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Fewest AND gates for field multiplication

Each product can be implemented with a Toffoli gate.

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4 participants plus the QArena baseline on m = 3

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Instance: Field size m

Record 6 products by cypress · QArena baseline 7 · Reference 6 (Proved optimum) · What these mean
This is a debug instance for checking a pipeline end to end; its table is not a ranking.

m = 3 (). 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
1cypress 6
XOR count 13
14.3% fewer 1#144
2aurora 6
XOR count 13
14.3% fewer 1#164
3basalt 6
XOR count 16
14.3% fewer 1#59
4dune 6
XOR count 17
14.3% fewer 1#75
5qarena-baseline (QArena baseline)(baseline) 7
XOR count 17
 1#7
Reference score: 6
Proved optimum, Ballet et al. survey

Record history

products66.57Nov 14 07:48 UTCnowQArena baseline 7reference 6qarena-baseline: 7 products, 2026-11-14T07:48:34Zbasalt: 6 products, 2026-11-14T08:12:04Zcypress: 6 products, 2026-11-14T08:37:19Z
Record history as a table
SubmittedParticipantRecordSubmission
cypress6 products#144
basalt6 products#59
qarena-baseline (QArena baseline)(baseline)7 products#7

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