Research
Potomac’s research connects elliptic-curve arithmetic to execution: smaller reversible circuits, AI research systems that find and test them, and the compilation and fault-tolerance work needed to run them on quantum hardware. This overview separates what has been published, what has been contributed since, and what is being developed.
Three kinds of work
ECDSA.Fail, an open study of AI-assisted optimization of elliptic-curve point-addition circuits for Shor’s algorithm (arXiv, September 2026; data cutoff 26 July 2026). Manuel B. Santos and Ruben M. L. Paschoarelli are coauthors with the MultiVM Labs affiliation.
The publicationLater submissions to the same public challenge by Ross Nkama and the research team. The accepted submission of 8 September 2026 reduced the average executed Toffoli count at unchanged qubit width and is recorded in the organizers’ repository. It postdates the paper and is not part of it.
The case studyCompilation, fault-tolerance modelling, mapping and scheduling, and execution on external quantum hardware, reported through the measurement framework. This work is in progress and has not yet produced hardware results.
How progress is reportedAlgorithms and execution
Research question
How do algorithm design, compilation, and error correction change the resources, runtime, and reliability of cryptanalytic workloads on quantum platforms?
Practical quantum cryptanalysis depends on how algorithms, compilation, error correction, scheduling, and hardware work together. We study the same cryptanalytic workload across every layer, so that an improvement in one place can be judged by its effect on the whole.
Track A
Develop and validate arithmetic kernels, reduce logical resource requirements, and compare designs under explicit correctness assumptions.
Track H
Investigate how target architectures, error correction, mapping, scheduling, and runtime constraints affect whether a workload can execute reliably.
Circuit compilation, quantum programming, and AI research systems support both tracks.
Published work
ECDSA is a widely used digital-signature scheme. Members of the team studied the quantum arithmetic relevant to its security and contributed to ECDSA.Fail under their MultiVM Labs affiliation. The paper gives the company a concrete starting point for its broader question: how improvements in logical circuits translate into realistic, fault-tolerant execution.
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.
Manuel B. Santos and Ruben M. L. Paschoarelli are coauthors listed with the MultiVM Labs affiliation. The paper predates Ross Nkama’s September 2026 submission, which is documented separately.
Scope, limits, and attribution
Methods
Research with frontier AI
Models propose candidate circuits and experiments; evaluators test correctness and resources; researchers decide what the results mean. The accepted ECDSA.Fail submission is documented as a case study.
The methodology and case studyMeasurement
A framework for reporting task, scale, resources, runtime, reliability, assumptions, and evidence status, and the proposed Maximum Reliable Kernel measure. Includes the illustrative research path to 256-bit arithmetic.
The frameworkHardware
Potomac intends to be a customer and application partner for quantum computing companies, with paid compute access, hardware integration, and joint experiments.
Collaboration paths