Benchmarking a randomized quantum algorithm for estimating expectation values of molecular observables

Randomized quantum algorithms for the estimation of expectation values of molecular observables offer a promising route to early fault-tolerant quantum advantage by trading circuit depth for an increased number of samples. However, this begs the question whether the resulting measurement overhead remains feasible for industrially relevant molecular systems. In this work, we benchmark the randomized sampling algorithm of Wang et al. [1] through numerical simulations on a hydrogen molecule and resource estimates for various active spaces of the cytochrome P450, an industry-relevant system in the pharmaceutical industry. Our numerical simulations reveal that the analytical error bounds significantly overestimate the actual sampling error, whereas the analytical bound on the required imaginary evolution time is comparatively tight, exceeding a direct DMRG estimate by roughly 44% for the active space where the comparison is feasible. The measurement overhead nevertheless remains prohibitively high: even for the smallest active spaces, the expectation-value estimation alone requires around 1010 samples, scaling to beyond 1015 for the largest active spaces considered. These results suggest that substantial improvements in measurement strategies or algorithmic scaling are necessary before randomized early-fault-tolerant algorithms become competitive for industrial quantum chemistry applications.