Circuit for Shor's algorithm using 2n+3 qubits

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 0(n3lg(n)) elementary quantum gates in a depth of 0(n3) 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.

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