A passive CPHASE gate via cross-Kerr nonlinearities

Understand

A fundamental and open question is whether cross-Kerr nonlinearities can be used to construct a controlled-phase (CPHASE) gate.

• Here we propose a gate constructed from a discrete set of atom-mediated cross-Kerr interaction sites with counter-propagating photons.
• We show that the average gate fidelity $F$ between a CPHASE and our proposed gate increases as the number of interaction sites increases and the spectral width of the photon decreases, e.g.
• with 12 sites we find $F > 99\%$.