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arXiv:1102.1916 · Journal of Modern Optics

Fusing imperfect photonic cluster states

Yaakov S. Weinstein

Published Aug 4, 2011• 3 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1080/09500340.2011.604437

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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.
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.
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.
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.
Despite linear-optical fusion (Bell measurement) being probabilistic, photonic cluster states for universal quantum computation can be prepared without feed-forward by fusing small n-photon entangled clusters, if the success probability of each fusion attempt is above a threshold, [Formula: see text]. We prove a general bound [Formula: see text], and develop a conceptual method to construct long-range-connected clusters where [Formula: see text] becomes the bond percolation threshold of a logical graph. This mapping lets us find constructions that require lower fusion success probabilities than currently known, and settle a heretofore open question by showing that a universal cluster state can be created by fusing 3-photon clusters over a 2D lattice with a fusion success probability that is achievable with linear optics and single photons, making this attractive for integrated-photonic realizations.
Photonic fusion operations are a central primitive in photonic quantum information processing and are commonly characterized by their success probability and resource cost. Here, we identify an additional way in which different implementations of fusion operations differ, namely in how they transform partial distinguishability. We consider distinguishability originating both from imperfect entangled resource states and from imperfect single photons. We find that different successful fusion events can induce markedly different distinguishability transformations depending on the fusion protocol, heralding outcome, and error model. Under a collective resource-state error model, we identify a modification to an existing fusion protocol that improves the fidelity of the remaining state on average. Generally, however, these transformations adversely affect distinguishability, and many successful fusion outcomes are accompanied by distinguishability degradation. Our results show that partial distinguishability is dynamically shaped by interference and measurements and should be considered alongside overall fusion success probability when evaluating photonic fusion protocols.
Microclusters are the basic building blocks used to construct cluster states capable of supporting fault-tolerant quantum computation. In this paper, we explore the consequences of errors on microcluster construction using two error models. To quantify the effect of the errors we calculate the fidelity of the constructed microclusters and the fidelity with which two such microclusters can be fused together. Such simulations are vital for gauging the capability of an experimental system to achieve fault tolerance.