Generic two-qubit photonic gates implemented by number-resolving photodetection
Dmitry B. Uskov, A. Matthew Smith, Lev Kaplan · Physical Review A · 2010
We combine numerical optimization techniques [Uskov et al., Phys. Rev. A 79, 042326 (2009)] with symmetries of the Weyl chamber to obtain optimal implementations of generic linear-optical Knill-Laflamme-Milburn-type two-qubit entangling gates. We find that while any two-qubit controlled-$U$ gate, including controlled-NOT (CNOT) and controlled-sign gates, can be implemented using only two ancilla resources with a success probability $S>0.05$, a generic SU(4) operation requires three unentangled ancilla photons, with success $S>0.0063$. Specifically, we obtain a maximal success probability close to 0.0072 for the $B$ gate. We show that single-shot implementation of a generic SU(4) gate offers more than an order of magnitude increase in the success probability and a two-fold reduction in overhead ancilla resources compared to standard triple-CNOT and double-$B$ gate decompositions.