  Recently, a generalization of the standard optical multiport was proposed
[Phys. Rev. A 93, 043845 (2016)]. These directionally unbiased multiports allow
photons to reverse direction and exit backwards from the input port, providing
a realistic linear optical scattering vertex for quantum walks on arbitrary
graph structures. Here, it is shown that arrays of these multiports allow the
simulation of a range of discrete-time Hamiltonian systems. Examples are
described, including a case where both spatial and internal degrees of freedom
are simulated. Because input ports also double as output ports, there is
substantial savings of resources compared to feed-forward networks carrying out
the same functions. The simulation is implemented in a scalable manner using
only linear optics, and can be generalized to higher dimensional systems in a
straightforward fashion, thus offering a concrete experimentally achievable
implementation of graphical models of discrete-time quantum systems.
