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surfaceCodeThreshold
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IndisputableMonolith.Information.QuantumErrorCorrection on GitHub at line 209.
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206
207 Below this error rate, arbitrarily long computation is possible.
208 Above it, errors accumulate faster than correction. -/
209noncomputable def surfaceCodeThreshold : ℝ := 0.01
210
211/-! ## RS Predictions -/
212
213/-- RS predictions for quantum error correction:
214
215 1. **8-tick codes**: Natural codes from phase structure
216 2. **Threshold from τ₀**: Error threshold related to τ₀ timescale
217 3. **Holographic codes**: Surface codes from holographic boundary
218 4. **Optimal codes**: Approach may reveal optimal QEC constructions -/
219def rsPredictions : List String := [
220 "8-tick structure provides natural encoding",
221 "Error threshold related to τ₀/gate_time ratio",
222 "Holographic error correction from ledger projection",
223 "Novel code families from φ-geometry"
224]
225
226/-! ## Implications for Quantum Computing -/
227
228/-- Quantum error correction enables:
229
230 1. **Fault-tolerant computation**: Arbitrarily long quantum computation
231 2. **Logical gates**: Operations on encoded qubits
232 3. **Magic state distillation**: Non-Clifford gates
233 4. **Quantum memory**: Long-term storage of quantum states -/
234def implications : List String := [
235 "Scalable quantum computers",
236 "Quantum communication over noisy channels",
237 "Quantum memory for quantum networks",
238 "Fault-tolerant universal gate sets"
239]