Related papers: A quantum Fourier transform (QFT) based note detec…
While many classical algorithms rely on Laplace transforms, it has remained an open question whether these operations could be implemented efficiently on quantum computers. In this work, we introduce the Quantum Laplace Transform (QLT),…
An alternative quantum algorithm for the discrete logarithm problem is presented. The algorithm uses two quantum registers and two Fourier transforms whereas Shor's algorithm requires three registers and four Fourier transforms. A crucial…
One of the most promising and versatile approaches to creating new quantum algorithms is based on the quantum hidden subgroup (QHS) paradigm, originally suggested by Alexei Kitaev. This class of quantum algorithms encompasses the…
We describe an array of quantum gates implementing Shor's algorithm for prime factorization in a quantum computer. The array includes a circuit for modular exponentiation with several subcomponents (such as controlled multipliers, adders,…
Despite significant advances in quantum algorithms, quantum programs in practice are often expressed at the circuit level, forgoing helpful structural abstractions common to their classical counterparts. Consequently, as many quantum…
The Discrete Fourier Transform (DFT) is central to the analysis of uniformly sampled signals, yet many practical applications involve non-uniform sampling, requiring the Non-Uniform Discrete Fourier Transform (NUDFT). While quantum…
Quantum Signal Processing (QSP) and Quantum Singular Value Transformation (QSVT) currently stand as the most efficient techniques for implementing functions of block encoded matrices, a central task that lies at the heart of most prominent…
Quantum computing with qudits, quantum systems with $d > 2$ levels, offers a powerful extension beyond qubits, expanding the computational possibilities of quantum systems, allowing the simplification of the implementation of several…
Quantum Image Processing (QIP)is an exciting new field showing a lot of promise as a powerful addition to the arsenal of Image Processing techniques. Representing image pixel by pixel using classical information requires an enormous amount…
Many quantum algorithms can be represented in a form of a classical circuit positioned between quantum Fourier transformations. Motivated by the search for new quantum algorithms, we turn to circuits where the latter transformation is…
This paper presents two efficient and stable algorithms for recovering phase factors in quantum signal processing (QSP), a crucial component of many quantum algorithms. The first algorithm, the ``Half Cholesky" method, which is based on…
Shor's factoring algorithm uses two quantum registers. By introducing more registers we show that the measured numbers in these registers which are of the same pre-measurement state, should be equal if the original Shor's complexity…
For the solution of partial differential equations (PDEs), we show that the quantum Fourier transform (QFT) can enable the design of quantum circuits that are particularly simple, both conceptually and with regard to hardware requirements.…
Quantum field theory (QFT) simulations are a potentially important application for noisy intermediate scale quantum (NISQ) computers. The ability of a quantum computer to emulate a QFT, therefore, constitutes a natural application-centric…
Simulating quantum computation on a classical computer is a difficult problem. The matrices representing quantum gates, and the vectors modeling qubit states grow exponentially with an increase in the number of qubits. However, by using a…
In recent decades, the field of quantum computing has experienced remarkable progress. This progress is marked by the superior performance of many quantum algorithms compared to their classical counterparts, with Shor's algorithm serving as…
Quantum error mitigation (QEM) has emerged as a powerful tool for the extraction of useful quantum information from quantum devices. Here, we introduce the Subspace Noise Tailoring (SNT) algorithm, which efficiently combines the cheap cost…
We describe an efficient quantum algorithm for the quantum Schur transform. The Schur transform is an operation on a quantum computer that maps the standard computational basis to a basis composed of irreducible representations of the…
Quantum process tomography (QPT) methods aim at identifying a given quantum process. The present paper focuses on the estimation of a unitary process. This class is of particular interest because quantum mechanics postulates that the…
We present quantum algorithms for the simulation of quantum systems in one spatial dimension, which result in quantum speedups that range from superpolynomial to polynomial. We first describe a method to simulate the evolution of the…