Resource-Optimized Grouping Shadow for Efficient Energy Estimation

Quantum 9, 1694 (2025).

https://doi.org/10.22331/q-2025-04-07-1694

The accurate and efficient energy estimation of quantum Hamiltonians consisting of Pauli observables is an essential task in modern quantum computing. We introduce a Resource-Optimized Grouping Shadow (ROGS) algorithm, which optimally allocates measurement resources by minimizing the estimation error bound through a novel overlapped grouping strategy and convex optimization. Our numerical experiments demonstrate that ROGS requires significantly fewer unique quantum circuits for accurate estimation accuracy compared to existing methods given a fixed measurement budget, addressing a major cost factor for compiling and executing circuits on quantum computers.