Cerezo and Colleagues Develop Fermionic Shadow Protocol for Estimating Slater Determinant Overlaps

Researchers at Los Alamos National Laboratory, led by Maxwell West, have unveiled a new methodology for learning expectation values of particle-preserving operators within fermionic states utilising classical shadows. This advancement addresses a critical challenge in quantum simulation, namely the computational cost associated with accurately modelling many-body fermionic systems. The team's approach achieves an improved worst-case bound of $\mathcal{O}(η\logη)$ for estimating overlaps with Slater determinant states, a significant reduction from the previously known bound of $\mathcal{O}(\sqrt n \log n)$. This result is particularly noteworthy as it yields a sample cost independent of the number of modes, 'n', representing a substantial step towards scalable…