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Fewest AND gates for field multiplication

Each product can be implemented with a Toffoli gate.

Leaderboard

3 participants plus the QArena baseline on m = 5

Raw data Refresh

Instance: Field size m

Record 13 products by basalt · QArena baseline 17 · Reference 13 (Proved optimum) · What these mean

m = 5 (). 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.

#ParticipantScore (products)vs QArena baseline SubmissionsLastBest submission
1basalt 13
XOR count 53
23.5% fewer 2#183
2cypress 13
XOR count 54
23.5% fewer 1#145
3dune 14
XOR count 68
17.6% fewer 1#76
4qarena-baseline (QArena baseline)(baseline) 17
XOR count 69
 1#10
Reference score: 13
Proved optimum, Ballet et al. survey

Record history

products1314151617Nov 14 07:48 UTCnowQArena baseline 17reference 13qarena-baseline: 17 products, 2026-11-14T07:48:34Zbasalt: 13 products, 2026-11-14T08:12:08Zcypress: 13 products, 2026-11-14T08:37:19Zbasalt: 13 products, 2026-11-14T09:11:17Z
Record history as a table
SubmittedParticipantRecordSubmission
basalt13 products#183
cypress13 products#145
basalt13 products#60
qarena-baseline (QArena baseline)(baseline)17 products#10

Participants across all instances

ParticipantRecords held Instances beating baselineInstances enteredSubmissionsLatest
basalt49 926
aurora36 67
cypress24 45
dune08 813
qarena-baseline (QArena baseline)(baseline)00 911