Related papers: QFT-based Homogenization
Test-time finetuning (TTFT) is a rapidly evolving paradigm that adapts a language model to each prompt by retrieving related sequences, updating the model on them, and then evaluating the prompt. However, TTFT is only practical if it is…
Conventional mutual information (MI) based feature selection (FS) methods are unable to handle heterogeneous feature subset selection properly because of data format differences or estimation methods of MI between feature subset and class…
Fourier Holographic Reduced Representations (FHRR) provide a compositional framework for encoding structured information with complex-valued hypervectors. FHRR rely on floating-point arithmetic, which limits their efficiency and…
The post-training quantization (PTQ) challenge of bringing quantized neural net accuracy close to original has drawn much attention driven by industry demand. Many of the methods emphasize optimization of a specific degree-of-freedom (DoF),…
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…
In this thesis we investigate two new Amplified Quantum Transforms. In particular we create and analyze the Amplified Quantum Fourier Transform (Amplified-QFT) and the Amplified-Haar Wavelet Transform. First, we provide a brief history of…
Density-functional theory (DFT) has revolutionized computer simulations in chemistry and material science. A faithful implementation of the theory requires self-consistent calculations. However, this effort involves repeatedly diagonalizing…
The quantum Fourier transform (QFT) is the principal algorithmic tool underlying most efficient quantum algorithms. We present a generic framework for the construction of efficient quantum circuits for the QFT by ``quantizing'' the…
The fractional Fourier transform (FrFT), a fundamental operation in physics that corresponds to a rotation of phase space by any angle, is also an indispensable tool employed in digital signal processing for noise reduction. Processing of…
We propose a new quantum state reconstruction method that combines ideas from compressed sensing, non-convex optimization, and acceleration methods. The algorithm, called Momentum-Inspired Factored Gradient Descent (\texttt{MiFGD}), extends…
Fast Fourier Transforms (FFTs) are exploited in a wide variety of fields ranging from computer science to natural sciences and engineering. With the rising data production bandwidths of modern FFT applications, judging best which…
In recent year, quantum image processing got a lot of attention in the field of image processing due to opportunity to place huge image data in quantum Hilbert space. Hilbert space or Euclidean space has infinite dimension to locate and…
The Fourier Transform is one of the most important linear transformations used in science and engineering. Cooley and Tukey's Fast Fourier Transform (FFT) from 1964 is a method for computing this transformation in time $O(n\log n)$.…
Quantum state tomography is a central technique for the characterization and verification of quantum systems. Standard tomography is widely used for low-dimensional systems, but for larger systems, it becomes impractical due to the…
Hamiltonian moments in Fourier space - expectation values of the unitary evolution operator under a Hamiltonian at different times - provide a convenient framework to understand quantum systems. They offer insights into the energy…
Neural network quantization is widely used to reduce model inference complexity in real-world deployments. However, traditional integer quantization suffers from accuracy degradation when adapting to various dynamic ranges. Recent research…
We propose a technique for performing quantum state tomography of photonic polarization-encoded multi-qubit states. Our method uses a single rotating wave plate, a polarizing beam splitter and two photon-counting detectors per photon mode.…
Quantum key distribution (QKD) and quantum message encryption protocols promise a secure way to distribute information while detecting eavesdropping. However, current protocols may suffer from significantly reduced eavesdropping protection…
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…
Fourier representations play a central role in operator learning methods for partial differential equations and are increasingly being explored in quantum machine learning architectures. The classical fast Fourier transform (FFT),…