Generation of Photonic Graph States with minimal number of quantum emitters

Konstantinos-Rafail Revis; Nils Tomke Ottink; Pierre-Emmanuel Emeriau; Paul Hilaire

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arXiv · 2609.30400

Generation of Photonic Graph States with minimal number of quantum emitters

Konstantinos-Rafail Revis·Nils Tomke Ottink·Pierre-Emmanuel Emeriau·Paul Hilaire

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Abstract

Graph states are a fundamental resource for measurement and fusion-based quantum computing, quantum networks, and sensing. Preparing them in a photonic system deterministically is, in principle, possible, but finding efficient schemes to prepare them was a long-standing problem addressed recently. Additionally, heuristic optimization schemes for reducing the required number of two-qubit gates were developed. However, the problem of reducing the number of emitters by optimizing the emission ordering was not addressed, due to its computational complexity, as it is connected to a well-known NP-hard problem from graph theory, the linear rank width computation. In this work, we focus on developing heuristic polynomial algorithms to reduce the number of emitters required. In total, we propose four distinct algorithms, which demonstrate up to $30\%$ emitter reduction on random graphs. Furthermore, we provide numerical and statistical evidence that the combination of our optimization schemes with the preexisting algorithms for optimizing the two-qubit gates of the preparation protocol can further reduce them by around $20\%$. Finally, we examine the developed algorithms for various useful graph state families, such as graphs useful for measurement-based quantum algorithms, and cluster states and graph codes used for quantum error correction, to determine the performance of each algorithm.

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Konstantinos-Rafail Revis, Nils Tomke Ottink, Pierre-Emmanuel Emeriau, Paul Hilaire. 2026-09-24. Generation of Photonic Graph States with minimal number of quantum emitters. https://arxiv.org/abs/2609.30400

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