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We propose and analyze the design of a programmable photonic integrated circuit for high-fidelity quantum computation and simulation. We demonstrate that the reconfigurability of our design allows us to overcome two major impediments to…
We present a method to synthesize phase screens for multi-wavelength, atmospheric wave optics simulations using fast Fourier transforms. We validate our work by comparing the theoretical, two-wavelength optical path length structure…
This paper shows that it is possible to improve the computational cost, the memory requirements and the accuracy of Quick Fourier Transform (QFT) algorithm for power-of-two FFT (Fast Fourier Transform) just introducing a slight modification…
Computer algebra systems are complex software systems that cover a wide range of scientific and practical problems. However, the absolute coverage cannot be achieved. Often, it is required to create a user extension for an existing computer…
A digital computer is generally believed to be an efficient universal computing device; that is, it is believed able to simulate any physical computing device with an increase in computation time of at most a polynomial factor. This may not…
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"…
We propose a scheme to mimic and directly measure the fractional particle number in a generalized Su-Schrieffer-Heeger model with ultracold fermions in one-dimensional optical lattices. We show that the fractional particle number in this…
Extensions of the split-step Fourier method (SSFM) for Schr\"odinger-type pulse propagation equations for simulating femto-second pulses in single- and two-mode optical communication fibers are developed and tested for Gaussian pulses. The…
Image processing has become a critical technology in a variety of science and engineering disciplines. While most image processing is performed digitally, optical analog processing has the advantages of being low-power and high-speed though…
The quantum Fourier transform (QFT) brings efficiency in many respects, especially usage of resource, for most operations on quantum computers. In this study, the existing QFT-based and non-QFT-based quantum arithmetic operations are…
This paper deals with circulant matrices. It is shown that a circulant matrix can be multiplied by a vector in time O(n log(n)) in a ring with roots of unity without making use of an FFT algorithm. With our algorithm we achieve a speedup of…
We propose a new formulation of the problem of prime factorization of integers. With replica exchange Monte Carlo simulation, the behavior which is seemed to indicate exponential computational hardness is observed. But this formulation is…
For bilinear Fourier multipliers that contain some oscillatory factors, boundedness of the operators between Lebesgue spaces is given including endpoint cases. Sharpness of the result is also considered.
Universal quantum computation may be realized based on quantum walk, by formulating it as a scattering problem on a graph. In this paper, we simulate quantum gates through electric circuits, following a recent report that a one-dimensional…
Photons are natural carriers of high-dimensional quantum information, and, in principle, can benefit from higher quantum information capacity and noise-resilience. However, schemes to generate the resources required for high-dimensional…
This paper discusses the compilation, optimization, and error mitigation of quantum algorithms, essential steps to execute real-world quantum algorithms. Quantum algorithms running on a hybrid platform with QPU and CPU/GPU take advantage of…
The rapidly increasing size of deep-learning models has caused renewed and growing interest in alternatives to digital computers to dramatically reduce the energy cost of running state-of-the-art neural networks. Optical matrix-vector…
We have developed an algorithm that constructs a model of a reconfigurable optical interferometer, independent of specific architectural constraints. The programming of unitary transformations on the interferometer's optical modes relies on…
Phase retrieval, i.e., the problem of recovering a function from the squared magnitude of its Fourier transform, arises in many applications such as X-ray crystallography, diffraction imaging, optics, quantum mechanics, and astronomy. This…
The computational demands of modern AI have spurred interest in optical neural networks (ONNs) which offer the potential benefits of increased speed and lower power consumption. However, current ONNs face various challenges,most…