Related papers: Fourier-based quantum signal processing
Using normalized Hermite functions, we construct bases in the space of square integrable functions on the unit circle ($L^2(\mathcal C)$) and in $l_2(\mathbb Z)$, which are related to each other by means of the Fourier transform and the…
Some properties of the fractional Fourier transform, which is used in information processing, are presented in connection with the tomography transform of optical signals. Relation of the Green function of the quantum harmonic oscillator to…
We introduce novel algorithms for the quantum simulation of molecular systems which are asymptotically more efficient than those based on the Trotter-Suzuki decomposition. We present the first application of a recently developed technique…
The agenda of quantum algorithmic information theory, ordered `top-down,' is the quantum halting amplitude, followed by the quantum algorithmic information content, which in turn requires the theory of quantum computation. The fundamental…
Fundamental matrix operations and solving linear systems of equations are ubiquitous in scientific investigations. Using the "Sender-Receiver" model, we propose quantum algorithms for matrix operations such as matrix-vector product,…
Quantum computing has the potential to solve many complex algorithms in the domains of optimization, arithmetics, structural search, financial risk analysis, machine learning, image processing, and others. Quantum circuits built to…
Quantum computing is a winsome field that concerns with the behaviour and nature of energy at the quantum level to improve the efficiency of computations. In recent years, quantum computation is receiving much attention for its capability…
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 work we take a closer look at the algebraic-operator correspondence between the momentum space and the position space which defines the form of the canonical momentum operator in position space in Quantum Mechanics (QM). Starting…
The partial oracles framework is a quantum search algorithm that has the potential to exceed the quadratic speedup of Grover's algorithm, up to a theoretical maximum of an exponential speedup. Until now, however, the framework has lacked an…
We present a probabilistic quantum processor for qudits. The processor itself is represented by a fixed array of gates. The input of the processor consists of two registers. In the program register the set of instructions (program) is…
We construct a quantum-inspired classical algorithm for computing the permanent of Hermitian positive semidefinite matrices, by exploiting a connection between these mathematical structures and the boson sampling model. Specifically, the…
In this paper, we consider a quantum algorithm for solving the following problem: ``Suppose $f$ is a function given as a black box (that is also called an oracle) and $f$ is invariant under some AND-mask. Examine a property of $f$ by…
The process of translating a quantum algorithm into a form suitable for implementation on a quantum computing platform is crucial but yet challenging. This entails specifying quantum operations with precision, a typically intricate task. In…
Until high-fidelity quantum computers with a large number of qubits become widely available, classical simulation remains a vital tool for algorithm design, tuning, and validation. We present a simulator for the Quantum Approximate…
Quantum symmetrization is the task of transforming a non-strictly increasing list of $n$ integers into an equal superposition of all permutations of the list (or more generally, performing this operation coherently on a superposition of…
In this paper, a quantum algorithm based on gaussian process regression model is proposed. The proposed quantum algorithm consists of three sub-algorithms. One is the first quantum subalgorithm to efficiently generate mean predictor. The…
Quantum computing has been increasingly applied in nuclear physics. In this work, we combine quantum computing with the complex scaling method to address the resonance problem. Due to the non-Hermiticity introduced by complex scaling,…
- In this paper we present a method to compute the coefficients of the fractional Fourier transform (FrFT) on a quantum computer using quantum gates of polynomial complexity of the order O(n^3). The FrFt, a generalization of the DFT, has…
As the most central and computationally intensive component of deep neural networks, the execution efficiency of matrix multiplication directly determines the training and inference performance of models. Harnessing the parallel processing…