Toffoli and C$^\text{n}$NOT (n$>2$) gates in a neutral-atom platform using Rydberg coupling and dark state resonances

Abstract: We propose a protocol for realizing a Toffoli gate using neutral-atom qubits in optical tweezers. Two ground-state hyperfine levels of the atoms are considered as qubit states. Our method relies on the strong and long-range interactions between atoms due to Rydberg excitations and the occurrence of dark states in the target qubit, with both control and target qubits being individually addressed with laser pulses. Our gate protocol enables precise control over the quantum states of individual qubits, effectively suppressing undesirable transitions to ensure high-fidelity gate performance. The gate fidelity is estimated to be about $96\%$ for realistic system parameters. We further demonstrate a C$^\text{n}$NOT gate with $n >2$ by exploiting the Rydberg antiblockade mechanism, which allows multiple atoms within the blockade radius to be simultaneously excited to the Rydberg states. Thus, our approach may open a promising route to multi-qubit controlled operations for quantum computation.