Fault-tolerant Quantum Error Correction Using a Linear Array of Emitters

Jintae Kim; Jung Hoon Han; Isaac H. Kim

doi:10.22331/q-2025-03-26-1676

Fault-tolerant Quantum Error Correction Using a Linear Array of Emitters

Jintae Kim^1,2, Jung Hoon Han¹, and Isaac H. Kim³

¹Department of Physics, Sungkyunkwan University, Suwon 16419, Korea
²Institute of Basic Science, Sungkyunkwan University, Suwon 16419, Korea
³Department of Computer Science, University of California, Davis, CA 95616, USA

Published:	2025-03-26, volume 9, page 1676
Editor:	Joschka Roffe
Eprint:	arXiv:2403.01376v2
Doi:	https://doi.org/10.22331/q-2025-03-26-1676
Citation:	Quantum 9, 1676 (2025).

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Abstract

We propose a fault-tolerant quantum error correction architecture consisting of a linear array of emitters and delay lines. In our scheme, a resource state for fault-tolerant quantum computation is generated by letting the emitters interact with a stream of photons and their neighboring emitters. Depending on the number of emitters $n_e$, we study the effect of delay line errors in two regimes: when $n_e$ is a small constant of order unity and when $n_e$ scales with the code distance. Between these two regimes, the logical error rate steadily decreases as $n_e$ increases, from a scaling of $\exp(-c\eta^{-1/2})$ to $\exp(-c'\eta^{-1})$, where $\eta$ is the error rate per unit length in the delay line, for some constants $c,c'\gt0$. We also carry out a detailed study of the break-even point and the fault-tolerance overhead. These studies suggest that the multi-emitter architecture, using the state-of-the-art delay lines, can be used to demonstrate error suppression, assuming other sources of errors are sufficiently small.

Featured image: Schematic description of our scheme to construct the cluster state, which is a linear array of emitters and delay lines. Each emitter $Q_i$ is connected to two delay lines, designated as navy and blue lines, through which the photons propagate. The detectors and the interactions between neighboring emitters are depicted using triangles and thunder signs, respectively. Each emitter is responsible for building a thin “slab'' of the cluster state located directly above it. (The cluster state depicted in the figure is a three-dimensional cluster state; however, other cluster states can be constructed in general.) The black dots represent photons within the slab, while the white dots indicate the positions of the corresponding photons in a different slab. Entanglement between the slabs of the cluster state, represented by red dotted lines, can be generated by applying entangling gates to adjacent emitters.

► BibTeX data

@article{Kim2025faulttolerant,
  doi = {10.22331/q-2025-03-26-1676},
  url = {https://doi.org/10.22331/q-2025-03-26-1676},
  title = {Fault-tolerant {Q}uantum {E}rror {C}orrection {U}sing a {L}inear {A}rray of {E}mitters},
  author = {Kim, Jintae and Han, Jung Hoon and Kim, Isaac H.},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {9},
  pages = {1676},
  month = mar,
  year = {2025}
}

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[1] William J. Huggins, Tanuj Khattar, Amanda Xu, Matthew Harrigan, Christopher Kang, Guang Hao Low, Austin Fowler, Nicholas C. Rubin, and Ryan Babbush, "The FLuid Allocation of Surface code Qubits (FLASQ) cost model for early fault-tolerant quantum algorithms", arXiv:2511.08508, (2025).

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