Data and code for "A Shifted Continued-Fraction Truncation for Order Finding in Shor's Algorithm with Sparse Control Qubits"

This research addresses the high requirement for control qubits in Shor’s algorithm for factoring N=21 and N=35 by a shifted truncation of the continued fraction expansion. For the orders encountered in these case studies, the number of control qubits required is governed by the order r rather than by N, and the candidate-pair post-processing allows this reduced number to suffice. The feasibility of this method is validated using N=21 and N=35 as case studies. Results demonstrate that the method enables accurate identification of the correct order in modular arithmetic on a full-amplitude quantum virtual machine, using compiled circuits for these small, short-period bases. Unlike conventional strategies relying on hardware scaling, this work focuses on post-processing improvements, offering a post-processing pathway for factorization on quantum resource-constrained devices. Further analysis confirms the self-consistency of the results for N=21 (a=4, a=11) and N=35 (a=16), with a modest additional classical overhead that grows as the control-qubit count decreases. This advancement clarifies the classical post-processing conditions under which sparse control-qubit implementations of Shor's algorithm remain viable. Future work will test the universality of this method for larger integers and explore its extension to other quantum algorithms dependent on phase estimation. This deposit contains the circuit definitions (OriginIR exports and OpenQASM 3.0 transcriptions), measurement counts, post-processing scripts and publication-ready figures for all three circuits.