High‐Fidelity and Low‐Cost Hyperparallel Quantum Gates for Photon Systems via Λ‐Type Systems

Quantum gates designed with minimized resources overhead have a crucial role in quantum information processing. Here, based on the degrees of freedom (DoFs) of photons and Λ‐type atom systems, two high‐fidelity and low‐cost protocols are presented for realizing polarization‐spatial hyperparallel controlled‐not (CNOT) and Toffoli gates on photon systems with only two and four two‐qubit polarization–polarization swap (P‐P‐SWAP) gates in each DoF, respectively. Moreover, the quantum gates can be extended feasibly to construct 2m‐target‐qubit hyperparallel CNOT and 2n‐control‐qubit Toffoli gates required only 4m and 4n P‐P‐SWAP gates on (m+1)$(m+1)$‐ and (n+1)$(n+1)$‐photon systems, respectively, which dramatically lower the costs and bridge the divide between the theoretical lower bounds and the current optimal syntheses for the photonic quantum computing. Further, the unique auxiliary atom of these quantum gates can be regarded as a temporary quantum memory that requires no initialization and measurement, and is reused within the coherence time, as the state of the atom remains unchanged after the hyperparallel quantum computing. Assisted by a three‐level Λ‐type atom, an underlying polarization–polarization swap (P‐P‐SWAP) quantum gate is constructed with near‐unit fidelity. Moreover, the hyper‐controlled‐not and hyper‐controlled‐controlled‐not gates are implemented perfectly with 2 and 4 P‐P‐SWAP gates, respectively, both of which are high fidelity in practical conditions and can work efficiently with a relatively lower‐Q factor.