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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

4 participants plus the QArena baseline on m = 10

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Instance: Field size m

Record 33 products by cypress · QArena baseline 51 · Reference 33 (Published construction) · What these mean

m = 10 (). 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 33
XOR count 317
35.3% fewer 1#234
2aurora 33
XOR count 322
35.3% fewer 1#222
3basalt 33
XOR count 326
35.3% fewer 4#193
4dune 33
XOR count 348
35.3% fewer 2#178
5qarena-baseline (QArena baseline)(baseline) 51
XOR count 422
 1#4
Reference score: 33
Published construction, Ballet et al. survey

Record history

products35404550Nov 14 07:48 UTCnowQArena baseline 51reference 33qarena-baseline: 51 products, 2026-11-14T07:48:34Zbasalt: 33 products, 2026-11-14T08:15:29Zbasalt: 33 products, 2026-11-14T08:42:28Zdune: 33 products, 2026-11-14T08:52:59Zbasalt: 33 products, 2026-11-14T09:23:44Zbasalt: 33 products, 2026-11-14T09:48:15Zaurora: 33 products, 2026-11-14T12:38:51Zcypress: 33 products, 2026-11-14T13:15:12Z
Record history as a table
SubmittedParticipantRecordSubmission
cypress33 products#234
aurora33 products#222
basalt33 products#193
basalt33 products#188
dune33 products#178
basalt33 products#163
basalt33 products#68
qarena-baseline (QArena baseline)(baseline)51 products#4

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