  Two-qubit systems typically employ 36 projective measurements for
high-fidelity tomographic estimation. The overcomplete nature of the 36
measurements suggests possible robustness of the estimation procedure to
missing measurements. In this paper, we explore the resilience of
machine-learning-based quantum state estimation techniques to missing
measurements by creating a pipeline of stacked machine learning models for
imputation, denoising, and state estimation. When applied to simulated
noiseless and noisy projective measurement data for both pure and mixed states,
we demonstrate quantum state estimation from partial measurement results that
outperforms previously developed machine-learning-based methods in
reconstruction fidelity and several conventional methods in terms of resource
scaling. Notably, our developed model does not require training a separate
model for each missing measurement, making it potentially applicable to quantum
state estimation of large quantum systems where preprocessing is
computationally infeasible due to the exponential scaling of quantum system
dimension.
