Nano-scale and multi-scale computational architectures using spin waves as a physical mechanism for device interconnection are provided. Solid-state spin-wave computing devices using nano-scale and multi-scale computational architectures comprised of a plurality of inputs and a plurality of outputs are described where such devices are configured to simultaneously transmit data elements from the inputs to the outputs by using spin-waves of differing frequencies. These devices include but are not limited to a spin-wave crossbar, a spin-wave reconfigurable mesh, a spin-wave fully-interconnected cluster, a hierarchical multi-scale spin-wave crossbar, a hierarchical multi-scale spin-wave reconfigurable mesh and a hierarchical multi-scale spin-wave fully-interconnected cluster.