[Submitted on 21 Sep 2026]
Title:Complete secp256k1 Point Addition with 1,601 Logical Qubits
Abstract: VQ provides a Lean-verified complete secp256k1 point-adder using 1,601 logical qubits and at most 3,070,200 Toffoli-class gates. The program adds a runtime classical point to a quantum accumulator, restores all 1,089 workspace qubits to zero, and handles the group identity, doubling, and inverse points. Its measured execution preserves finite superpositions with a common branch amplitude, and the correct output has probability one on every valid basis input. Checked resource theorems bound the Toffoli-class count on every execution path and its expectation by 3,070,200, with at most 1,959,699 measurements. The program uses 13,342 mutable classical bits and 512 immutable classical input bits.
| Comments: | 3 pages, 2 tables |
| Subjects: | Logic in Computer Science (cs.LO) |
| Cite as: | marXiv:2609.00016 [cs.LO] (or marXiv:2609.00016v1 [cs.LO] for this version) |
Submission history
[v1] Mon, 21 Sep 2026 18:06:48 UTC (271 KB)
Related work
- marXiv:2608.00049
- Gives the construction and checked resource bounds for the 1601-qubit complete point-adder summarized in the VQ system report.