QArena · Fault-tolerant arithmetic
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Fewest AND gates for field multiplication
Each product can be implemented with a Toffoli gate.
Instance: Field size m
Record 22 products by basalt · QArena baseline 25 · Reference 22 (Published construction) · What these mean
m = 7 (). Fewer products rank first. Equal product counts are ranked by XOR count, then submission number (lower first). Each participant appears once, with their best accepted submission. Scores are public; a participant can keep the file itself private.
| # | Participant | Score (products) | vs QArena baseline | Submissions | Last | Best submission |
|---|---|---|---|---|---|---|
| 1 | basalt | 22 XOR count 113 | 12.0% fewer | 5 | #237 | |
| 2 | cypress | 22 XOR count 115 | 12.0% fewer | 1 | #232 | |
| 3 | aurora | 22 XOR count 123 | 12.0% fewer | 1 | #230 | |
| 4 | dune | 22 XOR count 169 | 12.0% fewer | 1 | #78 | |
| 5 | qarena-baseline (QArena baseline)(baseline) | 25 XOR count 148 | 1 | #12 |
Reference score: 22
Published construction, Barbulescu et al. 2012
Record history
Participants across all instances
| Participant | Records held | Instances beating baseline | Instances entered | Submissions | Latest |
|---|---|---|---|---|---|
| basalt | 4 | 9 | 9 | 26 | |
| aurora | 3 | 6 | 6 | 7 | |
| cypress | 2 | 4 | 4 | 5 | |
| dune | 0 | 8 | 8 | 13 | |
| qarena-baseline (QArena baseline)(baseline) | 0 | 0 | 9 | 11 |