Quantum switching networks are derived from conventional switching networks by replacing the classical switches by quantum switches. We give the quantum circuit design and routing of an n \times m network, called a quantum concentrator that can direct quantum bit packets in arbitrary quantum states from any of its k inputs to some of its k outputs, where 1 \le k \le m \le n. Our designs are based on sparse crossbars which are rectangular grids of 2 \times 2 crosspoints. Sparse crossbar concentrator structures with theoretically minimum crosspoint complexities for any values of n and m are well known but no self-routing algorithms have been reported for such concentrators. We transform two such families of optimal concentrators, called fat-slim and banded sparse crossbars into quantum networks and provide self-routing algorithms for these families of concentrators. In this process, we extend the notion of packet concentration to a quantum network and design self-routing quantum crosspoints from quantum gates. We address issues critical to quantum operation like reversibility and localized self-routing and give a rigorous proof that quantum fat-slim and banded sparse crossbar concentrators are self-routable. The self-routing algorithms described in the paper can be used for both quantum and classical sparse crossbar concentrators by the linearity property of all quantum systems.