{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"0f6771ba88d40b1d91ca7309d7d431b3f7a6c55696d2b48227bc4c7d53b1f79c","created":"2026-10-03T07:18:09Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"62c41d97d75bdede27ace892c72963a7013fc72cba483412932a13bcfea2e9b9","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"value","assisted_by":[],"external_id":"qi.fault-tolerance-noise.true-threshold-value","kind":"well-posed","literature_status":"open","n":"1","parents":[],"plain":"Proven guarantees say error correction works for error rates up to roughly a hundredth of a percent, simulations reach about one percent, and impossibility proofs only start near one third. The true maximum tolerable error rate is unknown.","posed_since":"2008","precise":"Consider circuits of unitary two-qubit gates whose input wires each suffer depolarizing noise of strength $p$, with noise-free one-qubit unitaries and fresh ancilla qubits, as in Kempe, Regev, Unger and de Wolf (arXiv:0802.1464, 2008), who prove that above $p=35.7\\%$ ($29.3\\%$ if the only two-qubit gate is CNOT) the output of any deep enough circuit is independent of its input. Find $p_{\\mathrm{th}}$, the supremum of $p$ at which arbitrarily long computations remain reliable with polylogarithmic overhead. Constructive schemes reach of order $1\\%$ in simulation and rigorous lower bounds are of order $10^{-5}$ to $10^{-4}$ (approximate).","problem_ref":null,"references":"","settled_by":"Matching or near-matching upper and lower bounds on $p_{\\mathrm{th}}$ for the stated noise model.","status_note":"","title":"Largest noise rate allowing fault-tolerant universal quantum 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