  Efficiently estimating fermionic Hamiltonian expectation values is vital for
simulating various physical systems. Classical shadow (CS) algorithms offer a
solution by reducing the number of quantum state copies needed, but noise in
quantum devices poses challenges. We propose an error-mitigated CS algorithm
assuming gate-independent, time-stationary, and Markovian (GTM) noise. For
$n$-qubit systems, our algorithm, which employs the easily prepared initial
state $|0^n\rangle\!\langle 0^n|$ assumed to be noiseless, efficiently
estimates $k$-RDMs with $\widetilde{\mathcal O}(kn^k)$ state copies and
$\widetilde{\mathcal O}(\sqrt{n})$ calibration measurements for GTM noise with
constant fidelities. We show that our algorithm is robust against noise types
like depolarizing, damping, and $X$-rotation noise with constant strengths,
showing scalings akin to prior CS algorithms for fermions but with better noise
resilience. Numerical simulations confirm our algorithm's efficacy in noisy
settings, suggesting its viability for near-term quantum devices.
