  Constructing an integrated large-scale qubit system of realistic size
requires addressing the challenge of physical crowding among qubits. This
constraint poses an issue of coarse-grained (CG) measurement, wherein
information from the multi-qubit system is collectively gathered. In this work,
we introduce a novel approach to reconstruct the target density matrix from a
comprehensive set of Positive Operator-Valued Measures (POVM) using a
Parameterized Quantum Circuit (PQC) under the constraint of CG measurement. We
improve the robustness and stability of CG quantum state tomography (QST) by
optimizing the POVM set to achieve a generalized symmetric informationally
complete (GSIC) POVM through maximization of the von Neumann entropy. This
optimized construction of CG-POVMs is scalable to an N-qubit system. We further
discuss a more efficient construction of N-qubit CG-QST without exponential
increases in two-qubit gates or circuit depth per measurement. Our scheme
offers a viable pathway towards a detector-efficient large-scale solid-state
embedded qubit platform by reconstructing crucial quantum information from
collective measurements.
