  The quantum computing paradigm in photonics currently relies on the
multi-port interference in linear optical devices, which is intrinsically based
on probabilistic measurements outcome and thus non-deterministic. Devising a
fully deterministic, universal, and practically achievable quantum computing
platform based on integrated photonic circuits is still an open challenge. Here
we propose to exploit weakly nonlinear photonic devices to implement
deterministic entangling quantum gates, following the definition of dual rail
photonic qubits. It is shown that a universal set of single- and two-qubit
gates can be designed by a suitable concatenation of few optical
interferometric elements, with optimal fidelities arbitrarily close to 100%
theoretically demonstrated through a bound constrained optimization algorithm.
The actual realization would require the concatenation of a few tens of
elementary operations, as well as on-chip optical nonlinearities that are
compatible with some of the existing quantum photonic platforms, as it is
finally discussed.
