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arXiv:1006.3192 · Journal of Modern Optics

Storing small photonic cluster states in a dephasing environment

Yaakov S. Weinstein, Gerald N. Gilbert

Published Jul 3, 2010• 2 citations
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Abstract

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.

DOI
10.1080/09500340.2010.495460

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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.
The ability to construct large photonic cluster states capable of supporting universal quantum computation relies on fusing together cluster primitives. These fusion operations are probabilistic and the efficiency of the construction process relies on recycling remains of cluster primitives that have undergone failed fusion attempts. Here I consider the effects of the inevitible decoherence that must arise while storing cluster primitives. First, I explore the case where dephased two-qubit cluster states are the basic resource for the construction of all larger cluster states, all fusion operations are successful, and no further dephasing occurs during the construction process. This allows us to explore how decoherence of the most basic, primitive clusters translate into imperfections of the larger cluster states constructed from them. I then assume that decoherence occurs before every attempted fusion operation and determine the best way to build a five qubit cluster. This requires including the effects of the fusion operation failures. Fidelity is used as the measure of accuracy for the constructed cluster states. Finally, I include a short discussion of photon loss and how it affects the construction of simple photonic clusters.
The ability to construct large photonic cluster states capable of supporting universal quantum computation relies on fusing together cluster primitives. These fusion operations are probabilistic and the efficiency of the construction process relies on recycling remains of cluster primitives that have undergone failed fusion attempts. Here I consider the effects of the inevitable decoherence that must arise while storing cluster primitives. First, I explore the case where dephased two-qubit cluster states are the basic resource for the construction of all larger cluster states, all fusion operations are successful, and no further dephasing occurs during the construction process. This allows us to explore how decoherence of the most basic, primitive clusters translates into imperfections of the larger cluster states constructed from them. I then assume that decoherence occurs before every attempted fusion operation and determine the best way to build a five-qubit cluster. This requires including the effects of the fusion operation failures. Fidelity is used as the measure of accuracy for the constructed cluster states. Finally, I include a short discussion of photon loss and how it affects the construction of simple photonic clusters.
Photons are excellent carriers of quantum information; their polarization remains coherent for long times and it is easy to measure and precisely rotate. The fundamental hurdle with photon-based quantum information processing is the lack of direct photon-photon interactions to provide entanglement between pairs of photons. Recent proposals show the ability to build large cluster states from small entangled states using non-deterministic operations, but the generation of deterministic high-fidelity small entangled states remains a challenge. In this talk, we will show how the necessary cluster-state building blocks for large-scale quantum computation can be created from coupled solid-state quantum emitters without the need for any two-qubit gates and regardless of whether the emitters are identical. We provide a recipe for the generation of two-dimensional, ‘cluster-state’ entangled photons that can be carried out with existing experimental capabilities.
Measurement-based quantum computing relies on the generation of large entangled cluster states that act as a universal resource on which logical circuits can be imprinted and executed through local measurements. A number of strategies for constructing sufficiently large photonic cluster states propose fusing many smaller resource states generated by a series of quantum emitters. However, the fusion process is inherently probabilistic with a 50% success probability in standard guise. A recent proposal has shown that, in the limit of low loss, the probability of achieving successful fusion may be boosted to near unity by redundantly encoding the vertices of linear graph states using Greenberger-Horne-Zeilinger states [Quantum 7, 992 (2023)]. Here we present a protocol for deterministically generating redundantly encoded photonic resource states using single quantum emitters, and study the impact of protocol errors and photonic losses on the generated resource states and type-II photonic fusion. Our work provides a route for efficiently constructing complex entangled photonic qubit states for photonic quantum computing and quantum repeaters.