Year: 2026
Type: article
Abstract: We present a protocol for integer factorization for all integers N below a certain cut-off Λ=2d, grounded in the theory of quantum measurement. In this framework, the factorization of an integer N≤Λ is achieved in a number of steps equal to the total number I of primes present in its factorization; explicitly, the procedure consists of a sequence of I quantum measurements. The method requires a single-purpose quantum device designed to perform measurements of an observable with a prescribed spectrum. Crucially, the construction of this device involves solving, once and for all, a set of approximately 2d differential equations, independently of the specific integer to be factorized. We argue that the initialization task of this device can be efficiently implemented on a quantum computer in d steps, thereby decoupling the computational cost of device preparation from the factorization process itself.
Source: Entropy
DOI: 10.3390/e28030363
Authors: Giuseppe Mussardo, Andrea Trombettoni
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,137
Funder: NextGenerationEU
Award: G8283306702
OpenAlex ID: W7140114049