Factoring numbers with a single interferogram
arXiv:1506.02907 · doi:10.1103/PhysRevA.83.020304
Abstract
We construct an analog computer based on light interference to encode the hyperbolic function f(ζ) = 1/ζ into a sequence of skewed curlicue functions. The resulting interferogram when scaled appropriately allows us to find the prime number decompositions of integers. We implement this idea exploiting polychromatic optical interference in a multipath interferometer and factor seven-digit numbers. We give an estimate for the largest number that can be factored by this scheme.
4 pages, 2 figures
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- Multipath Correlation Interference and Controlled-NOT Gate Simulation with a Thermal Source
- Characterization of two distant double-slits by chaotic light second-order interference
- Spatial interference between pairs of disjoint optical paths with a single chaotic source
- Factorization of numbers with Gauss sums: II. Suggestions for implementations with chirped laser pulses
- Analogue algorithm for parallel factorization of an exponential number of large integers II. Optical implementation
- Chirped quasi-phase-matching with Gauss sums for production of biphotons
- Distance sensing emerging from second-order interference of thermal light
- Analogue algorithm for parallel factorization of an exponential number of large integers I. Theoretical description
- The physics of thermal light second-order interference beyond coherence
- Factorization of numbers with Gauss sums: III. Algorithms with Entanglement
- Ghost factors in Gauss-sum factorization with transmon qubits
- Simple wave-optical superpositions as prime number sieves
- Number-theoretic expressions obtained through analogy between prime factorization and optical interferometry
- An optical Eratosthenes' sieve for large prime numbers