  Integrated quantum photonics is an appealing platform for quantum information
processing, quantum communication and quantum metrology. In all these
applications it is necessary not only to be able to create and detect Fock
states of light but also to program the photonic circuits that implements some
desired logical operation. Here we demonstrate a reconfigurable controlled
two-qubit operation on a chip using a multiwaveguide interferometer with a
tunable phase shifter. We find excellent agreement between theory and
experiment, with a 0.98 \pm 0.02 average similarity between measured and ideal
operations.
