Related papers: Factoring numbers with a single interferogram

Let $P(m)$ denote the largest prime factor of an integer $m\geq 2$, and put $P(0)=P(1)=1$. For an integer $k\geq 2$, let $(F_{n}^{(k)})_{n\geq 2-k}$ be the $k-$generalized Fibonacci sequence which starts with $0,...,0,1$ ($k$ terms) and…

Motivated by recent proposals for quantum proof of work protocols, we investigate approaches for simulating linear optical interferometers using digital quantum circuits. We focus on a second quantisation approach, where the quantum…

Entangled photons can be used to make measurements with an accuracy beyond that possible with classical light. While most implementations of quantum metrology have used states made up of a single colour of photons, we show that entangled…

Let $T$ be a square matrix with a real spectrum, and let $f$ be an analytic function. The problem of the approximate calculation of $f(T)$ is discussed. Applying the Schur triangular decomposition and the reordering, one can assume that $T$…

Programmable photonic circuits of reconfigurable interferometers can be used to implement arbitrary operations on optical modes, facilitating a flexible platform for accelerating tasks in quantum simulation, signal processing, and…

We demonstrate optical interferometry beyond the limits imposed by the photon wavelength using 'triggered' entangled photon pairs from a semiconductor quantum dot. Interference fringes of the entangled biphoton state reveals a periodicity…

The optical elements comprised of sub-diffractive light scatterers, or metasurfaces, hold a promise to reduce the footprint and unfold new functionalities of optical devices. A particular interest is focused on metasurfaces for manipulation…

We introduce an algorithm to compute the functions belonging to a suitable set ${\mathscr F}$ defined as follows: $f\in {\mathscr F}$ means that $f(s,x)$, $s\in A\subset {\mathbb R}$ being fixed and $x>0$, has a power series expansion…

Shor's factoring algorithm is one of the most anticipated applications of quantum computing. However, the limited capabilities of today's quantum computers only permit a study of Shor's algorithm for very small numbers. Here we show how…

Quantum entanglement-based imaging promises significantly increased resolution by extending the spatial separation of optical collection apertures used in very-long-baseline interferometry for astronomy and geodesy. We report a table-top…

A configuration of light pulses is generated, together with emitters and receptors, that allows computing. The computing is extraordinarily high in number of flops per second, exceeding the capability of a quantum computer for a given size…

Sub-picosecond coincidence timing from nonlocal intensity interference of entangled photons allows quantum interferometry for plasmas. Using a warm plasma dispersion relation, we correlate phase measurement sensitivity with different plasma…

The light's image is the primary source of information carrier in nature. Indeed, a single photon's image possesses a vast information capacity that can be harnessed for quantum information processing. Our scheme for implementing quantum…

We propose a Heisenberg-limited quantum interferometer whose input is twin optical beams from which one or more photons have been indistinguishably subtracted. Such an interferometer can yield Heisenberg-limited performance while at the…

This paper builds on top of a paper we have published very recently, in which we have proposed a novel approach to prime factorization (PF) by quantum annealing, where 8,219,999=32,749x251 was the highest prime product we were able to…

This paper introduces quantum circuit methodologies for pointwise multiplication and convolution of complex functions, conceptualized as "processing through encoding". Leveraging known techniques, we describe an approach where multiple…

Matrix factorization methods are important tools in data mining and analysis. They can be used for many tasks, ranging from dimensionality reduction to visualization. In this paper we concentrate on the use of matrix factorizations for…

The availability of working quantum computers has led to several proposals and claims of quantum advantage. In 2023, this has included claims that quantum computers can successfully factor large integers, by optimizing the search for nearby…

High-order methods gain more and more attention in computational fluid dynamics. However, the potential advantage of these methods depends critically on the availability of efficient elliptic solvers. With spectral-element methods, static…

The probabilistic nature of single-photon sources and photon-photon interactions encourages encoding as much quantum information as possible in every photon for the purpose of photonic quantum information processing. Here, by encoding…