If you don't feel like reading, you can take a look at the poster or even just the lights of NY ✨

@albertobaiardi.bsky.social, Max Rossmannek, Almudena Carrera Vazquez, @qfta.bsky.social, Stefano Mensa, PhD MBCS, Edoardo Altamura PhD MInstP, Ali Alavi, Mario Motta, @jrobledomoreno.bsky.social, William Kirby, @kunalq.bsky.social, @antoniomezzacapo.bsky.social, Ivano Tavernelli

This work is the result of the collective efforts of an amazing team: a heartfelt thank you goes to all my collaborators, from whom I have learned a lot and who have made this project truly fun to work on!

When combined, these elements enable a rigorous approach to estimating the ground state energy for quantum chemistry Hamiltonians on today's quantum computers. 💫

The advantages of SqDRIFT are a significantly reduced circuit depth and the ability to systematically build progressively better solutions. 🛠️

In this work we introduce SqDRIFT, a sample-based quantum diagonalization algorithm that combines sample-based Krylov quantum diagonalization with qDRIFT, producing randomized time-evolution circuits and a quantum/classical workflow with provable convergence guarantees. 🎲

🙏 Huge thanks to my co-authors @qfta.bsky.social, Ivano Tavernelli and @gppcarleo.bsky.social for their feedback and insights!

🔬 Why care? RGFs connect quantum theory to experimental probes such as neutron scattering, ARPES and pump–probe spectroscopy. Ancilla‑free, shot‑efficient extraction means those comparisons can now be attempted on superconducting QPUs with today’s compilers and high‑throughput sampling.

💫 A 4‑site Hubbard model keeps its frequency peaks even with a realistic two‑qubit depolarizing channel. From the resulting time traces we fit the full space-time Green’s tensor, Fourier‑transform it, and recover dynamical structure factors that closely match exact diagonalization.

🧪 We benchmark our methods on both spin- and fermionic Hamiltonians. On a 10‑qubit Heisenberg ring, SCP converges to the exact Trotter dynamics with the expected 1 / √shots law and shows no degradation as the chain grows.

🌊 Both embed the external force directly into the circuit using what we call circuit perturbations, thus sidestepping Hadamard tests and keeping the hardware footprint exactly equal to a vanilla simulation - same qubits, same connectivity.

🔍 We first show a clean analytical bridge between the parameter‑shift rule and the linear‑response commutator and then introduce two complementary implementations: Local Circuit Perturbation (LCP) and its shot‑savvy sibling, Simultaneous Circuit Perturbation (SCP).