Circuit research for Shor’s algorithm

Shor’s algorithm for the elliptic-curve discrete logarithm problem repeatedly adds points on the curve inside a quantum circuit. Point addition is the dominant arithmetic, so the size of its reversible circuit, measured in the logical qubits it occupies and the non-Clifford gates it executes, largely sets the cost of the whole computation.

ECDSA.Fail asks how small that circuit can be made. It uses an open benchmark with automated evaluation, so that every submitted circuit is checked for correctness on sampled inputs and scored under one declared convention before it counts.

Open Autoresearch describes the format: humans and AI agents propose candidate circuits to a public leaderboard, an evaluator verifies them, and the record of what improved and how is public.

The paper’s data cutoff is 26 July 2026. On 8 September 2026 the challenge organizers accepted a submission by Ross Nkama that reduced the average executed Toffoli count from 904,049 to 902,838 at an unchanged qubit width of 1,260. That contribution is recorded in the organizers’ repository and on the community leaderboard, and is documented here as a case study in research with frontier AI. It is separate from the paper, and Ross is not a coauthor of it.

The result is a logical-circuit result. It does not compile the circuit to a fault-tolerant architecture, does not account for error-correction overhead or scheduling on a specific machine, and does not demonstrate the recovery of any key on quantum hardware.

Comparisons with other published circuits depend on accounting conventions and interfaces that differ between papers, so a headline percentage is only meaningful alongside the exact submission, baseline, metric, and validation status. Potomac therefore cites the paper, the benchmark, and specific dated submissions rather than summarizing rankings.

The paper has many authors across several institutions; the arXiv submission was made by Jieyi Long. Manuel B. Santos and Ruben M. L. Paschoarelli are coauthors listed with the affiliation MultiVM Labs, the team whose work Potomac builds on.

Manuel leads cryptography research at Potomac. Ruben’s coauthorship is part of the historical record and does not indicate current Potomac team membership. Potomac did not author or submit the paper as an institution; the contribution belongs to the individuals and to the collaboration that produced it.

Source: Author affiliations (arXiv HTML)