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  "slug": "error-correction-properties-of-covariant-bosonic-encodings-a-quantitative-assess",
  "title": "Error Correction Properties of Covariant Bosonic Encodings: A Quantitative Assessment",
  "authors": [
    "Rowan Brad Quni-Gudzinas"
  ],
  "abstract": "Bosonic modes provide a hardware‑efficient substrate for quantum error correction (QEC) because logical information can be encoded in continuous‑variable states with built‑in symmetries. Recent work introduced a representation‑theoretic framework in which a physical representation of a finite group, a logical representation, and a seed state together define covariant bosonic codewords. Within this framework the QEC matrix becomes a morphism of group representations, and Schur’s lemma guarantees the vanishing of entire irreducible blocks, thereby simplifying error analysis. In this paper we instantiate the formalism for the simplest non‑trivial finite group, the cyclic group C₂, and evaluate the logical error probability under a single‑photon‑loss channel. By choosing a coherent‑state seed |α⟩ with α=1 we obtain closed‑form expressions for the overlap of logical codewords, propagate the loss probability p=10^-3 through the covariant encoding, and compute a heuristic logical error probability p_L≈1.961×10^-3 and a corresponding fidelity F≈0.9980. [...]",
  "abstract_markdown": "Bosonic modes provide a hardware‑efficient substrate for quantum error correction (QEC) because logical information can be encoded in continuous‑variable states with built‑in symmetries. Recent work introduced a representation‑theoretic framework in which a physical representation of a finite group, a logical representation, and a seed state together define covariant bosonic codewords. Within this framework the QEC matrix becomes a morphism of group representations, and Schur’s lemma guarantees the vanishing of entire irreducible blocks, thereby simplifying error analysis. In this paper we instantiate the formalism for the simplest non‑trivial finite group, the cyclic group $C_{2}$, and evaluate the logical error probability under a single‑photon‑loss channel. By choosing a coherent‑state seed $|\\alpha\\rangle$ with $\\alpha=1$ we obtain closed‑form expressions for the overlap of logical codewords, propagate the loss probability $p=10^{-3}$ through the covariant encoding, and compute a heuristic logical error probability $p_{\\mathrm{L}}\\approx1.961\\times10^{-3}$ and a corresponding fidelity $F\\approx0.9980$. [...]",
  "date": "2026-10-09",
  "first_published": "2026-10-09",
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  "url": "https://papers.qnfo.org/papers/error-correction-properties-of-covariant-bosonic-encodings-a-quantitative-assess",
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        "name": "Rowan Brad Quni-Gudzinas",
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    "titles": [
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        "title": "Error Correction Properties of Covariant Bosonic Encodings: A Quantitative Assessment"
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        "description": "Bosonic modes provide a hardware‑efficient substrate for quantum error correction (QEC) because logical information can be encoded in continuous‑variable states with built‑in symmetries. Recent work introduced a representation‑theoretic framework in which a physical representation of a finite group, a logical representation, and a seed state together define covariant bosonic codewords. Within this framework the QEC matrix becomes a morphism of group representations, and Schur’s lemma guarantees the vanishing of entire irreducible blocks, thereby simplifying error analysis. In this paper we instantiate the formalism for the simplest non‑trivial finite group, the cyclic group C₂, and evaluate the logical error probability under a single‑photon‑loss channel. By choosing a coherent‑state seed |α⟩ with α=1 we obtain closed‑form expressions for the overlap of logical codewords, propagate the loss probability p=10^-3 through the covariant encoding, and compute a heuristic logical error probability p_L≈1.961×10^-3 and a corresponding fidelity F≈0.9980. [...]",
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