Convergence of reconstructed density matrix to a pure state using
  maximal entropy approach
Impressive progress has been made in the past decade in the study of
technological applications of varied types of quantum systems. With industry
giants like IBM laying down their roadmap for scalable quantum devices with
more than 1000-qubits by the end of 2023, efficient validation techniques are
also being developed for testing quantum processing on these devices. The
characterization of a quantum state is done by experimental measurements
through the process called quantum state tomography (QST) which scales
exponentially with the size of the system. However, QST performed using
incomplete measurements is aptly suited for characterizing these quantum
technologies especially with the current nature of noisy intermediate-scale
quantum (NISQ) devices where not all mean measurements are available with high
fidelity. We, hereby, propose an alternative approach to QST for the complete
reconstruction of the density matrix of a quantum system in a pure state for
any number of qubits by applying the maximal entropy formalism on the pairwise
combinations of the known mean measurements. This approach provides the best
estimate of the target state when we know the complete set of observables which
is the case of convergence of the reconstructed density matrix to a pure state.
Our goal is to provide a practical inference of a quantum system in a pure
state that can find its applications in the field of quantum error mitigation
on a real quantum computer that we intend to investigate further.
Rishabh Gupta Sabre Kais Raphael D. Levine