منابع مشابه
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 usual ...
متن کاملar 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...
متن کاملFactoring with n + 2 clean qubits and n − 1 dirty qubits
We present reversible classical circuits for performing various arithmetic operations aided by dirty ancillae (i.e. extra qubits in an unknown state that must be restored before the circuit ends). We improve the number of clean qubits needed to factor an n-bit number with Shor’s algorithm [12] from 2n + 2 [15, 8] to n + 2, and the total number of qubits needed from 2n+2 to 2n+ 1, without increa...
متن کاملFactoring using $2n+2$ qubits with Toffoli based modular multiplication
We describe an implementation of Shor’s quantum algorithm to factor n-bit integers using only 2n+2 qubits. In contrast to previous space-optimized implementations, ours features a purely Toffoli based modular multiplication circuit. The circuit depth and the overall gate count are in O(n3) and O(n3 logn), respectively. We thus achieve the same space and time costs as Takahashi et al. [1], while...
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ژورنال
عنوان ژورنال: Scientific Reports
سال: 2013
ISSN: 2045-2322
DOI: 10.1038/srep03023