Factoring 51 and 85 with 8 qubits
نویسندگان
چکیده
We construct simplified quantum circuits for Shor's order-finding algorithm for composites N given by products of the Fermat primes 3, 5, 17, 257, and 65537. Such composites, including the previously studied case of 15, as well as 51, 85, 771, 1285, 4369, … have the simplifying property that the order of a modulo N for every base a coprime to N is a power of 2, significantly reducing the usual phase estimation precision requirement. Prime factorization of 51 and 85 can be demonstrated with only 8 qubits and a modular exponentiation circuit consisting of no more than four CNOT gates.
منابع مشابه
ar X iv : 1 30 4 . 01 28 v 1 [ qu an t - ph ] 3 0 M ar 2 01 3 Factoring 51 and 85 with 8 qubits
We construct simplified quantum circuits for Shor’s order-finding algorithm for composites N given by products of the Fermat primes 3, 5, 17, 257, and 65537. Such composites, including the previously studied case of 15, as well as 51, 85, 771, 1285, 4369, . . . have the simplifying property that the order of a modulo N for every base a coprime to N is a power of 2, significantly reducing the us...
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