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 4 T gates by basalt · QArena baseline 4 · Reference 4 (Published count) · What these mean
This is a debug instance for checking a pipeline end to end; its table is not a ranking.
3 data qubits, 1 spare (debug) (CCZ; debug instance). 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 | 4 Operations 13 · Ancilla wires 1 | 1 | #483 | ||
| 2 | qarena-baseline (QArena baseline)(baseline) | 4 Operations 14 · Ancilla wires 1 | 1 | #436 |
Reference score: 4
Published count, Jones, arXiv:1212.5069; Gidney, arXiv:1709.06648
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 |