  We present a novel ground-state energy estimation algorithm that is robust
under global depolarizing error channels. Building upon the recently developed
Quantum Exponential Least Squares (QCELS) algorithm, our new approach
incorporates significant advancements to ensure robust estimation while
maintaining a polynomial cost in precision. By leveraging the spectral gap of
the Hamiltonian effectively, our algorithm overcomes limitations observed in
previous methods like quantum phase estimation (QPE) and robust phase
estimation (RPE). Going beyond global depolarizing error channels, our work
underscores the significance and practical advantages of utilizing randomized
compiling techniques to tailor quantum noise towards depolarizing error
channels. Our research demonstrates the feasibility of ground-state energy
estimation in the presence of depolarizing noise, offering potential
advancements in error correction and algorithmic-level error mitigation for
quantum algorithms.
