Measurement-efficient energy estimator for quantum chemistry of photodynamic materials

Abstract: Accurate modelling of chemical reaction rates requires precise correlated energy differences. Quantum computing offers a potential route to their determination, but extracting energies from quantum-prepared states can demand prohibitive sampling. We demonstrate measurement-efficient correlated energy estimation using an electronically challenging H$_2$DBB--Ru model derived from a Ru-functionalized hafnium metal-organic framework relevant to radiodynamic and photodynamic therapies. The mixed estimator combines a quantum-prepared target with sparse multiconfiguration references and recovers ground-state corrections using magnitude-only compute-uncompute measurements. Analytical variance estimates predict 1.6 mHa precision with a few hundred shots, about 100 times fewer than the single-determinant formulation and three orders of magnitude fewer than optimized Hamiltonian-term sampling. With approximate targets, it reaches comparable accuracy using simpler state preparation than direct expectation-value estimation. Emulator and trapped-ion experiments on Quantinuum Helios validate the approach up to (10,10), including a 50-qubit circuit combining AI-assisted state preparation with error detection, providing a measurement-efficient route to correlated energy differences for challenging chemical problems.