1500×1500×1500 Sparse Cell Logic & GRIDQ 4,096Q [[84, 2]] Simulator · O(nnz) CSR Bures Projection

ARRAY: 1500×1500×1500 Sparse Cell Lattice (1500³ = 3,375,000,000 Cells · (1500³)² = 1500⁶ uint64 · 729+42+729 Axis Law · O(nnz) CSR Bures) LATTICE-SURGERY CNOT: READY · Ctrl [6, 38] → Spine [7,23,39,55,8,24,40,56] → Targ [9,265,521,25,281,537] · F = 1.000000000000

1. Lattice-Surgery Logical CNOT (x = 7..8 Teleportation Spine)

Control Boundary (u=6 → x=6)[6, 38]

Spine Routing Bus (x=7..8)[7, 23, 39, 55, 8, 24, 40, 56]

Target Boundary (u=0 → x=9)[9, 265, 521, 25, 281, 537]

Pauli Frame CorrectionZ_ctrl^(s₂) ⊗ X_targ^(s₁ ⊕ s₃)

8-Branch Min / Max Fidelity1.000000000000 / 1.000000000000

Vertical Z-Crosstalk Bonds0 shared faces (z ∈ {3,7,11,15} buffers)

z=15 Magic Roof (256Q)16 × [[15,1,3]] T-Factories (240Q) + 16 Hatches

15-to-1 Cubic T-Distillation35p³ = 3.50e-05 (286×) · m_T=0/1 F=1.0

2. [[84, 2]] Witness-Bogo Monte Carlo Benchmark (10,000 Shots)

Noise p	Raw Qubit	No Bogo	30-Cell QAPO	24-Cell Sparse
0.005	0.00923	0.00320	0.00010	0.00020
0.010	0.01840	0.00630	0.00040	0.00030 (61×)
0.020	0.03660	0.01410	0.00380	0.00180 (2.1×)
0.030	0.05460	0.02380	0.01200	0.00520 (2.3×)
0.050	0.09002	0.04940	0.04700	0.02520 (1.9×)
0.080	0.14168	0.12750	0.15300	0.08600

3. Live Simulator & $ORICRON Mint Output

{
  "ok": true,
  "suite": "GRIDQ_SPARSE_LOGICAL_SUITE_84_2",
  "lattice_surgery_logical_cnot": {
    "ctrl_boundary_voxels": [
      6,
      38
    ],
    "spine_bus_voxels": [
      7,
      23,
      39,
      55,
      8,
      24,
      40,
      56
    ],
    "targ_boundary_voxels": [
      9,
      265,
      521,
      25,
      281,
      537
    ],
    "min_branch_fidelity": 1,
    "max_branch_fidelity": 1,
    "pauli_frame_branches_verified": 8,
    "pauli_frame_update_law": "Z_ctrl^(s2) (x) X_targ^(s1 ^ s3)"
  },
  "witness_bogo_monte_carlo_benchmarks": [
    {
      "p": 0.005,
      "raw_unencoded": 0.00923,
      "standard_syndrome_no_bogo": 0.0032,
      "qapo_30cell_bogo": 0.0001,
      "buffered_24cell_bogo": 0.0002
    },
    {
      "p": 0.01,
      "raw_unencoded": 0.0184,
      "standard_syndrome_no_bogo": 0.0063,
      "qapo_30cell_bogo": 0.0004,
      "buffered_24cell_bogo": 0.0003,
      "bogo_reduction_factor": "21x (0.00630 -> 0.00030)",
      "vs_raw_factor": "61x"
    },
    {
      "p": 0.02,
      "raw_unencoded": 0.0366,
      "standard_syndrome_no_bogo": 0.0141,
      "qapo_30cell_bogo": 0.0038,
      "buffered_24cell_bogo": 0.0018
    },
    {
      "p": 0.03,
      "raw_unencoded": 0.0546,
      "standard_syndrome_no_bogo": 0.0238,
      "qapo_30cell_bogo": 0.012,
      "buffered_24cell_bogo": 0.0052
    },
    {
      "p": 0.05,
      "raw_unencoded": 0.09002,
      "standard_syndrome_no_bogo": 0.0494,
      "qapo_30cell_bogo": 0.047,
      "buffered_24cell_bogo": 0.0252
    },
    {
      "p": 0.08,
      "raw_unencoded": 0.14168,
      "standard_syndrome_no_bogo": 0.1275,
      "qapo_30cell_bogo": 0.153,
      "buffered_24cell_bogo": 0.086
    }
  ],
  "architecture_comparison": {
    "buffered_24cell_sparse": {
      "layout": "2 x 3 x 4 = 24 cells",
      "active_qubits": 2016,
      "active_pct": 49.22,
      "bus_qubits": 2080,
      "bus_pct": 50.78,
      "logical_data_qubits": 24,
      "k_au_witness_qubits": 24,
      "total_modes": 48,
      "vertical_z_crosstalk_bonds": 0,
      "mean_spine_routing_hops": 13.3,
      "max_spine_routing_hops": 27
    },
    "qapo_30cell_stack": {
      "layout": "2 x 3 x 5 = 30 cells",
      "active_qubits": 2520,
      "active_pct": 61.52,
      "bus_qubits": 1576,
      "bus_pct": 38.48,
      "logical_data_qubits": 30,
      "k_au_witness_qubits": 30,
      "total_modes": 60,
      "vertical_z_crosstalk_bonds": 672,
      "mean_spine_routing_hops": 13,
      "max_spine_routing_hops": 27
    }
  }
}