Experimental realization of a programmable quantum gate

We experimentally demonstrate a programmable single-qubit quantum gate. This device applies a unitary phase shift operation to a data qubit with the value of the phase shift being fully determined by the state of a program qubit. Our linear optical implementation is based on the encoding of qubits into polarization states of single photons, two-photon interference on a polarizing beam splitter, and measurement on the output program qubit. We fully characterize the programmable gate by quantum process tomography. The achieved average quantum process fidelity exceeding 97% illustrates very good performance of the gate for all values of the encoded phase shift. We also show that by using a different set of program states the device can operate as a programmable partial polarization filter.