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

Quantum simulation of discrete-time Hamiltonians using directionally unbiased linear optical multiports