Heralded quantum gates for hybrid systems via waveguide-mediated photon scattering

Universal quantum gates play a critical role in quantum information processing. Here, based on the scattering property of photons off single emitters in one-dimensional waveguides, we present some heralded protocols for realizing controlled-NOT, Toffoli, and Fredkin gates on hybrid systems. The control qubit of our gates is encoded on a flying photon, and the target qubits are encoded in the degenerate ground states of the emitter. In our schemes, the faulty scattering processes between emitters and photons caused by system imperfections can be transformed into the detection of photon polarization. That is, our three quantum gates are accomplished in a heralded way. Moreover, the quantum circuits for the three gates are versatile and compact, and no additional qubits are required. With current technique on manipulating the emitter-waveguide system, our protocols may be experimentally feasible. This work provides an effective avenue for implementing quantum logic gates.