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Compendium of Quantum Physics

Cluster States

Hans J. Briegel

Published Jan 1, 2009• 5 citations
Publisher
DOI
10.1007/978-3-540-70626-7_30

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Abstract Complex and multi-dimensional cluster states of light are a critical resource for one-way quantum computers. We exploit the frequency, time and polarization domains to generate all-photonic cluster-states in a two-dimensional, 2N qubit, in a 2xN configuration. Cluster states of two dimensions or higher can serve as a resource for universal measurement-based quantum computation, and our approach allows for the realization of measurement-based two-qubit operations in an all-photonic platform. To generate the cluster states, we employ a process in which we construct dual-rail cluster states in time, frequency and polarization, as sequences of dual-color photon pairs encoded in polarization. The demonstrated discrete-variable, multi-photon, 4- and 6-qubit 2xN cluster states are shown to have high lower-bound fidelities of 0.84 and 0.57, respectively. By implementing more frequency bins the cluster state can be extended further, as well as the use of additional photonic degrees of freedom (like spatial modes) for higher dimensional cluster-states.

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We consider the effects of decoherence on the entanglement of photonic cluster states. Large photonic cluster states can be constructed via so-called fusion operations from smaller photonic cluster states. Due to this construction process, it is necessary to store these primitive cluster states in some way so as to have them available for attempted fusion operations. While in storage the photonic cluster states may undergo dephasing. The effects of dephasing on primitive cluster states is explored here with the aim of determining how to locally rotate the qubits of the cluster state in the hopes of losing the least amount of entanglement due to the dephasing process.
We demonstrate a method of constructing L-shape cluster states by exploiting equivalence class properties of graph states. The L-shape cluster state is a primitive which can be used to construct cluster states capable of supporting universal quantum computation. The method is device independent but is shown to be considerably more efficient than previously proposed approaches for photonic cluster construction. Two-dimensional photonic cluster states can be efficiently built via local unitaries and type-I fusion only. To allow for a complete calculation of the cost of two-dimensional photonic cluster-state construction, we also provide a recursion relation relating the length of a photonic cluster chain to the average resources required.
Abstract Complex and multi-dimensional cluster states of light are a critical resource for one-way quantum computers. We exploit the frequency, time and polarization domains to generate all-photonic cluster-states in a two-dimensional, 2N qubit, in a 2xN configuration. Cluster states of two dimensions or higher can serve as a resource for universal measurement-based quantum computation, and our approach allows for the realization of measurement-based two-qubit operations in an all-photonic platform. To generate the cluster states, we employ a process in which we construct dual-rail cluster states in time, frequency and polarization, as sequences of dual-color photon pairs encoded in polarization. The demonstrated discrete-variable, multi-photon, 4- and 6-qubit 2xN cluster states are shown to have high lower-bound fidelities of 0.84 and 0.57, respectively. By implementing more frequency bins the cluster state can be extended further, as well as the use of additional photonic degrees of freedom (like spatial modes) for higher dimensional cluster-states.