  Quantum state tomography is an integral part of quantum computation and
offers the starting point for the validation of various quantum devices. One of
the central tasks in the field of state tomography is to reconstruct with high
fidelity, the quantum states of a quantum system. From an experiment on a real
quantum device, one can obtain the mean measurement values of different
operators. With such a data as input, in this report we employ the maximal
entropy formalism to construct the least biased mixed quantum state that is
consistent with the given set of expectation values. Even though in principle,
the reported formalism is quite general and should work for an arbitrary set of
observables, in practice we shall demonstrate the efficacy of the algorithm on
an informationally complete (IC) set of Hermitian operators. Such a set
possesses the advantage of uniquely specifying a single quantum state from
which the experimental measurements have been sampled and hence renders the
rare opportunity to not only construct a least-biased quantum state but even
replicate the exact state prepared experimentally within a preset tolerance.
The primary workhorse of the algorithm is re-constructing an energy function
which we designate as the effective Hamiltonian of the system, and
parameterizing it with Lagrange multipliers, according to the formalism of
maximal entropy. These parameters are thereafter optimized variationally so
that the reconstructed quantum state of the system converges to the true
quantum state within an error threshold. To this end, we employ a parameterized
quantum circuit and a hybrid quantum-classical variational algorithm to obtain
such a target state making our recipe easily implementable on a near-term
quantum device.
