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Fault-tolerant modular quantum computing with surface codes using single-shot emission-based hardware

Siddhant Singh1,*, Rikiya Kashiwagi2,3, Kazufumi Tanji3, Wojciech Roga3, Daniel Bhatti4, Masahiro Takeoka3,5,†, and David Elkouss1,4,‡

  • *Contact author: siddhant.singh@tudelft.nl
  • †Contact author: takeoka@elec.keio.ac.jp
  • ‡Contact author: david.elkouss@oist.jp
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Phys. Rev. Applied 26, 024005 – Published 5 August, 2026

DOI: https://doi.org/10.1103/6mqy-sd3d

Abstract

Fault-tolerant modular quantum computing requires stabilizer measurements across the modules in a quantum network. For this, entangled states of high quality and rate must be distributed. Currently, two main types of entanglement distribution protocols exist, namely emission-based and scattering-based, each with its own advantages and drawbacks. On the one hand, scattering-based protocols with cavities or waveguides are fast but demand stringent hardware such as high-efficiency integrated circulators or strong waveguide coupling. On the other hand, emission-based platforms are experimentally feasible but have so far relied on Bell-pair fusion with extensive use of slow two-qubit memory gates, limiting thresholds to approximately 0.16%. Here, we consider a fully distributed surface code using emission-based entanglement schemes that generate GHZ states in a single shot, i.e., without the need for Bell-pair fusions. We show that our optical setup produces Bell pairs, W states, and GHZ states, enabling both memory-based and optical protocols for distilling high-fidelity GHZ states with significantly improved success rates. Furthermore, we introduce protocols that completely eliminate the need for memory-based two-qubit gates, achieving thresholds of approximately 0.19% with modest hardware enhancements, increasing to above approximately 0.24% with photon-number-resolving detectors. These results show the feasibility of emission-based architectures for scalable fault-tolerant operation.

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Phys. Rev. Applied 26, 024005– Published 5 August, 2026
  • Received 21 January 2026
  • Revised 3 April 2026
  • Accepted 1 July 2026
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