Factoring 51 and 85 with 8 qubits

Michael R. Geller; Zhongyuan Zhou

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Factoring 51 and 85 with 8 qubits

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arxiv 1304.0128 v1 pith:HH4O3QDE submitted 2013-03-30 quant-ph

Factoring 51 and 85 with 8 qubits

Michael R. Geller , Zhongyuan Zhou This is my paper

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keywords compositesqubitsalgorithmbasecasecircuitcircuitscnot

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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.

Factoring 51 and 85 with 8 qubits

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