We present a scheme to generate any two-dimensional cluster state efficiently. The number of the basic gate (entangler) operations is on the order of the entanglement bonds of a cluster state. This deterministic scheme, which demands few ancilla resources and no quantum memory, is suitable for large-scale quantum computation.
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.
The cluster state model for quantum computation has paved the way for schemes that allow scalable quantum computing, even when using non-deterministic quantum gates. Here the initial step is to prepare a large entangled state using non-deterministic gates. A key question in this context is the relative efficiencies of different 'strategies', i.e. in what order should the non-deterministic gates be applied, in order to maximize the size of the resulting cluster states? In this paper we consider this issue in the context of 'large' cluster states. Specifically, we assume an unlimited resource of qubits and ask what the steady state rate at which 'large' clusters are prepared from this resource is, given an entangling gate with particular characteristics. We measure this rate in terms of the number of entangling gate operations that are applied. Our approach works for a variety of different entangling gate types, with arbitrary failure probability. Our results indicate that strategies whereby one preferentially bonds together clusters of identical length are considerably more efficient than those in which one does not. Additionally, compared to earlier analytic results, our numerical study offers substantially improved resource scaling.
Cluster states can be used to perform measurement-based quantum computation. The cluster state is a useful resource, because once it has been generated only local operations and measurements are needed to perform universal quantum computation. In this paper, we explore techniques for quickly and deterministically building a cluster state. In particular, we consider generating cluster states on a qubus quantum computer, a computational architecture which uses a continuous variable ancilla to generate interactions between qubits. We explore several techniques for building the cluster, with the number of operations required depending on whether we allow the ability to destroy previously created controlled-phase links between qubits. In the case where we cannot destroy these links, we show how to create an $n\ifmmode\times\else\texttimes\fi{}m$ cluster using just $3nm\ensuremath{-}2n\ensuremath{-}\ensuremath{\lceil}3m/2\ensuremath{\rceil}+3$ operations. This gives more than a factor of 2 savings over a naive method. Further savings can be obtained if we include the ability to destroy links, in which case we only need $\ensuremath{\lceil}\frac{1}{3}(8nm\ensuremath{-}4n\ensuremath{-}4m\ensuremath{-}8)\ensuremath{\rceil}$ operations. Unfortunately, the latter scheme is more complicated so choosing the correct order to interact the qubits is considerably more difficult. A halfway scheme, that keeps a modular generation but saves additional operations over never destroying links requires only $3nm\ensuremath{-}2n\ensuremath{-}2m+4$ operations. The first scheme and the last scheme are the most practical for building a cluster state because they split up the generation into the repetition of simple sections.
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].