{
  "id": "oai:papers.qnfo.org:falsifying-geometrically-inspired-quantum-error-correcting-codes-via-distinct-lo",
  "slug": "falsifying-geometrically-inspired-quantum-error-correcting-codes-via-distinct-lo",
  "title": "Falsifying Geometrically Inspired Quantum Error‑Correcting Codes via Distinct Logical‑Error Scaling",
  "authors": [
    "Rowan Brad Quni-Gudzinas"
  ],
  "abstract": "Geometric constructions of quantum error‑correcting codes (QECCs) have been proposed as alternatives to standard topological codes, yet their physical relevance remains ambiguous. Existing proposals lack a testable prediction that distinguishes them from surface‑code scaling of logical error rates. We identify this gap and formulate a falsifiability criterion: a geometrically motivated code must exhibit a logical error scaling p_L∝ p_phys^ d/2 where p_phys is the physical error probability per qubit and d the code distance, in contrast to the surface‑code scaling p_L∝ p_phys^ d. We develop a systematic method to extract the exponent from any stabilizer description, simulate the associated Lindblad dynamics, and compute the expected logical error curve. Using experimentally reported ancilla bit‑flip rates from a fluxonium‑based bosonic QEC platform [8] together with the derived scaling law, we obtain a concrete numerical prediction: for a physical error probability p_phys=2.19×10^-2 and distance d=5, the geometric code predicts p_L=7.1×10^-5 whereas the surface code predicts p_L=5.1×10^-9. This separation is experimentally resolvable with current superconducting hardware. Our result changes the design decision for quantum architects: if the geometric scaling holds, logical qubits can be realized with fewer physical resources, but the criterion also provides a clear falsification pathway.",
  "abstract_markdown": "Geometric constructions of quantum error‑correcting codes (QECCs) have been proposed as alternatives to standard topological codes, yet their physical relevance remains ambiguous. Existing proposals lack a testable prediction that distinguishes them from surface‑code scaling of logical error rates. We identify this gap and formulate a falsifiability criterion: a geometrically motivated code must exhibit a logical error scaling  \n\\(p_{L}\\propto p_{\\mathrm{phys}}^{\\,d/2}\\)  \nwhere \\(p_{\\mathrm{phys}}\\) is the physical error probability per qubit and \\(d\\) the code distance, in contrast to the surface‑code scaling \\(p_{L}\\propto p_{\\mathrm{phys}}^{\\,d}\\). We develop a systematic method to extract the exponent from any stabilizer description, simulate the associated Lindblad dynamics, and compute the expected logical error curve. Using experimentally reported ancilla bit‑flip rates from a fluxonium‑based bosonic QEC platform \\([8]\\) together with the derived scaling law, we obtain a concrete numerical prediction: for a physical error probability \\(p_{\\mathrm{phys}}=2.19\\times10^{-2}\\) and distance \\(d=5\\), the geometric code predicts \\(p_{L}=7.1\\times10^{-5}\\) whereas the surface code predicts \\(p_{L}=5.1\\times10^{-9}\\). This separation is experimentally resolvable with current superconducting hardware. Our result changes the design decision for quantum architects: if the geometric scaling holds, logical qubits can be realized with fewer physical resources, but the criterion also provides a clear falsification pathway.",
  "date": "2026-10-18",
  "first_published": "2026-10-18",
  "last_revised": "2026-10-18T00:00:00Z",
  "modified": "2026-10-18T00:00:00Z",
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  "url": "https://papers.qnfo.org/papers/falsifying-geometrically-inspired-quantum-error-correcting-codes-via-distinct-lo",
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  "version_url": "https://papers.qnfo.org/papers/falsifying-geometrically-inspired-quantum-error-correcting-codes-via-distinct-lo/v/1.0.0",
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        "name": "Rowan Brad Quni-Gudzinas",
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    "titles": [
      {
        "title": "Falsifying Geometrically Inspired Quantum Error‑Correcting Codes via Distinct Logical‑Error Scaling"
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    "publicationYear": "2026",
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        "date": "2026-10-18",
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        "description": "Geometric constructions of quantum error‑correcting codes (QECCs) have been proposed as alternatives to standard topological codes, yet their physical relevance remains ambiguous. Existing proposals lack a testable prediction that distinguishes them from surface‑code scaling of logical error rates. We identify this gap and formulate a falsifiability criterion: a geometrically motivated code must exhibit a logical error scaling p_L∝ p_phys^ d/2 where p_phys is the physical error probability per qubit and d the code distance, in contrast to the surface‑code scaling p_L∝ p_phys^ d. We develop a systematic method to extract the exponent from any stabilizer description, simulate the associated Lindblad dynamics, and compute the expected logical error curve. Using experimentally reported ancilla bit‑flip rates from a fluxonium‑based bosonic QEC platform [8] together with the derived scaling law, we obtain a concrete numerical prediction: for a physical error probability p_phys=2.19×10^-2 and distance d=5, the geometric code predicts p_L=7.1×10^-5 whereas the surface code predicts p_L=5.1×10^-9. This separation is experimentally resolvable with current superconducting hardware. Our result changes the design decision for quantum architects: if the geometric scaling holds, logical qubits can be realized with fewer physical resources, but the criterion also provides a clear falsification pathway.",
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