  Linear-optical systems can implement photonic quantum walks that simulate
systems with nontrivial topological properties. Here, such photonic walks are
used to jointly entangle polarization and winding number. This joint
entanglement allows information processing tasks to be performed with
interactive access to a wide variety of topological features. Topological
considerations are used to suppress errors, with polarization allowing easy
measurement and manipulation of qubits. We provide three examples of this
approach: production of two-photon systems with entangled winding number
(including topological analogs of Bell states), a topologically error-protected
optical memory register, and production of entangled topologicallyprotected
boundary states. In particular it is shown that a pair of quantum memory
registers, entangled in polarization and winding number, with
topologically-assisted error suppression can be made with qubits stored in
superpositions of winding numbers; as a result, information processing with
winding number-based qubits is a viable possibility.
