  Multi-mode optical interferometers represent the most viable platforms for
the successful implementation of several quantum information schemes that take
advantage of optical processing. Examples range from quantum communication,
sensing and computation, including optical neural networks, optical reservoir
computing or simulation of complex physical systems. The realization of such
routines requires high levels of control and tunability of the parameters that
define the operations carried out by the device. This requirement becomes
particularly crucial in light of recent technological improvements in
integrated photonic technologies, which enable the implementation of
progressively larger circuits embedding a considerable amount of tunable
parameters. In this work, we formulate efficient procedures for the
characterization of optical circuits in the presence of imperfections that
typically occur in physical experiments, such as unbalanced losses and phase
instabilities in the input and output collection stages. The algorithm aims at
reconstructing the transfer matrix that represents the optical interferometer
without making any strong assumptions about its internal structure and
encoding. We show the viability of this approach in an experimentally relevant
scenario, defined by a tunable integrated photonic circuit, and we demonstrate
the effectiveness and robustness of our method. Our findings can find
application in a wide range of optical setups, based both on bulk and
integrated configurations.
