Table 1.
Performance of BB codes
| [[n, k, d]] | Net encoding rate, r | Circuit-level distance, dcirc | Pseudo-threshold, p0 | pL (10−3) | pL (10−4) |
|---|---|---|---|---|---|
| [[72, 12, 6]] | 1/12 | ≤6 | 0.0048 | 7 × 10−5 | 7 × 10−8 |
| [[90, 8, 10]] | 1/23 | ≤8 | 0.0053 | 5 × 10−6 | 4 × 10−10 |
| [[108, 8, 10]] | 1/27 | ≤8 | 0.0058 | 3 × 10−6 | 1 × 10−10 |
| [[144, 12, 12]] | 1/24 | ≤10 | 0.0065 | 2 × 10−7 | 8 × 10−13 |
| [[288, 12, 18]] | 1/48 | ≤18 | 0.0069 | 2 × 10−12 | 1 × 10−22 |
Small examples of BB LDPC codes and their performance for the circuit-based noise model. All codes have weight-6 checks, depth-7 syndrome measurement circuit, and the Tanner graph composed of two planar subgraphs. A code with parameters [[n, k, d]] requires 2n physical qubits in total and achieves the net encoding rate r = k/2n (we round r down to the nearest inverse integer). Circuit-level distance dcirc is the minimum number of faulty operations in the syndrome measurement circuit required to generate a logical error without triggering any syndromes.