{"ID":2858062,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.08027","arxiv_id":"2510.08027","title":"Integer Factoring with Unoperations","abstract":"This work introduces the notion of unoperation $\\mathfrak{Un}(\\hat{O})$ of some operation $\\hat{O}$. Given a valid output of $\\hat{O}$, the corresponding unoperation produces a set of all valid inputs to $\\hat{O}$ that produce the given output. Further, the working principle of unoperations is illustrated using the example of addition. A device providing that functionality is constructed utilising a quantum circuit performing the unoperation of addition - referred to as unaddition. To highlight the potential of the approach the unaddition quantum circuit is employed to construct a device for factoring integer numbers $N$, which is then called unmultiplier. This approach requires only a number of qubits $\\in \\mathcal{O}((\\log{N})^2)$, rivalling the best known factoring algorithms to date.","short_abstract":"This work introduces the notion of unoperation $\\mathfrak{Un}(\\hat{O})$ of some operation $\\hat{O}$. Given a valid output of $\\hat{O}$, the corresponding unoperation produces a set of all valid inputs to $\\hat{O}$ that produce the given output. Further, the working principle of unoperations is illustrated using the exa...","url_abs":"https://arxiv.org/abs/2510.08027","url_pdf":"https://arxiv.org/pdf/2510.08027v1","authors":"[\"Paul Kohl\"]","published":"2025-10-09T10:04:43Z","proceeding":"quant-ph","tasks":"[\"quant-ph\",\"cs.DS\"]","methods":"[]","has_code":false}