Fusing imperfect photonic cluster states

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.

Frequency-encoded linear cluster states with coherent Raman photons

“…Robust highly-entangled 'cluster' states are of paramount importance for measurement-based quantum computation [1][2][3][4] . The experimental challenges of obtaining high-dimensional cluster states can be significantly reduced by probabilistically 'fusing' qubits from adjacent 1D linear cluster (LC) states [5][6][7] , or 'glueing' together micro-clusters 8 . Several platforms for generating photonic LC states have been proposed, varying from condensed matter emitters such as quantum dots 6,[9][10][11][12][13] and crystal defects 11,14 to parametric downconversion 15,16 , all presenting their own sets of advantages and challenges.…”

Imperfect construction of microclusters

“…In addition, because the errors and fusion operations do not commute, which of the fusion operations between leaves is successful will also effect the fidelity of the resulting two qubit cluster. In a real system the microclusters would likely be stored in some imperfect storage unit in between fusion attempts lowering the cluster state fidelity as explained in [13]. Here we assume no errors except those associated with the fusion operations.…”

“…We then fuse together imperfect microclusters and determine the accuracy of constructing the fused microclusters also via a fidelity. We note that other aspects of realistic photonic cluster state construction including the need to store cluster states (though imperfectly) during construction and effects of dephasing have been explored elsewhere [13][14][15].…”