Related papers: Multiplication with Fourier Optics Simulating 16-b…
The technique for hardware multiplication based upon Fourier transformation has been introduced. The technique has the highest efficiency on multiplication units with up to 8 bit range. Each multiplication unit is realized on base of the…
Optics is a promising platform in which to help realise the next generation of fast, parallel and energy-efficient computation. We demonstrate a reconfigurable free-space optical multiplier that is capable of over 3000 computations in…
An efficient numerical algorithm is presented for massively parallel simulations of dispersion-managed wavelength-division-multiplexed optical fiber systems. The algorithm is based on a weak nonlinearity approximation and independent…
In recent years, with the rapid development of electro-optic modulators, optical computing has become a potential excellent candidate for various computing tasks. New structures and devices for optical computing are emerging one after…
Modular arithmetic is widely used in crytography and symbolic computation. This paper presents a vectorized Montgomery algorithm for modular multiplication, the key to fast modular arithmetic, that fully utilizes the SIMD instructions. We…
Unitary Fourier transform lies at the core of the multitudinous computational and metrological algorithms. Here we show experimentally how the unitary Fourier transform-based phase estimation protocol, used namely in quantum metrology, can…
Shor's algorithm for the prime factorization of numbers provides an exponential speedup over the best known classical algorithms. However, nontrivial practical applications have remained out of reach due to experimental limitations. The…
CMOS-transistors circuits have been used as a conventional approach for designing an analog multiplier in modern era of industrial electronics. However, previous studies have shown, that based on the working region of transistors, such as…
Neuromorphic computing describes the use of VLSI systems to mimic neuro-biological architectures and is also looked at as a promising alternative to the traditional von Neumann architecture. Any new computing architecture would need a…
All-quantum signal processing techniques are at the core of the successful advancement of most information-based quantum technologies. This paper develops coherent and comprehensive methodologies and mathematical models to describe Fourier…
Additive Fourier Transform is sdudied. A fast multiplication algorithm for polynomials over the binary field is given. The bit complexity of the algorithm is $O(n(log n)(\log\log n)^2)$.
We present some basic integer arithmetic quantum circuits, such as adders and multipliers-accumulators of various forms, as well as diagonal operators, which operate on multilevel qudits. The integers to be processed are represented in an…
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…
Resolving the details of an object from coarse-scale measurements is a classical problem in applied mathematics. This problem is usually formulated as extrapolating the Fourier transform of the object from a bounded region to the entire…
We give an $O(N\cdot \log N\cdot 2^{O(\log^*N)})$ algorithm for multiplying two $N$-bit integers that improves the $O(N\cdot \log N\cdot \log\log N)$ algorithm by Sch\"{o}nhage-Strassen. Both these algorithms use modular arithmetic.…
Modular integer arithmetic occurs in many algorithms for computer algebra, cryptography, and error correcting codes. Although recent microprocessors typically offer a wide range of highly optimized arithmetic functions, modular integer…
We report an experimental demonstration of a complied version of Shor's algorithm using four photonic qubits. We choose the simplest instance of this algorithm, that is, factorization of N=15 in the case that the period $r=2$ and exploit a…
Fast algorithms for integer and polynomial multiplication play an important role in scientific computing as well as in other disciplines. In 1971, Sch{\"o}nhage and Strassen designed an algorithm that improved the multiplication time for…
Fourier ptychographic microscopy enables gigapixel-scale imaging, with both large field-of-view and high resolution. Using a set of low-resolution images that are recorded under varying illumination angles, the goal is to computationally…
In this article, we proposed a programmable 16-channel photonic solver for quadratic unconstrained binary optimization (QUBO) problems. The solver is based on a hybrid optoelectronic scheme including a photonic chip and the corresponding…