  In recent years, there has been growing interest in using photonic technology
to perform the underlying linear algebra operations required by different
applications, including neuromorphic photonics, quantum computing and microwave
processing, mainly aiming at taking advantage of the silicon photonics' (SiPho)
credentials to support high-speed and energy-efficient operations. Mapping,
however, a targeted matrix with absolute accuracy into the optical domain
remains a huge challenge in linear optics, since state-of-the-art linear
optical circuit architectures are highly sensitive to fabrication
imperfections. This leads to reduced fidelity metrics that degrade faster as
the insertion losses of the constituent optical matrix node or the matrix
dimensions increase. In this work, we present for the first time a novel
coherent SiPho crossbar (Xbar) that can support on-chip fidelity restoration
while implementing linear algebra operations, realizing the first experimental
demonstration of perfect on-chip arbitrary linear optical transformations. We
demonstrate the experimental implementation of 10000 arbitrary linear
transformations in the photonic domain achieving a record high fidelity of
99.997%+-0.002, limited mainly by the statistical error enforced by the
measurement equipment. Our work represents the first integrated universal
linear optical circuit that provides almost unity and loss-independent fidelity
in the realization of arbitrary matrices, opening new avenues for exploring the
use of light in resolving universal computational tasks.
