{
  "annotation_id": "069f85f5-4cfe-449c-8eb8-c0ec106932a4",
  "date_created": "2026-03-02T18:02:02.803000Z",
  "date_modified": "2026-03-02T18:02:02.803000Z",
  "file_hash": "004340e6fb1cbe16005da173dc0e6dddcf6c7733b45c1cec845db057e58820f9",
  "private": false,
  "record": {
    "abstract": "Let $\\eta_0$ be the supremum of those $\\eta$ for which every poly-size\nquantum circuit can be simulated by another poly-size quantum circuit with\ngates of fan-in $\\leq 2$ that tolerates random noise independently occurring on\nall wires at the constant rate $\\eta$. Recent fundamental results showing the\nprincipal fact $\\eta_0\u003e0$ give estimates like $\\eta_0\\geq 10^{-6}-10^{-4}$,\nwhereas the only upper bound known before is $\\eta_0\\leq 0.74$.\n  In this note we improve the latter bound to $\\eta_0\\leq 1/2$, under the\nassumption $QP\\not\\subseteq QNC^1$. More generally, we show that if the\ndecoherence rate $\\eta$ is greater than 1/2, then we can not even store a\nsingle qubit for more than logarithmic time. Our bound also generalizes to the\nsimulating circuits allowing gates of any (constant) fan-in $k$, in which case\nwe have $\\eta_0\\leq 1-1/k$.",
    "arxiv_id": "quant-ph/0310136",
    "authors": [
      "Alexander A. Razborov"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "An Upper Bound on the Threshold Quantum Decoherence Rate",
    "url": "https://arxiv.org/abs/quant-ph/0310136"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "df324adb-82ae-4817-8e1b-1bd7ea01395a",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}