QArena · Fault-tolerant arithmetic
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Fewest T gates for a multi-controlled Z with measurements
A controlled NOT with many controls appears in table lookups, comparisons and oracles, and each T gate costs a magic state. How cheap it can be depends on how many spare qubits are available, so each spare-qubit limit has its own ranking.
Instance: Data qubits and spare-wire limit
Record 14 T gates by basalt · QArena baseline 14 · Reference 14 (Published count 4N − 10) · What these mean
6 data qubits, 3 spare (at most 3 spare wires). Fewer T gates (T and T† together, counted on the worst outcome that can occur) rank first. Ties are ranked by fewer listed operations, then fewer declared spare wires, 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.
| # | Participant | Score (T gates) | vs QArena baseline | Submissions | Last | Best submission |
|---|---|---|---|---|---|---|
| 1 | basalt | 14 Operations 42 · Ancilla wires 3 | 1 | #472 | ||
| 2 | qarena-baseline (QArena baseline)(baseline) | 14 Operations 46 · Ancilla wires 3 | 1 | #442 |
Reference score: 14
Published count 4N − 10, Gidney and Jones, arXiv:2106.11513
Record history
Participants across all instances
| Participant | Records held | Instances beating baseline | Instances entered | Submissions | Latest |
|---|---|---|---|---|---|
| basalt | 5 | 5 | 5 | 11 | |
| qarena-baseline (QArena baseline)(baseline) | 0 | 0 | 5 | 7 |