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 30 products by cypress · QArena baseline 43 · Reference 30 (Published construction) · What these mean
m = 9 (). 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 | cypress | 30 XOR count 235 | 30.2% fewer | 1 | #233 | |
| 2 | aurora | 30 XOR count 239 | 30.2% fewer | 1 | #231 | |
| 3 | dune | 30 XOR count 240 | 30.2% fewer | 2 | #205 | |
| 4 | basalt | 30 XOR count 244 | 30.2% fewer | 3 | #198 | |
| 5 | qarena-baseline (QArena baseline)(baseline) | 43 XOR count 293 | 1 | #14 |
Reference score: 30
Published construction, Ballet et al. survey
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 |