If you follow Wikipedia's reference [1] for the quantum factorization of 21 for instance, you read > We implement a scalable iterative quantum algorithm with a

If you follow Wikipedia's reference [1] for the quantum factorization of 21 for instance, you read > We implement a scalable iterative quantum algorithm with a compiled version of the quantum order finding routine where the circuit is constructed for a particular factoring case (here N = 21 and x = 4) admitting an experimentally tractable implementation, as shown in Fig. 2a. > There are several steps to compilations, common to previous demonstrations6–9,21. Firstly, for N = 21 and x = 4, unitaries and their decompositions can be calculated explicitly, as can the full state evolution; secondly, redundant elements of these unitaries are omitted. > Finally, and specific to our own demonstration, since only 3 of the possible 25 levels of the conventional 5 qubit work register are ever accessed, a single qutrit is used for the work register, instead of 5 qubits, to realise a hybrid qubit-qutrit system. So the whole factorization is done on 1 qubit + 1 qutrit. [1] https://en.wikipedia.org/wiki/Integer_factorization_records#cite_note-23 https://en.wikipedia.org/wiki/Integer_factorization_records#...