  Photonic graph states, quantum light states where multiple photons are
mutually entangled, are key resources for optical quantum technologies. They
are notably at the core of error-corrected measurement-based optical quantum
computing and all-optical quantum networks. In the discrete variable framework,
these applications require high efficiency generation of cluster-states whose
nodes are indistinguishable photons. Such photonic cluster states can be
generated with heralded single photon sources and probabilistic quantum gates,
yet with challenging efficiency and scalability. Spin-photon entanglement has
been proposed to deterministically generate linear cluster states. First
demonstrations have been obtained with semiconductor spins achieving high
photon indistinguishablity, and most recently with atomic systems at high
collection efficiency and record length. Here we report on the efficient
generation of three partite cluster states made of one semiconductor spin and
two indistinguishable photons. We harness a semiconductor quantum dot inserted
in an optical cavity for efficient photon collection and electrically
controlled for high indistinguishability. We demonstrate two and three particle
entanglement with fidelities of 80 % and 63 % respectively, with photon
indistinguishability of 88%. The spin-photon and spin-photon-photon
entanglement rates exceed by three and two orders of magnitude respectively the
previous state of the art. Our system and experimental scheme, a monolithic
solid-state device controlled with a resource efficient simple experimental
configuration, are very promising for future scalable applications.
