Captured weight and boundary leakage bound the error of sample-based spectral functions

Sample-based quantum diagonalization builds a subspace from a device's measured bitstrings. From one protocol -- computational-basis samples of a real-time evolved probe, no Hadamard test -- we reconstruct the single-particle $A(ω)$ and $A(k,ω)$ of the 1D Hubbard model on that subspace. We prove tha