My end goal is to recover the quantum state in its computational basis or reduced density matrix of a high number qubit circuit in a real QPU. Taking into account that the number of qubits will be high (+16 or +32 qubits) getting the density matrix as it is done in the common quantum state tomography algorithms is unfeasible.
My idea is to try tomography with Pauli basis measurements to get the individual reduced density matrix of each qubit, but due to the high number of qubits, the number of measurements required will be huge too.
I was wondering if there is a feasible way to get this or in case there isn't which option would be the least unfeasible to continue researching on it. Thanks in advance.
Pd: the circuit is a 16 or 32 qubit circuit with some hadamard, cnot and u(rotation) gates.