Related papers: Factoring numbers with a single interferogram
High-dimensional entanglement offers a variety of advantages for both fundamental and applied applications in quantum information science. A central building block for such applications is a programmable processor of entangled states, which…
Programmable linear optical interferometers are important for classical and quantum information technologies, as well as for building hardware-accelerated artificial neural networks. Recent results showed the possibility of constructing…
We introduce a programmable 8-port interferometer with the recently proposed error-tolerant architecture capable of performing a broad class of transformations. The interferometer has been fabricated with femtosecond laser writing and it is…
We investigate prime factorization from two perspectives: quantum annealing and computational algebraic geometry, specifically Gr\"obner bases. We present a novel scalable algorithm which combines the two approaches and leads to the…
In this paper, we present an approach to integer factorization using distributed representations formed with Vector Symbolic Architectures. The approach formulates integer factorization in a manner such that it can be solved using neural…
Shor's quantum factoring algorithm finds the prime factors of a large number exponentially faster than any other known method a task that lies at the heart of modern information security, particularly on the internet. This algorithm…
Quantum algorithms are at the heart of the ongoing efforts to use quantum mechanics to solve computational problems unsolvable on ordinary classical computers. Their common feature is the use of genuine quantum properties such as…
Inverse design coupled with adjoint optimization is a powerful method to design on-chip nanophotonic devices with multi-wavelength and multi-mode optical functionalities. Although only two simulations are required in each iteration of this…
We investigate the problem of factorization of large numbers on a quantum computer which we imagine to be realized within a linear ion trap. We derive upper bounds on the size of the numbers that can be factorized on such a quantum…
Factoring large integers using a quantum computer is an outstanding research problem that can illustrate true quantum advantage over classical computers. Exponential time order is required in order to find the prime factors of an integer by…
We propose two algorithms to factor numbers using Gauss sums and entanglement: (i) in a Shor-like algorithm we encode the standard Gauss sum in one of two entangled states and (ii) in an interference algorithm we create a superposition of…
We explore applications of quantum computing for radio interferometry and astronomy using recent developments in quantum image processing. We evaluate the suitability of different quantum image representations using a toy quantum computing…
We propose a photonic native procedure for computing the QR factorization of a matrix using a programmable unitary interferometer mesh. The method configures the mesh through a sequence of local power routing steps within tunable two mode…
We have developed a framework to convert an arbitrary integer factorization problem to an executable Ising model by first writing it as an optimization function and then transforming the k-bit coupling ($k\geq 3$) terms to quadratic terms…
Disentanglement of constituent factors of a sensory signal is central to perception and cognition and hence is a critical task for future artificial intelligence systems. In this paper, we present a compute engine capable of efficiently…
The number of steps any classical computer requires in order to find the prime factors of an $l$-digit integer $N$ increases exponentially with $l$, at least using algorithms known at present. Factoring large integers is therefore…
Upcoming radio interferometers are aiming to image the sky at new levels of resolution and sensitivity, with wide-band image cubes reaching close to the Petabyte scale for SKA. Modern proximal optimization algorithms have shown a potential…
We consider the problem of factoring permutations as a product of special types of transpositions, namely, those transpositions involving two positions with bounded distances. In particular, we investigate the minimum number, $\delta$, such…
Classical, interferometric, optical lithography is diffraction limited to writing features of a size lambda/2 or greater, where lambda is the optical wavelength. Using nonclassical photon number states, entangled N at a time, we show that…
We have realized an interferometer using a thermal cloud of magnetically trapped rubidium 87 atoms on a chip. The interferometer resembles a Ramsey interferometer with a state selective spatial splitting of the two internal states as…