A one-dimensional circulating switch may be defined by connections between several switch modules and one or more temporal cyclic rotators. Where a switch module that is part of a first one-dimensional circulating switch is also connected one or more temporal cyclic rotators that define a second one-dimensional circulating switch, a two-dimensional circulating switch is formed. A two-dimensional circulating switch is flexible and may scale to capacities ranging from a few gigabits per second to multiple Petabits per second.