Dynamical spectral functions from bitstring-sampled quantum subspaces: entanglement, not one-body magic, tracks the sampling cost

Sample-based quantum diagonalization (SQD) and quantum-selected configuration interaction (QSCI) are the electronic-structure methods with most hardware traction, yet their canonical target - the ground-state energy - is where classical methods have caught up. We move the target to dynamics and the resource question. From one bitstring-sampling primitive - computational-basis measurements of a shallow real-time circuit, with no Hadamard or controlled unitaries - we reconstruct, from sampled subspaces, the single-particle spectral functions A\(omega\) and A\(k,omega\) and the neutral-sector dynamical structure factors S\(q,omega\) and S^zz\(q,omega\), each built classically in the Lehmann representation from its own subspace. The reconstruction matches exact diagonalization on Hubbard chains and, for A\(omega\), across nineteen molecules (FCI-verified to $