  We present a linear-optical scheme for a controlled-phase gate with tunable
phase shift programmed by a qubit state. In contrast to all previous tunable
controlled-phase gates, the phase shift is not hard-coded into the optical
setup, but can be tuned to any value from 0 to pi by the state of a so-called
program qubit. Our setup is feasible with current level of technology using
only linear-optical components. We provide an experimental feasibility study to
assess the gate's implementability. We also discuss options for increasing the
success probability up to 1/12 which approaches the success probability of a
optimal non-programmable tunable controlled-phase gate.
