfied by a broad class of Hamiltonians in condensed matter physics and quantum chemistry, including the Fermi--Hubbard and Heisenberg models -- we introduce a tailored quench spectroscopy scheme that recovers both the real and imaginary parts of two-point time correlators, from which Green's functions can be reconstructed via efficient classical signal processing. We further develop a tailored symmetric quantum Gibbs sampler that prepares parity-resolved (symmetric and antisymmetric) thermal states, enabling finite-temperature extensions within the same framework. Finally, we show that the same symmetry-based measurement primitive extends naturally to out-of-time-ordered correlators (OTOCs). Our results provide a practical route to estimating symmetry-resolved dynamical correlators on near-term and early fault-tolerant quantum hardware.