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Zhongguo kexue. Wulixue Lixue Tianwenxue

Efficient generation of three-dimensional cluster state with cross-phase modulation

Qing Lin

Published Jan 1, 2011• 0 citations
Publisher

Abstract

Based on the former structures in the generation of two-dimensional cluster states, we first propose a scheme to generate linear three-dimensional (3D) cluster state. After that, we develop the former structures to three-dimension, and then we could use them to generate universal 3D cluster states. In final, we provide two new structures, which could make the generation of a special type of 3D cluster state very efficient. All the proposals work with cross-phase modulation, so they are deterministic, highly efficient, fast, compared with the former schemes. It will make the requirement of quantum memory much relax, thus it is more feasible and suitable for large-scale one-way quantum computation.

DOI
10.1360/132010-972

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Based on the former structures in the generation of two-dimensional cluster states, we first propose a scheme to generate linear three-dimensional (3D) cluster state. After that, we develop the former structures to three-dimension, and then we could use them to generate universal 3D cluster states. In final, we provide two new structures, which could make the generation of a special type of 3D cluster state very efficient. All the proposals work with cross-phase modulation, so they are deterministic, highly efficient, fast, compared with the former schemes. It will make the requirement of quantum memory much relax, thus it is more feasible and suitable for large-scale one-way quantum computation.
A scheme is proposed for generating a polarization four-photon cluster, which is believed to be suitable to achieve the one-way quantum computing via single-qubit projective measurements, with the help of only cross-Kerr nonlinearity and current linear optical systems. Compared with the existing schemes, the distinct advantage of the present scheme is that cluster states can be achieved with high success probability close to unity. Our scheme is experimentally demanding but efficient. Based on the present scheme, the cluster state of 3N + 1 photons can be obtained with the help of linear optical elements.
Measurement based quantum computation requires the generation of a cluster state (quantum resource) prior to starting a computation. Generation of this entangled state can be difficult with many schemes already proposed. We present an abstract scheme which can create 2D cluster states as a universal resource for quantum computing. We find a linear scaling of grid size with cluster depth. The scheme is also capable of creating more exotic topologies including 3D structures and the unit cell for topological error correction. We note its relevance to the cavity QED scheme in [30] although it could be applied to various architectures.
One-way quantum computation is a promising scheme for realizing large-scale quantum computation, where computation is done via measurements on a universal multi-mode entangled resource called cluster state. The capability of this method is determined by the size and the dimension of the cluster state; the size is roughly equivalent to the number of input modes times number of operation steps, while the dimension determines universality and fault tolerance of the computation. To achieve universality, two-dimensional cluster state is required. Among many approaches, time-domain multiplexing using optical system [1, 2] is a promising method where quantum state is encoded in a temporal wave packet. Although universality is still lacking, one-million-mode one-dimensional cluster state has been demonstrated with this approach [3].
We propose an efficient approach for deterministically generating scalable cluster states with photons. This approach involves unitary transformations performed on atoms coupled to optical cavities. Its operation cost scales linearly with the number of qubits in the cluster state, and photon qubits are encoded such that single-qubit operations can be easily implemented by using linear optics. Robust optical one-way quantum computation can be performed since cluster states can be stored in atoms and then transferred to photons that can be easily operated and measured. Therefore, this proposal could help in performing robust large-scale optical one-way quantum computation.
Entanglement is the key resource for measurement-based quantum computing. It is stored in quantum states known as cluster states, which are prepared offline and enable quantum computing by means of purely local measurements. Universal quantum computing requires cluster states that are both large and possess (at least) a two-dimensional topology. Continuous-variable cluster states-based on bosonic modes rather than qubits-have previously been generated on a scale exceeding one million modes, but only in one dimension. Here, we report generation of a large-scale two-dimensional continuous-variable cluster state. Its structure consists of a 5- by 1240-site square lattice that was tailored to our highly scalable time-multiplexed experimental platform. It is compatible with Bosonic error-correcting codes that, with higher squeezing, enable fault-tolerant quantum computation.