Research
An open challenge to reduce the cost of reversible elliptic-curve point addition in Shor’s algorithm. Our work began at MultiVM Labs.
Publication
AI-assisted optimization of reversible elliptic-curve point-addition circuits for Shor's algorithm, evaluated on a public benchmark with automated verification. Data cutoff 26 July 2026.
MultiVM Labs
Our team contributed 5 promoted submissions that improved the challenge’s Q × T record, building on the wider community’s work. Q × T multiplies peak logical qubits by average executed Toffoli gates; lower is better.
Our team’s improvements include tighter register widths, arithmetic simplifications and recursive squaring. The results below show the score reached and the reduction against the prior record at the time of each submission.
| Date | Q × T | Reduction |
|---|---|---|
| 1,699,653,032 | 0.0820% | |
| 1,676,067,120 | 0.1070% | |
| 1,658,352,828 | 0.0006% | |
| 1,137,575,880 | 0.1340% |
The 12 June row combines two consecutive submissions. Each row has a different prior baseline; the reductions are not cumulative.
Our team is also working on the trade-off between qubits and gates. A circuit that uses fewer qubits can be useful even when it needs more gates and has a higher Q × T score.
On 22 July 2026, our team advanced the low-qubit frontier with an 824-qubit circuit using 192,458,651 Toffoli gates, a reduction of 31,419 gates at the same width.
These are logical-circuit results under the challenge’s evaluation conditions, including sampled inputs and approximate circuit stages. Hardware execution and complete key recovery are separate milestones.
Quantum FDN
Ivan Miskovic talks with quantum researchers on Quantum FDN. Watch the conversations below.
Published on the Quantum FDN channel. The guests appear as interviewees, not as advisers to or endorsers of PotomaQ.Quantum FDN on YouTube