Plot a comparison between Short\'s algorithm and the general number field sieve

Question

Plot a comparison between Short's algorithm and the general number field sieve algorithm. What does this mean in context of Big O Notation? On a quantum computer, to factor an integer N, Short's algorithm runs in polynomial time (the time taken is polynomial in log N, which is the size of the input). Specifically it takes time 0((log A/)3), demonstrating that the integer factorization problem can be efficiently solved on a quantum computer. This is exponentially faster than the most efficient known classical factoring algorithm, the general number field sieve, which works in sub-exponential time - about

Explanation / Answer

Dear... Shor's algorithm: Shor's algorithm is a quantum algorithm for integer factorizations. It solves about an integer N and find its prime factors. It was demonstrated by a group at IBM, who factored 15 into 3 × 5, using an NMR implementation of a quantum computer with 7 qubits. From the given data, the algorithm is to find a square root b of 1, other than 1 and ? 1; such a b will lead to a factorization of N, as in other factoring algorithms like the quadratic sieve. Procedure for Shor's algorithm: Pick a random number a

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