The State of Factoring on Quantum Computers

We report on the current state of factoring integers on both digital andanalog quantum computers. For digital quantum computers, we study the effect oferrors for which one can formally prove that Shor's factoring algorithm fails.For analog quantum computers, we experimentally test three factorisationmethods and provide evidence for a scaling performance that is absolutely andasymptotically better than random guessing but still exponential. We concludewith an overview of future perspectives on factoring large integers on quantumcomputers.