Implementation of a quantum Fredkin gate using an entanglement resource

Summary form only given. Photonic qubit logic provides flexible, low noise scheme for quantum information processing. However, implementation of increasing scale requires numbers of resources beyond what is readily available. A recent demonstration [1] has shown how to add a control operation to existing unitary transformations, providing a practical method for moving to medium-scale quantum circuits. Here we use the entanglement-based version of this scheme to implement a complex quantum gate - the Fredkin, or 3-qubit swap gate - with significantly less resources than its decomposition into a 2-qubit gate array.In the technique proposed in [1], the Hilbert space is expended in order to have a four-level system for each qubit. Each system is composed of a qubit sub-system on which the target operation acts, and a second qubit sub-system, which remains unaffected. The control is added by gates that switch between the different subsystems according to the control qubit. Despite its conceptual simplicity, this technique still uses too many gates for practical implementations with current photonic technology. A more feasible way is a version that replaces the gates with pre-existing entanglement between the gates with qubit system and the second subsystem. The experiment is based on four possible photon pairs -called x, o, s and e - with photons either only in x and e, leading to the swapping, or only in o and s, leading to no swapping (Fig. 1). Each qubit is encoded twice and the two last modes are only used for triggering. The coincidences and the polarization beam splitter on two first mode ensure that the possibilities for the origin of the photons are linked to the state of the control qubit.The four possible photon pairs are encoding in the polarization mode coming from two polarization entangling down-conversion crystals. One crystal give a photon pair either in modes x or o and the second one a pair in mode s or e . We then separate spatially the polarization m- de using beam displacer or Sagnac interferometers to preserve the phase stability (Fig . 2) . From the simulation we expect a fidelity around 85% for the truth table.