  Integrated optics is an engineering solution proposed for exquisite control
of photonic quantum information. Here we use silicon photonics and the linear
combination of quantum operators scheme to realise a fully programmable
two-qubit quantum processor. The device is fabricated with readily available
CMOS based processing and comprises four nonlinear photon-sources, four
filters, eighty-two beam splitters and fifty-eight individually addressable
phase shifters. To demonstrate performance, we programmed the device to
implement ninety-eight various two-qubit unitary operations (with average
quantum process fidelity of 93.2$\pm$4.5%), a two-qubit quantum approximate
optimization algorithm and efficient simulation of Szegedy directed quantum
walks. This fosters further use of the linear combination architecture with
silicon photonics for future photonic quantum processors.
