  We use a constrained convex optimization (CCO) method to experimentally
characterize arbitrary quantum states and unknown quantum processes on a
two-qubit NMR quantum information processor. Standard protocols for quantum
state and quantum process tomography are based on linear inversion, which often
result in an unphysical density matrix and hence an invalid process matrix. The
CCO method on the other hand, produces physically valid density matrices and
process matrices, with significantly improved fidelity as compared to the
standard methods. The constrainedoptimization problem is solved with the help
of a semi-definite programming (SDP) protocol. We use the CCO method to
estimate the Kraus operators and characterize gates in the presence of errors
due to decoherence. We then assume Markovian system dynamics and use a Lindblad
master equation in conjunction with the CCO method to completely characterize
the noise processes present in the NMR qubits.
