Related papers: Multiplication with Fourier Optics Simulating 16-b…
We present a novel learning-based method to build a differentiable computational model of a real fluorescence microscope. Our model can be used to calibrate a real optical setup directly from data samples and to engineer point spread…
An approach reported recently by Alexandrov et al. on optical scatter imaging, termed digital Fourier microscopy (DFM), represents an adaptation of digital Fourier holography to selective imaging of biological matter. Holographic mode of…
It is demonstrated that Kerr frequency comb generation described by coupled mode equations can be numerically simulated using Fast Fourier Transform methods. This allows broadband frequency combs spanning a full octave to be efficiently…
The achievable data rates of current fiber-optic wavelength-division-multiplexing (WDM) systems are limited by nonlinear interactions between different subchannels. Recently, it was thus proposed to replace the conventional Fourier…
Fourier synthesis is one of the foundations of physical optics. Spatial Fourier optics is a basis for understanding optical imaging, microscopy, and holography. In conventional Fourier optics, the complex spatial field distribution in the…
We introduce two efficient algorithms for computing the partial Fourier transforms in one and two dimensions. Our study is motivated by the wave extrapolation procedure in reflection seismology. In both algorithms, the main idea is to…
There is a recent trend in artificial intelligence (AI) inference towards lower precision data formats down to 8 bits and less. As multiplication is the most complex operation in typical inference tasks, there is a large demand for…
Polynomial multiplication is a key algorithm underlying computer algebra systems (CAS) and its efficient implementation is crucial for the performance of CAS. In this paper we design and implement algorithms for polynomial multiplication…
We present a numerical method for the reconstruction and optimization of complex field synthesis using coherent pulse combination systems. A genetic algorithm utilizing a Fourier optics based propagation method is developed for accurate…
Multiplications are responsible for most of the computational cost involved in neural network training and inference. Recent research has thus looked for ways to reduce the cost associated with them. Inspired by Mogami (2020), we replace…
Compilation optimizes quantum algorithms performances on real-world quantum computers. To date, it is performed via classical optimization strategies. We introduce a class of quantum algorithms to perform compilation via quantum computers,…
Shor's algorithms for factorization and discrete logarithms on a quantum computer employ Fourier transforms preceding a final measurement. It is shown that such a Fourier transform can be carried out in a semi-classical way in which a…
In this paper, the authors propose the idea of a combined integer and floating point multiplier(CIFM) for FPGAs. The authors propose the replacement of existing 18x18 dedicated multipliers in FPGAs with dedicated 24x24 multipliers designed…
Prime factorization (P = M*N) is considered to be a promising application in quantum computations. We perform 4-bit factorization in experiments using a superconducting flux qubit toward quantum annealing. Our proposed method uses a…
We present conditions for the efficient simulation of a broad class of optical quantum circuits on a classical machine: this class includes unitary transformations, amplification, noise, and measurements. Various proposed schemes for…
This paper describes a method of calculating the transforms, currently obtained via Fourier and reverse Fourier transforms. The method allows calculating efficiently the transforms of a signal having an arbitrary dimension of the digital…
We show that a classical algorithm efficiently simulating the modular exponentiation circuit, for certain product state input and with measurements in a general product state basis at the output, can efficiently simulate Shor's factoring…
The Quantum Fourier Transform offers an interesting way to perform arithmetic operations on a quantum computer. We review existing Quantum Fourier Transform adders and multipliers and propose some modifications that extend their…
We have developed a concrete quantum simulation scheme and experimentally simulated a pairing model on an NMR quantum computer. The design of our experiment includes choosing an appropriate initial state in order to make our scheme scalable…
We investigate a modified split-step Fourier method (SSFM) by including low-pass filters in the linear steps. This method can simultaneously achieve a higher simulation accuracy and a slightly reduced complexity.