Related papers: Fourier-based quantum signal processing
Quantum information processing and its subfield, quantum image processing, are rapidly growing fields as a result of advancements in the practicality of quantum mechanics. In this paper, we propose a quantum algorithm for processing…
Quantum computing can provide speedups in solving many problems as the evolution of a quantum system is described by a unitary operator in an exponentially large Hilbert space. Such unitary operators change the phase of their eigenstates…
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…
In this article, we compare the methods implementing the real-time evolution operator generated by a unitary diagonal matrix where its entries obey a known underlying real function. When the size of the unitary diagonal matrix is small, a…
Quantum Fourier transform (QFT) is a widely used building block for quantum algorithms, whose scalable implementation is challenging in experiments. Here, we propose a protocol of quadratic quantum Fourier transform (QQFT), considering cold…
We present a quantum algorithm for the simulation of molecular systems that is asymptotically more efficient than all previous algorithms in the literature in terms of the main problem parameters. As in previous work [Babbush et al., New…
Quantum Mechanics and Signal Processing in the line R, are strictly related to Fourier Transform and Weyl-Heisenberg algebra. We discuss here the addition of a new discrete variable that measures the degree of the Hermite functions and…
We present a new primitive for quantum algorithms that implements a discrete Hermite transform efficiently, in time that depends logarithmically in both the dimension and the inverse of the allowable error. This transform, which maps basis…
Quantum algorithms for diverse problems, including search and optimization problems, require the implementation of a reflection operator over a target state. Commonly, such reflections are approximately implemented using phase estimation.…
The results of quantum process tomography on a three-qubit nuclear magnetic resonance quantum information processor are presented, and shown to be consistent with a detailed model of the system-plus-apparatus used for the experiments. The…
We construct operator analogues of Hermite functions which form an orthonormal basis for the Hilbert space $ \mathcal{S}_2$ of Hilbert-Schmidt operators on $ L^2(\R^n).$ We use this orthonormal basis to define Fourier transform on $…
Quantum signal processing is a powerful framework in quantum algorithms, playing a central role in Hamiltonian simulation and related applications. The sequence of polynomials implemented at each step of this protocol provides a polynomial…
We propose an approach to factorize the time-evolution operator of a quantum system through a (finite) sequence of elementary operations that are time-ordered. Our proposal borrows from previous approaches based on Lie algebra techniques…
This paper introduces a factorization for the inverse of discrete Fourier integral operators that can be applied in quasi-linear time. The factorization starts by approximating the operator with the butterfly factorization. Next, a…
In this paper we present a novel approach to emulating a universal quantum computer with a classical system, one that uses a signal of bounded duration and amplitude to represent an arbitrary quantum state. The signal may be of any modality…
Quantum signal processing allows for quantum eigenvalue transformation with Hermitian matrices, in which each eigenspace component of an input vector gets transformed according to its eigenvalue. In this work, we introduce the multivariate…
Quantum Fourier Transform (QFT) plays a principal role in the development of efficient quantum algorithms. Since the number of quantum bits that can currently built is limited, while many quantum technologies are inherently three- (or more)…
The conventional Quantum Fourier Transform, with exponential speedup compared to the classical Fast Fourier Transform, has played an important role in quantum computation as a vital part of many quantum algorithms (most prominently, the…
The matrix functions can be defined by Cauchy's integral formula and can be approximated by the linear combination of inverses of shifted matrices using a quadrature formula. In this paper, we show a concrete construction of a framework to…
Probabilistic machine learning models are distinguished by their ability to integrate prior knowledge of noise statistics, smoothness parameters, and training data uncertainty. A common approach involves modeling data with Gaussian…