  We introduce "holographic shadows", a new class of randomized measurement
schemes for classical shadow tomography that achieves the optimal scaling of
sample complexity for learning geometrically local Pauli operators at any
length scale, without the need for fine-tuning protocol parameters such as
circuit depth or measurement rate. Our approach utilizes hierarchical quantum
circuits, such as tree quantum circuits or holographic random tensor networks.
Measurements within the holographic bulk correspond to measurements at
different scales on the boundary (i.e. the physical system of interests),
facilitating efficient quantum state estimation across observable at all
scales. Considering the task of estimating string-like Pauli observables
supported on contiguous intervals of $k$ sites in a 1D system, our method
achieves an optimal sample complexity scaling of $\sim d^k\mathrm{poly}(k)$,
with $d$ the local Hilbert space dimension. We present a holographic minimal
cut framework to demonstrate the universality of this sample complexity scaling
and validate it with numerical simulations, illustrating the efficacy of
holographic shadows in enhancing quantum state learning capabilities.
