  This thesis actively focuses on designing, analyzing, and experimentally
implementing various QST and QPT protocols using an NMR ensemble quantum
processor and superconducting qubit-based IBM cloud quantum processor. Part of
the thesis also includes a study of duality quantum simulation algorithms and
Sz-Nagy's dilation algorithm on NMR where several 2-qubit non-unitary quantum
channels were simulated using only a single ancilla qubit. The work carried out
in the thesis mainly addresses several important issues in experimental QST and
QPT which include: i) dealing with invalid experimental density (process)
matrices using constraint convex optimization (CCO) method, ii) scalable QST
and QPT using incomplete measurements via compressed sensing (CS) algorithm and
artificial neural network (ANN) technique, iii) selective and direct
measurement of unknown quantum states and processes using the concept of
quantum 2-design states and weak measurement (WM) approach and iv) quantum
simulation and characterization of open quantum dynamics using the dilation
technique.
