title: Quantum computation based on photonic systems with two degrees of freedom assisted by the weak cross-Kerr nonlinearity.
abstract: Most of previous quantum computations only take use of one degree of freedom (DoF) of photons. An experimental system may possess various DoFs simultaneously. In this paper, with the weak cross-Kerr nonlinearity, we investigate the parallel quantum computation dependent on photonic systems with two DoFs. We construct nearly deterministic controlled-not (CNOT) gates operating on the polarization spatial DoFs of the two-photon or one-photon system. These CNOT gates show that two photonic DoFs can be encoded as independent qubits without auxiliary DoF in theory. Only the coherent states are required. Thus one half of quantum simulation resources may be saved in quantum applications if more complicated circuits are involved. Hence, one may trade off the implementation complexity and simulation resources by using different photonic systems. These CNOT gates are also used to complete various applications including the quantum teleportation and quantum superdense coding.
authors.affiliation: Information Security and National Computing Grid Laboratory, School of Information Science and Technology, Southwest Jiaotong University, Chengdu 610031, China.|Department of Physics, University of Michigan, Ann Arbor, MI 48109, USA.
authors.forename: Ming-Xing
authors.initials: MX
authors.lastname: Luo
authors.affiliation: Information Security and National Computing Grid Laboratory, School of Information Science and Technology, Southwest Jiaotong University, Chengdu 610031, China.
authors.forename: Hui-Ran
authors.initials: HR
authors.lastname: Li
authors.affiliation: School of Computer and Information Science, Southwest University, Chongqing 400715, China.
authors.forename: Hong
authors.initials: H
authors.lastname: Lai