Related papers: Computing Shor's algorithmic steps with classical …
We report on the successful operation of an analogue computer designed to factor numbers. Our device relies solely on the interference of classical light and brings together the field of ultrashort laser pulses with number theory. Indeed,…
The derivation of a function is a fundamental tool for solving problems in calculus. Consequently, the motivations for investigating physical systems capable of performing this task are numerous. Furthermore, the potential to develop an…
The Quantum Fourier Transform (QFT) is a key component of many important quantum algorithms, most famously as being the essential ingredient in Shor's algorithm for factoring products of primes. Given its remarkable capability, one would…
Light scattering is one of the most important elementary processes in near-field optics. We build up the Born series for scattering by dielectric bodies with step boundaries. The Green function for a 2-dimensional homogeneous dielectric…
We propose an optical parallel computation similar to quantum computation that can be realized by introducing pseudorandom phase sequences into classical optical fields with two orthogonal modes. Based on the pseudorandom phase sequences,…
The growing demand for real-time data processing in applications such as neural networks and embedded control systems has spurred the search for faster, more efficient alternatives to traditional electronic systems. In response, we…
In this work we present a simple code to calculate tightly focused vectorial light fields (propagating and evanescent) generated by input fields that have arbitrary amplitude, phase and polarization. The program considers results from…
Quantum computers have the potential to perform computational tasks beyond the reach of classical machines. A prominent example is Shor's algorithm for integer factorization and discrete logarithms, which is of both fundamental importance…
We present two economical one-step error-correction protocols for multipartite polarization-entangled systems in a Greenberger-Horne-Zeilinger state. One uses spatial entanglement to correct errors in the polarization entanglement of an…
Quantum computation has attracted much attention since it was shown by Shor and Grover the possibility to implement quantum algorithms able to realize, respectively, factoring and searching in a faster way than any other known classical…
In this paper we generalize the quantum algorithm for computing short discrete logarithms previously introduced by Eker{\aa} so as to allow for various tradeoffs between the number of times that the algorithm need be executed on the one…
With the advancement of non-classical light sources such as single-photon and entangled-photon sources, innovative microscopy based on the quantum principles has been proposed over traditional microscopy. This paper introduces the…
We review the well-known polarization optics matrix methods, i.e., Jones and Stokes-Mueller calculus, and show how they can be formulated in terms of four-dimensional (4d) rotations of the four independent electromagnetic field quadratures.…
We develop an entangled-probe scattering theory, including quantum detection, that extends the scope of standard scattering approaches. We argue that these probes may be revolutionary in studying entangled matter such as unconventional…
We describe a quantum algorithm that solves combinatorial optimization problems by quantum simulation of a classical simulated annealing process. Our algorithm exploits quantum walks and the quantum Zeno effect induced by evolution…
We report the realization of a nuclear magnetic resonance (NMR) quantum computer which combines the quantum Fourier transform (QFT) with exponentiated permutations, demonstrating a quantum algorithm for order-finding. This algorithm has the…
We present improved quantum circuit for modular exponentiation of a constant, which is the most expensive operation in Shor's algorithm for integer factorization. While previous work mostly focuses on minimizing the number of qubits or the…
The polarisation of light is a powerful and widely used degree of freedom to encode information, both in classical and quantum applications. In particular, quantum information technologies based on photons are being revolutionised by the…
Coupled nonlinear Schr\"odinger equations model various physical phenomena, such as wave propagation in nonlinear optics, multi-component Bose-Einstein condensates, and shallow water waves. Despite their extensive applications, analytical…
Photonics has been a promising platform for implementing quantum technologies owing to its scalability and robustness. In this Letter, we demonstrate the encoding of information in 32 time bins or dimensions of a single photon. A practical…