| ⍝ Quantum Error Correction: APL Code Generator | |
| ⍝ Systematic exploration of stabilizer codes | |
| ⍝ Generates candidate codes and tests properties | |
| ∇ result ← GenerateStabilizerCode n k;S;i;j;pauli | |
| ⍝ Generate random stabilizer code [[n,k,d]] | |
| ⍝ n: physical qubits, k: logical qubits | |
| ⍝ Need n-k stabilizer generators | |
| S ← ⍬ | |
| :For i :In ⍳(n-k) | |
| ⍝ Random Pauli string (I,X,Y,Z = 0,1,2,3) | |
| pauli ← ?(n⍴4) | |
| S ← S,⊂pauli | |
| :EndFor | |
| ⍝ Verify commutativity (all stabilizers must commute) | |
| :If ~VerifyCommutativity S | |
| result ← ⍬ ⍝ Invalid code | |
| →0 | |
| :EndIf | |
| ⍝ Compute distance (simplified) | |
| d ← ComputeDistance S n | |
| result ← (n k d S) | |
| ∇ | |
| ∇ valid ← VerifyCommutativity stabilizers;s1;s2 | |
| ⍝ Check if all stabilizers commute | |
| valid ← 1 | |
| :For s1 :In stabilizers | |
| :For s2 :In stabilizers | |
| :If ~Commute s1 s2 | |
| valid ← 0 | |
| →0 | |
| :EndIf | |
| :EndFor | |
| :EndFor | |
| ∇ | |
| ∇ commutes ← Commute p1 p2;pauli_product | |
| ⍝ Check if two Pauli strings commute | |
| ⍝ Pauli strings commute if they differ in even number of positions | |
| ⍝ where both are non-identity and different | |
| pauli_product ← +/((p1≠0)∧(p2≠0)∧(p1≠p2)) | |
| commutes ← ~2|pauli_product ⍝ Even number of anti-commuting pairs | |
| ∇ | |
| ∇ d ← ComputeDistance stabilizers n;min_weight;weight;error | |
| ⍝ Compute code distance (minimum weight logical operator) | |
| ⍝ Simplified: search for low-weight errors | |
| min_weight ← n ⍝ Start with maximum | |
| ⍝ Search for errors of weight 1, 2, 3, ... | |
| :For weight :In ⍳3 | |
| :For each error of weight weight | |
| ⍝ Check if error commutes with all stabilizers | |
| ⍝ but is not in stabilizer group | |
| :If (CommutesWithAll error stabilizers) ∧ (~InStabilizerGroup error stabilizers) | |
| min_weight ← ⌊/min_weight weight | |
| :EndIf | |
| :EndFor | |
| :EndFor | |
| d ← min_weight | |
| ∇ | |
| ∇ result ← SearchCodeSpace n_min n_max;best_code;best_score;code;score | |
| ⍝ Systematic search over code parameters | |
| best_code ← ⍬ | |
| best_score ← 0 | |
| :For n :In ⍳(n_max-n_min+1)+n_min-1 | |
| :For k :In ⍳n-1 | |
| code ← GenerateStabilizerCode n k | |
| :If code ≢ ⍬ ⍝ Valid code | |
| ⍝ Score: balance rate, distance, and threshold | |
| rate ← k÷n | |
| score ← rate × code[3] × 0.01 ⍝ Simplified threshold | |
| :If score > best_score | |
| best_score ← score | |
| best_code ← code | |
| ⎕←'Found: [[',n,',',k,',',code[3],']] rate=',rate | |
| :EndIf | |
| :EndIf | |
| :EndFor | |
| :EndFor | |
| result ← (best_code best_score) | |
| ∇ | |
| ∇ sealed ← SealToWORM code;hash;timestamp | |
| ⍝ Seal discovered code to WORM ledger | |
| hash ← SHA256 ⍕code | |
| timestamp ← ⍕⎕TS | |
| sealed ← 'qec-',hash,'-',timestamp | |
| ⍝ Append to ledger | |
| 'qec_worm.jsonl' AppendToFile sealed,'|',⍕code | |
| ∇ | |
| ⍝ Known codes for comparison | |
| ∇ codes ← KnownCodes | |
| ⍝ Return list of known quantum codes | |
| codes ← ⊂ | |
| (5,1,3) ⍝ Perfect code | |
| (7,1,3) ⍝ Steane code | |
| (9,1,3) ⍝ Shor code | |
| (23,1,7) ⍝ Golay-based code | |
| ∇ | |
| ⍝ Surface code benchmark | |
| ∇ surface ← SurfaceCode d | |
| ⍝ Surface code with distance d | |
| ⍝ Uses 2d²-1 physical qubits, encodes 1 logical qubit | |
| surface ← (2×d*2)-1 | |
| surface ← (surface,1,d) | |
| ∇ | |
| ⍝ Example usage: | |
| ⍝ result ← SearchCodeSpace 5 15 | |
| ⍝ best_code ← result[1] | |
| ⍝ best_score ← result[2] | |
| ⍝ SealToWORM best_code | |