QArena · Fault-tolerant arithmetic
Submit
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 files
Each JSON file defines one instance of this problem. Instances differ by data qubits and spare-wire limit. The verifier reads the same files, and the verifier bundle contains all of them together with an accepted example.
| File | Instance | Parameters | Size |
|---|---|---|---|
| mcz3-a1.json | 3 data qubits, 1 spare (debug) | CCZ; debug instance | 0.2 KB |
| mcz4-a1.json | 4 data qubits, 1 spare (debug) | CCCZ; debug instance | 0.2 KB |
| mcz5-a1.json | 5 data qubits, 1 spare | at most 1 spare wire | 0.2 KB |
| mcz5-a2.json | 5 data qubits, 2 spare | at most 2 spare wires | 0.2 KB |
| mcz6-a1.json | 6 data qubits, 1 spare | at most 1 spare wire | 0.2 KB |
| mcz6-a2.json | 6 data qubits, 2 spare | at most 2 spare wires | 0.2 KB |
| mcz6-a3.json | 6 data qubits, 3 spare | at most 3 spare wires | 0.2 KB |