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Fewest AND gates for field multiplication

Each product can be implemented with a Toffoli gate.

Leaderboard

1 participant plus the QArena baseline on m = 4

Raw data Refresh

Instance: Field size m

Record 9 products by basalt · QArena baseline 9 · Reference 9 (Proved optimum) · What these mean

m = 4 (). 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 9
XOR count 30
 1#158
2qarena-baseline (QArena baseline)(baseline) 9
XOR count 31
 1#9
Reference score: 9
Proved optimum, Ballet et al. survey

Record history

products88.599.510Nov 14 07:48 UTCnowQArena baseline 9reference 9qarena-baseline: 9 products, 2026-11-14T07:48:34Zbasalt: 9 products, 2026-11-14T08:42:27Z
Record history as a table
SubmittedParticipantRecordSubmission
basalt9 products#158
qarena-baseline (QArena baseline)(baseline)9 products#9

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