B.3 Benchmark data ledger
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B.3.1 Exact weight two
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The JSON file data/benchmark_records.json contains the values in Table 4.1, together with the parity, half-filled, and leakage records.
B.3.2 Half filling
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| \(n\) | \(k\) | full dim. | sector dim. | apply gain | one-shot gain | memory gain |
|---|---|---|---|---|---|---|
| 8 | 4 | 256 | 70 | 1.212 | 1.083 | 3.657 |
| 10 | 5 | 1,024 | 252 | 1.234 | 0.7513 | 4.063 |
| 12 | 6 | 4,096 | 924 | 2.083 | 0.5092 | 4.433 |
| 14 | 7 | 16,384 | 3,432 | 3.24 | 0.2092 | 4.774 |
| 16 | 8 | 65,536 | 12,870 | 7.041 | 1.501 | 5.092 |
| 18 | 9 | 262,144 | 48,620 | 7.757 | 0.7458 | 5.392 |
| 20 | 10 | 1,048,576 | 184,756 | 7.396 | 0.6529 | 5.675 |
All recorded relative errors were zero at the displayed precision. The one-shot result can be below one because compilation dominates a single application.
B.3.3 Parity
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| \(n\) | full dim. | packet dim. | apply gain | one-shot gain | memory gain |
|---|---|---|---|---|---|
| 8 | 256 | 128 | 1.06 | 1.19 | 2.0 |
| 10 | 1,024 | 512 | 1.15 | 1.33 | 2.0 |
| 12 | 4,096 | 2,048 | 1.49 | 1.37 | 2.0 |
| 14 | 16,384 | 8,192 | 1.78 | 1.75 | 2.0 |
| 16 | 65,536 | 32,768 | 2.0 | 3.7 | 2.0 |
B.3.4 Symmetry-breaking controls
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| Test | retained probability | leakage |
|---|---|---|
| Break exact weight with pair gate | 0.891 | 0.109 |
| Break parity with \(X\) rotation | 0.869 | 0.131 |
| Break weight modulo four with pair gate | 0.928 | 0.0723 |
These controls demonstrate that a packet restriction must be audited after every symmetry-breaking operation.