Parallel Implementation of CNOT^N and C₂NOT² Gates via Homonuclear and Heteronuclear F?rster Interactions of Rydberg Atoms

We analyze schemes of high-fidelity multi-qubit CNOTN and C2NOT2 gates for alkali metal neutral atoms used as qubits. These schemes are based on the electromagnetically induced transparency and Rydberg blockade. The fidelity of homonuclear multi-qubit CNOTN gate based on Rydberg blockade was limited by the undesirable interaction between the target atoms and by the coupling laser intensity. We propose overcoming these limits by using strong heteronuclear dipole-dipole interactions via F & ouml;rster resonances for control and target atoms, while the target atoms are coupled by a weaker van der Waals interaction. We optimized the gate performance in order to achieve higher fidelity, while keeping the coupling laser intensity as small as possible in order to improve the experimental feasibility of the gate schemes. We also considered the optimization of the schemes of the C2NOT2 gates, where the fidelity is affected by the relation between the control-control, control-target and target-target interaction energies. Our numeric simulations confirm that the fidelity of the CNOT4 gate (single control and four target atoms) can be up to 99.3% and the fidelity of the C2NOT2 (two control and two target atoms) is up to 99.7% for the conditions which are experimentally feasible.