Shared Lookups and Lazy Residues: Fewer Toffoli Gates for Factoring RSA-2048

arXiv:2611.08907v1 Announce Type: new Abstract: Gidney's 2025 construction for factoring RSA-2048 with few logical qubits spends most of its Toffoli gates on discrete-log table lookups and residue uncomputation. We reduce both costs. Shared lookups return entries for several primes of a residue number system at once because they have the same address. Retained intermediate residues remove recomputation during cleanup and enable lazy arithmetic with a single final modular reduction. We prove output preservation and estimate resources with an open benchmark built on the reference simulator.