# Analogue algorithm for parallel factorization of an exponential number of large integers: I - theoretical description

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**Analogue algorithm for parallel factorization of an exponential number of large integers : I - theoretical description.** / Tamma, Vincenzo.

Research output: Contribution to journal › Article

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*Quantum Information Processing*, vol. 15, no. 12, pp. 5259-5280. https://doi.org/10.1007/s11128-015-1190-y

### APA

*Quantum Information Processing*,

*15*(12), 5259-5280. https://doi.org/10.1007/s11128-015-1190-y

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TY - JOUR

T1 - Analogue algorithm for parallel factorization of an exponential number of large integers

T2 - I - theoretical description

AU - Tamma, Vincenzo

PY - 2016/12/1

Y1 - 2016/12/1

N2 - We describe a novel analogue algorithm that allows the simultaneous factorization of an exponential number of large integers with a polynomial number of experimental runs. It is the interference-induced periodicity of “factoring” interferograms measured at the output of an analogue computer that allows the selection of the factors of each integer. At the present stage, the algorithm manifests an exponential scaling which may be overcome by an extension of this method to correlated qubits emerging from n-order quantum correlations measurements. We describe the conditions for a generic physical system to compute such an analogue algorithm. A particular example given by an “optical computer” based on optical interference will be addressed in the second paper of this series (Tamma in Quantum Inf Process 11128:1189, 2015).

AB - We describe a novel analogue algorithm that allows the simultaneous factorization of an exponential number of large integers with a polynomial number of experimental runs. It is the interference-induced periodicity of “factoring” interferograms measured at the output of an analogue computer that allows the selection of the factors of each integer. At the present stage, the algorithm manifests an exponential scaling which may be overcome by an extension of this method to correlated qubits emerging from n-order quantum correlations measurements. We describe the conditions for a generic physical system to compute such an analogue algorithm. A particular example given by an “optical computer” based on optical interference will be addressed in the second paper of this series (Tamma in Quantum Inf Process 11128:1189, 2015).

KW - Quantum computation

KW - Interference

KW - Algorithms

KW - Analogue computers

KW - Factorization

KW - Exponential sums

KW - Gauss sums

U2 - 10.1007/s11128-015-1190-y

DO - 10.1007/s11128-015-1190-y

M3 - Article

VL - 15

SP - 5259

EP - 5280

JO - Quantum Information Processing

JF - Quantum Information Processing

SN - 1570-0755

IS - 12

ER -

ID: 5090666