Software defined networking (SDN) is a model for network control, based on the idea that network traffic flow can be made programmable at scale, thus enabling new dynamic models for traffic management.
OpenFlow, an "open" protocol to control the traffic flows of multiple switches from a centralized controller, is an example of SDN. The OpenFlow initiative is led by the Open Networking Foundation and the ONF’s founding members are exclusively service providers including Yahoo, Google and Verizon. OpenFlow 1.1 specification is available, although networking vendors are currently using the 1.0 specification (find both specs here).
OpenStack, an open source software initiative for building clouds, has a network connectivity project named Quantum (see project page here). The Quantum project looks to provide "network connectivity as a service" between interface devices (e.g., vNICs) managed by other OpenStack services. Quantum was originally proposed in April 2011 and in less than six months the v1.0 API was made available; it is described as a “young project”, and documentation is a work-in-progress.
UPDATE: The OpenStack Quantum project has been renamed Neutron.
How does OpenFlow relate to Quantum?
Quantum is an application-level abstraction of networking that relies on plug-in implementations to map the abstraction(s) to reality. OpenFlow-based networking systems are one possible mechanism to be used by a plug-in to deliver a Quantum abstraction.
OpenFlow itself does not provide a network abstraction; that takes software that implements the protocol. Quantum itself does not talk to switches directly; that takes additional software (in the form of a plug-in). Those software components may be one and the same, or a Quantum plug-in might talk to OpenFlow-based controller software via an API (like the Open vSwitch API).
Footnotes: The comparison of OpenFlow to Quantum comes courtesy of James Urquhart’s CNET article, which he gave permission to curate here.