00993nas a2200169   4500000000100000008004100001100001900042700002100061700001700082700001900099700001700118700001800135700002300153245004800176856003700224520056200261       2024                            d1 aDennis Willsch1 aPhilipp Hanussek1 aGeorg Hoever1 aMadita Willsch1 aFengping Jin1 aHans De Raedt1 aKristel Michielsen00aThe State of Factoring on Quantum Computers  uhttps://arxiv.org/abs/2410.143973 a<p>We report on the current state of factoring integers on both digital and analog quantum computers. For digital quantum computers, we study the effect of errors for which one can formally prove that Shor's factoring algorithm fails. For analog quantum computers, we experimentally test three factorisation methods and provide evidence for a scaling performance that is absolutely and asymptotically better than random guessing but still exponential. We conclude with an overview of future perspectives on factoring large integers on quantum computers.</p>