  The reduced density matrix (RDM) is crucial in quantum many-body systems for
understanding physical properties, including all local physical quantity
information. This study aims to minimize various error constraints that causes
challenges in higher-order RDMs estimation in quantum computing. We identify
the optimal balance between statistical and systematic errors in higher-order
RDM estimation in particular when cumulant expansion is used to suppress the
sample complexity. Furthermore, we show via numerical demonstration of quantum
subspace methods for one and two dimensional Fermi Hubbard model that, biased
yet efficient estimations better suppress hardware noise in excited state
calculations. Our work paves a path towards cost-efficient practical quantum
computing that in reality is constrained by multiple aspects of errors.
