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QArena · Fault-tolerant arithmetic Submit

Fewest AND gates for field multiplication

Each product can be implemented with a Toffoli gate.

Leaderboard

3 participants plus the QArena baseline on m = 16

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Instance: Field size m

Record 60 products by aurora · QArena baseline 81 · Reference 60 (Published construction) · What these mean

m = 16 (). 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
1aurora 60
XOR count 1058
25.9% fewer 1#228
2basalt 60
XOR count 1094
25.9% fewer 3#212
3dune 60
XOR count 1108
25.9% fewer 2#203
4qarena-baseline (QArena baseline)(baseline) 81
XOR count 946
 1#5
Reference score: 60
Published construction, Ballet et al. survey

Record history

products6065707580Nov 14 07:48 UTCnowQArena baseline 81reference 60qarena-baseline: 81 products, 2026-11-14T07:48:34Zbasalt: 60 products, 2026-11-14T08:15:29Zbasalt: 60 products, 2026-11-14T08:44:50Zdune: 60 products, 2026-11-14T10:29:19Zbasalt: 60 products, 2026-11-14T11:30:12Zaurora: 60 products, 2026-11-14T12:59:52Z
Record history as a table
SubmittedParticipantRecordSubmission
aurora60 products#228
basalt60 products#212
dune60 products#203
basalt60 products#166
basalt60 products#69
qarena-baseline (QArena baseline)(baseline)81 products#5

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