Related papers: Factoring integers with Young's N-slit interferome…
We construct an analog computer based on light interference to encode the hyperbolic function f({\zeta}) = 1/{\zeta} into a sequence of skewed curlicue functions. The resulting interferogram when scaled appropriately allows us to find the…
The scheme of Clauser and Dowling (Phys. Rev. A 53, 4587 (1996)) for factoring $N$ by means of an N-slit interference experiment is translated into an experiment with a single Mach-Zehnder interferometer. With dispersive phase shifters the…
Young's double-slit experiment requires two waves produced simultaneously at two different points in space. In quantum mechanics the waves correspond to a single quantum object, even as complex as a big molecule. An interference is present…
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"…
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…
Recent theoretical results confirm that quantum theory provides the possibility of new ways of performing efficient calculations. The most striking example is the factoring problem. It has recently been shown that computers that exploit…
Factorization of numbers with the help of Gauss sums relies on an intimate relationship between the maxima of these functions and the factors. Indeed, when we restrict ourselves to integer arguments of the Gauss sum we profit from a…
Thomas Young's slit experiment lies at the heart of classical interference and quantum mechanics. Over the last fifty years, it has been shown that particles (e.g. photons, electrons, large molecules), even individual particles, generate an…
The arithmetic problem of factoring an integer $N$ can be translated into the physics of a quantum device, a result that supports P\'olya's and Hilbert's conjecture to prove Riemann's hypothesis. The energies of this system, being…
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…
An algorithm is given to factor an integer with $N$ digits in $\ln^m N$ steps, with $m$ approximately 4 or 5. Textbook quadratic sieve methods are exponentially slower. An improvement with the aid of an a particular function would provide a…
A theoretical model of a quantum device which can factorize any number N in two steps i.e. by preparing an input state and performing a measurement is discussed. The analysis reveals that the duration of state preparation and measurement is…
If the states of spins in solids can be created, manipulated, and measured at the single-quantum level, an entirely new form of information processing, quantum computing, will be possible. We first give an overview of quantum information…
We define an approximate version of the Fourier transform on $2^L$ elements, which is computationally attractive in a certain setting, and which may find application to the problem of factoring integers with a quantum computer as is…
We show that $n$-bit integers can be factorized by independently running a quantum circuit with $\tilde{O}(n^{3/2})$ gates for $\sqrt{n}+4$ times, and then using polynomial-time classical post-processing. The correctness of the algorithm…
We report on a universal method to measure the genuine indistinguishability of n-photons - a crucial parameter that determines the accuracy of optical quantum computing. Our approach relies on a low-depth cyclic multiport interferometer…
In the experiments considered here, we measure the y-component of momentum for a particle passing through a system of slits. The source-slit system is the preparation apparatus that determines the state vector. Recognizing that a system of…
A simple variation of the traditional Young's double slit experiment can demonstrate several subtleties of interference with polarized light, including Berry and Pancharatnam's phase. Since the position of the fringes depends on the…
A proposal for a scalable, solid-state implementation of a quantum computer is presented. Qubits are fluorine nuclear spins in a solid crystal of fluorapatite [Ca_5 F(PO_4)_3] with resonant frequencies separated by a large field gradient.…
To factor an integer N, given that it is equal to the product of two primes, it suffices to find an integer d satisfying a certain simple numerical test. In this approach, the factorization problem equates to the problem of designing an…