Related papers: Quantum signal processing and nonlinear Fourier an…
A non trace-preserving map describing a probabilistic but heralded noiseless linear amplifier has recently been proposed and experimentally demonstrated. Here, we exhibit another remarkable feature of this peculiar transformation, namely…
We provide a rigorous derivation of a quantum filter for the case of multiple measurements being made on a quantum system. We consider a class of measurement processes which are functions of bosonic field operators, including combinations…
Quantum processors enable computational speedups for machine learning through parallel manipulation of high-dimensional vectors. Early demonstrations of quantum machine learning have focused on processing information with qubits. In such…
In this study, we apply 1D quantum convolution to address the task of time series forecasting. By encoding multiple points into the quantum circuit to predict subsequent data, each point becomes a feature, transforming the problem into a…
In this article, we study the properties of the nonlinear Fourier spectrum in order to gain better control of the temporal support of the signals synthesized using the inverse nonlinear Fourier transform (NFT). In particular, we provide…
We introduce a particular nonlinear generalization of quantum mechanics which has the property that it is exactly solvable in terms of the eigenvalues and eigenfunctions of the Hamiltonian of the usual linear quantum mechanics problem. We…
Signal processing stands as a pillar of classical computation and modern information technology, applicable to both analog and digital signals. Recently, advancements in quantum information science have suggested that quantum signal…
Fourier series multiscale method, a concise and efficient analytical approach for multiscale computation, will be developed out of this series of papers. The second paper is concerned with simultaneous approximation to functions and their…
This paper introduces and analyzes symmetric and anti-symmetric quantum binary functions. Generally, such functions uniquely convert a given computational basis state into a different basis state, but with either a plus or a minus sign.…
Frequency is a central concept in Mathematics, Physics, and Signal Processing. It is the main tool for describing the oscillatory behavior of signals, which is usually argued to be the manifestation of some of their key features, depending…
The continuous quantum measurement within the probability representation of quantum mechanics is discussed. The partial classical propagator of the symplectic tomogram associated to a particular measurement outcome is introduced, for which…
Quantum computing and quantum sensing represent two distinct frontiers of quantum information science. In this work, we harness quantum computing to solve a fundamental and practically important sensing problem: the detection of weak…
Quantum phase estimation (QPE) is the key subroutine of several quantum computing algorithms as well as a central ingredient in quantum computational chemistry and quantum simulation. While QPE strategies have focused on the estimation of a…
Quantum mechanics requires the operation of quantum computers to be unitary, and thus makes it important to have general techniques for developing fast quantum algorithms for computing unitary transforms. A quantum routine for computing a…
The quasilinearization method (QLM) of solving nonlinear differential equations is applied to the quantum mechanics by casting the Schr\"{o}dinger equation in the nonlinear Riccati form. The method, whose mathematical basis in physics was…
In this paper, we focus on the links between Boolean function theory and quantum computing. In particular, we study the notion of what we call fully-balanced functions and analyse the Fourier--Hadamard and Walsh supports of those functions…
We propose an alternative approach that avoids the nonlinear equations for the Fourier coefficients that appear in the method of harmonic balance. We apply it to two simple illustrative examples.
We propose a universal quantum circuit design that can estimate any arbitrary one-dimensional periodic functions based on the corresponding Fourier expansion. The quantum circuit contains N-qubits to store the information on the different…
Starting from square-integrable wave functions on a Lie group, we build an invertible Fourier transform mapping them on wave functions on the dual of the Lie algebra. This is a group-theoretic version of the map from position space to…
We introduce a general framework of phase reduction theory for quantum nonlinear oscillators. By employing the quantum trajectory theory, we define the limit-cycle trajectory and the phase according to a stochastic Schr\"{o}dinger equation.…