Circuit for Shor's algorithm using 2n+3 gubits
We try to minimize the number of qubits needed to factor an integer of n bits using Shor's algorithm on a quantum computer. We introduce a circuit which uses 2n + 3 qubits and O(n(3)lg(n)) elementary quantum gates in a depth of O(n(3)) to implement the factorization algorithm. The circuit is computable in polynomial time on a classical computer and is completely general as it does not rely on any property of the number to be factored.
factorization quantum circuits modular arithmetics