Related papers: Multiplication with Fourier Optics Simulating 16-b…
We present a novel set of reversible modular multipliers applicable to quantum computing, derived from three classical techniques: 1) traditional integer division, 2) Montgomery residue arithmetic, and 3) Barrett reduction. Each multiplier…
Optical computing harnesses the speed of light to perform vector-matrix operations efficiently. It leverages interference, a cornerstone of quantum computing algorithms, to enable parallel computations. In this work, we interweave quantum…
In calculating integral or discrete transforms, use has been made of fast algorithms for multiplying vectors by matrices whose elements are specified as values of special (Chebyshev, Legendre, Laguerre, etc.) functions. The currently…
Digital cameras and displays utilise picture elements (pixels) that perform a single function: detecting or emitting light intensity. To exploit the full information content of electromagnetic waves, more advanced elements are required.…
Since simulating quantum computers requires exponentially more classical resources, efficient algorithms are extremely helpful. We analyze algorithms that create single qubit and specific controlled qubit matrix representations of gates.…
Montgomery modular multiplication is widely-used in public key cryptosystems (PKC) and affects the efficiency of upper systems directly. However, modulus is getting larger due to the increasing demand of security, which results in a heavy…
A common starting point of traditional quantum algorithm design is the notion of a universal quantum computer with a scalable number of qubits. This convenient abstraction mirrors classical computations manipulating finite sets of symbols,…
This paper proposes four quadrant analog multiplier using CMOS-memristor circuit. Currently, there are plenty of analog multipliers using resistors and CMOS transistors. They can attain perfect multiplication but have several disadvantages…
A large number of applications in classical and quantum photonics require the capability of implementing arbitrary linear unitary transformations on a set of optical modes. In a seminal work by Reck et al. it was shown how to build such…
This paper describes an integer multiplier for the orbital angular momentum (OAM) of light through the parallel implementation of multiple circular-sector transformations, whereby the cross-sectional circular shape of the OAM mode is…
A scheme to encode arbitrarily long integer pairs on degenerate optical parametric oscillations multiplexed in time is proposed. The classical entanglement between the polarization directions and the phases of the oscillating pulses,…
A systematic method for simulating small-scale quantum circuits by use of linear optical devices is presented. It relies on the representation of several quantum bits by a single photon, and on the implementation of universal quantum gates…
Multiplication is an indispensable operation in most of digital signal processing systems. Recently, many systems need to execute different types of algorithms on a multiplier. Therefore, it needs complicated computation and large area…
Manufacturing end-of-fiber optical components able to realize optical functions ranging from a simple lens to more complex functions such as mode selective components is a decisive but \emph{a priori} complex task owing to the fiber core…
We demonstrate a new computational illumination technique that achieves large space-bandwidth-time product, for quantitative phase imaging of unstained live samples in vitro. Microscope lenses can have either large field of view (FOV) or…
We present recursive multiport schemes for implementing quantum Fourier transforms and the inversion step in Grover's algorithm on an integrated linear optics device. In particular, each scheme shows how to execute a quantum operation on…
Fourier Ptychographic Microscopy (FPM) is a computational technique that achieves a large space-bandwidth product imaging. It addresses the challenge of balancing a large field of view and high resolution by fusing information from multiple…
Nanoscale integrated photonic devices and circuits offer a path to ultra-low power computation at the few-photon level. Here we propose an optical circuit that performs a ubiquitous operation: the controlled, random-access readout of a…
Fourier ptychographic microscopy (FPM) is a recently developed imaging modality that uses angularly varying illumination to extend a system performance beyond the limit defined by its optical elements. The FPM technique applies a novel…
We introduce a novel parameterization of complex unitary matrices, which allows for the efficient photonic implementation of arbitrary linear discrete unitary operators. The proposed architecture is built on factorizing an $N \times N$…