abstract: Linear optical networks, which comprise a large number of optical modes have been investigated intensively over the last two decades in various theoretical proposals. Most recently their relevance for studies of photonic quantum walk systems has attracted attention, because they can be considered as a standard model to describe the dynamics of quantum particles in a discretized environment and serve as a test bed for quantum algorithms. However their experimental realization requires setups with increasing complexity in terms of number of modes and control of the system parameters.
We employ time-multiplexing using pulsed light in combination with a specific fiber loop geometry to demonstrate a fully coherent photonic quantum walk over 28 steps, corresponding to a network of over four hundred beam splitters. By introducing a fast optical modulator we can precisely control the dynamics of the photonic walk and study influences of noise and decoherence. We expand our setup to realize quantum walks on 2D lattices by a sophisticated combination of polarization and spatial degrees of freedom. In this way we are able to create a dynamic 4D quantum coin, which can be controlled by our fast optical modulator. The resulting quantum walk on the 2D lattice over up to 11 steps can then be used to simulate other quantum systems like two interacting particles walking on a line. The full dynamic coin control makes it even possible to influence the range and quality of the interaction.