Changhao Yi

We present a symmetry-enabled direct quantum algorithm 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 analysis. We further develop a tailored quantum Gibbs sampler that prepares parity-resolved (symmetric and antisymmetric) thermal states, enabling finite-temperature applications within the same framework. Finally, we show that the same symmetry-based measurement primitive extends naturally to out-of-time-ordered correlators (OTOCs), providing a practical path toward probing finite-temperature dynamics of strongly correlated quantum systems on near-term and early fault-tolerant quantum hardware.

We introduce a Pauli-measurement-based algorithm to certify the Schmidt number of $n$-qubit pure states. Our protocol achieves an average-case sample complexity of $\caO(\mathrm{poly}(n)\chi^2)$, a substantial improvement over the $\caO(2^n \chi)$ worst-case bound. By utilizing local pseudorandom unitaries, we ensure the worst case can be transformed into the average-case with high probability. This work establishes a scalable approach to high-dimensional entanglement certification and introduces a proof framework for random Pauli sampling.