 118    Decode by majority vote.
 119
 120    Can correct 3 errors (majority still correct). -/
 121def eightTickCode : ErrorCode := ⟨8, 1, 8⟩
 122
 123theorem eight_tick_corrects_3 :
 124    -- 8-tick code corrects up to 3 errors
 125    (eightTickCode.d - 1) / 2 = 3 := by rfl
 126
 127/-! ## Quantum Error Correction -/
 128
 129/-- Quantum error correction is different:
 130
 131    - Can't measure without disturbing
 132    - No cloning
 133    - Errors are continuous (not just bit flips)
 134
 135    Yet QEC is possible! Using entanglement and syndrome measurement.
 136
 137    In RS: 8-tick phases provide natural QEC through phase correlations. -/
 138def quantumErrorCorrection : String :=
 139  "Protect quantum states using redundancy and syndromes"
 140
 141/-- For majority voting on 8 phases, the threshold is p < 3/8.
 142    Below this error rate, the majority is always correct. -/
 143theorem threshold_majority_voting :
 144    (eightTickCode.d - 1) / 2 < eightTickCode.n ∧
 145    (eightTickCode.d - 1) / 2 = 3 := by
 146  unfold eightTickCode; constructor <;> norm_num
 147
 148/-! ## Topological Codes -/
 149
 150/-- Topological error correction:
 151

papers checked against this theorem

No papers in the current corpus map onto this theorem yet.