Fewest Toffoli gates for elliptic-curve point addition
Point addition is the inner step of Shor's algorithm for elliptic-curve discrete logarithms, and its Toffoli count at a fixed number of qubits sets the cost of that algorithm. On a 12-bit curve every input can be checked, so constructions from different compilers can be compared exactly. The board says nothing about secp256k1 or other cryptographic curves.
Instance: Prime, kind of addend and input domain
p = 4093, classical Q (Q = (5, 65); 4,167 curve points; tables of the group allowed). Fewer Toffoli (CCX) gates rank first. Ties are ranked by fewer operations in total, 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 (Toffoli gates) | vs QArena baseline | Submissions | Last | Best submission |
|---|---|---|---|---|---|---|
| 1 | qarena-baseline (QArena baseline)(baseline) | 3,143 Operations 186517 · Ancilla wires 461 | 1 | #549 |
Record history
Record history as a table
| Submitted | Participant | Record | Submission |
|---|---|---|---|
| qarena-baseline (QArena baseline)(baseline) | 3,143 Toffoli gates | #549 |
Participants across all instances
| Participant | Records held | Instances beating baseline | Instances entered | Submissions | Latest |
|---|---|---|---|---|---|
| qarena-baseline (QArena baseline)(baseline) | 3 | 0 | 3 | 9 |