  Entanglement--one of the most delicate phenomena in nature--is an essential
resource for quantum information applications. Large entangled cluster states
have been predicted to enable universal quantum computation, with the required
single- qubit measurements readily implemented with photons. Useful large-scale
systems must generate and control qubit entanglement on-chip, where quantum
information is naturally encoded in photon path. Here we report a silicon
photonic chip which integrates resonant-enhanced sources, filters, and
reconfigurable optics to generate a path-entangled two-qubit state--the
smallest non-trivial cluster state--and analyse its entanglement. We show that
ring-resonator-based spontaneous four-wave mixing sources can be made highly
indistinguishable, despite their nonlinear dynamics, and the first evidence
that their frequency correlations are small, as predicted. We use quantum state
tomography, and the strict Bell-CHSH inequality to quantify entanglement in the
device, confirming its high performance. This work integrates essential
components for building devices and systems to harness quantum entanglement on
the large scale.
