Speaker
Description
Finding an algorithm to prepare a desired quantum state of a correlated ab initio electronic system on a quantum computer is not the end of the story – we still need to extract out arbitrary properties from this state. This is where a significant and unsolved ‘variance problem’ emerges for arbitrary observables, across both near-term and fault-tolerant algorithms in this field, due to the large number of shots required to reach a statistical uncertainty suitable for chemical and materials science applications. We combine classical heuristic methods with partial shadow tomography to enable an efficient protocol to dramatically reduce this variance and extract information for ab initio systems. We propose using a correlation energy functional and sampling excitation amplitudes to demonstrate an almost two order of magnitude reduction in required number of shots for a given statistical error in the energy estimate, as well as observing a linear scaling to accessible system sizes. Furthermore, we find a high-degree of noise resilience of these estimators on real quantum devices, with up to an order of magnitude increase in the tolerated noise compared to traditional techniques. While these approaches are expected to break down asymptotically, we find strong evidence that these large system arguments do not prevent algorithmic advantage from these simple protocols in many systems of interest. We further extend this to consider the extraction of beyond-energetic properties by mapping to a coupled cluster surrogate model, as well as a natural combination within a quantum embedding framework. This embedding framework avoids the unstable self-consistent requirements of previous quantum embedding approaches interfaced with quantum solvers, enabling application to realistic correlated materials science, where we demonstrate the volume-dependence of the spin gap of Nickel Oxide.
Ref: Lenihan et. al, ArXiv:2506.15438 (2025)
