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  "slug": "low-overhead-quantum-error-correction-with-boundary-connected-planar-modules-a-r",
  "title": "Low-Overhead Quantum Error Correction with Boundary-Connected Planar Modules: A Reconciled Quantitative Assessment",
  "authors": [
    "Rowan Brad Quni-Gudzinas"
  ],
  "abstract": "The planar surface code protects quantum information robustly but pays for its two-dimensional layout with an encoding rate that vanishes as the distance grows, so fault-tolerant memories require hundreds to thousands of physical qubits per logical qubit. A recent proposal constructs modular hyperbolic surface and color codes by partitioning a quantum processor into flat Euclidean modules and wiring sparse, static boundary connections between them, yielding semi-hyperbolic codes with constant encoding rate [1,4]. In this paper we provide an independent, fully explicit quantitative analysis of that proposal. Taking the reported parameters — encoding rate $k/n = 1/16$ and distance d ≥ 22 — as inputs, we compute that a twelve-logical-qubit modular memory requires n_mod = 192 physical qubits, versus $11100$ data qubits for twelve distance-$22$ rotated surface-code patches, a raw overhead reduction of 57.8×; the reduction remains ≥ 30× even if the true modular implementation uses up to $370$ physical qubits. [...]",
  "abstract_markdown": "The planar surface code protects quantum information robustly but pays for its two-dimensional layout with an encoding rate that vanishes as the distance grows, so fault-tolerant memories require hundreds to thousands of physical qubits per logical qubit. A recent proposal constructs modular hyperbolic surface and color codes by partitioning a quantum processor into flat Euclidean modules and wiring sparse, static boundary connections between them, yielding semi-hyperbolic codes with constant encoding rate [1,4]. In this paper we provide an independent, fully explicit quantitative analysis of that proposal. Taking the reported parameters — encoding rate $k/n = 1/16$ and distance $d \\geq 22$ — as inputs, we compute that a twelve-logical-qubit modular memory requires $n_{\\mathrm{mod}} = 192$ physical qubits, versus $11100$ data qubits for twelve distance-$22$ rotated surface-code patches, a raw overhead reduction of $57.8\\times$; the reduction remains $\\geq 30\\times$ even if the true modular implementation uses up to $370$ physical qubits. [...]",
  "date": "2026-10-05",
  "first_published": "2026-10-05",
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    "titles": [
      {
        "title": "Low-Overhead Quantum Error Correction with Boundary-Connected Planar Modules: A Reconciled Quantitative Assessment"
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        "description": "The planar surface code protects quantum information robustly but pays for its two-dimensional layout with an encoding rate that vanishes as the distance grows, so fault-tolerant memories require hundreds to thousands of physical qubits per logical qubit. A recent proposal constructs modular hyperbolic surface and color codes by partitioning a quantum processor into flat Euclidean modules and wiring sparse, static boundary connections between them, yielding semi-hyperbolic codes with constant encoding rate [1,4]. In this paper we provide an independent, fully explicit quantitative analysis of that proposal. Taking the reported parameters — encoding rate $k/n = 1/16$ and distance d ≥ 22 — as inputs, we compute that a twelve-logical-qubit modular memory requires n_mod = 192 physical qubits, versus $11100$ data qubits for twelve distance-$22$ rotated surface-code patches, a raw overhead reduction of 57.8×; the reduction remains ≥ 30× even if the true modular implementation uses up to $370$ physical qubits. [...]",
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