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  • Open Access

Adaptive framework for failure-aware protocols in fusion-based graph-state generation

Korbinian Staudacher1,*, Bhilahari Jeevanesan2,†, and Tobias Guggemos1,2,3,‡

  • *Contact author: staudacher@nm.ifi.lmu.de
  • †Contact author: bhilahari.jeevanesan@dlr.de
  • ‡Contact author: guggemos@nm.ifi.lmu.de; tobias.guggemos@dlr.de
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Phys. Rev. A 114, 032614 – Published 17 September, 2026

DOI: https://doi.org/10.1103/2z98-6bsp

Abstract

We consider the generation of photonic graph states in a linear optics setting where sequential nondeterministic fusion measurements are used to build large graph states out of small linear clusters and develop a framework to optimize the building process using graph-theoretic characterizations of fusion networks. We present graph-state generation protocols for linear cluster resource states and type-I/type-II fusions which are adaptive to fusion failure, that is, they reuse leftover graph states in the remaining building process. To estimate hardware costs, we interpret our protocols as finite Markov processes. This viewpoint allows us to cast the expected number of fusion measurements until success as a first passage problem. We then deploy a pipeline of polynomial algorithms to optimize arbitrary graph states, extract fusion networks, and find beneficial orderings of fusions. We check the effectiveness of these algorithms by verifying that the corresponding mean first passage times are decreased. We evaluate our pipeline for different initial resource states and fusion mechanisms with varying success probabilities. Results show reductions in the fusion overhead by several orders of magnitude when compared to simple repeat until success protocols and by up to 40% when compared to state-of-the-art graph-state generation protocols, especially for realistic fusion success probabilities between 50% and 75%.

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Phys. Rev. A 114, 032614– Published 17 September, 2026
  • Received 21 January 2026
  • Accepted 29 July 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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