  All existing optical quantum walk approaches are based on the use of
beamsplitters and multiple paths to explore the multitude of unitary
transformations of quantum amplitudes in a Hilbert space. The beamsplitter is
naturally a directionally biased device: the photon cannot travel in reverse
direction. This causes rapid increases in optical hardware resources required
for complex quantum walk applications, since the number of options for the
walking particle grows with each step. Here we present the experimental
demonstration of a directionally-unbiased linear-optical multiport, which
allows reversibility of photon direction. An amplitude-controllable probability
distribution matrix for a unitary three-edge vertex is reconstructed with only
linear-optical devices. Such directionally-unbiased multiports allow direct
execution of quantum walks over a multitude of complex graphs and in tensor
networks. This approach would enable simulation of complex Hamiltonians of
physical systems and quantum walk applications in a more efficient and compact
setup, substantially reducing the required hardware resources.
