Related papers: Quantum Algorithms Using the Curvelet Transform
This review paper is intended to give a useful guide for those who want to apply discrete wavelets in their practice. The notion of wavelets and their use in practical computing and various applications are briefly described, but rigorous…
We introduce new rounding methods to improve the accuracy of finite precision quantum arithmetic. These quantum rounding methods are applicable when multiple samples are being taken from a quantum program. We show how to use multiple…
Quantum computing is a promising new area of computing with quantum algorithms offering a potential speedup over classical algorithms if fault tolerant quantum computers can be built. One of the first applications of the classical computer…
This paper extends the quantum search class of algorithms to the multiple solution case. It is shown that, like the basic search algorithm, these too can be represented as a rotation in an appropriately defined two dimensional vector space.…
The optimal quantum control theory is employed to determine electric pulses capable of producing quantum gates with high fidelity (higher than 0.9997). Particularly, these quantum gates were chosen to perform the permutation algorithm (Z.…
Quantum computers can solve many number theory problems efficiently. Using the efficient quantum algorithm for order finding as an oracle, this paper presents an algorithm that computes the Carmichael function for any integer $N$ with a…
Machine learning algorithms perform well on identifying patterns in many different datasets due to their versatility. However, as one increases the size of the dataset, the computation time for training and using these statistical models…
Quantum algorithms have the potential to provide exponential speedups over some of the best known classical algorithms. These speedups may enable quantum devices to solve currently intractable problems such as those in the fields of…
Quantum entanglement is one of the core features of quantum theory. While it is typically revealed by measurements along carefully chosen directions, here we review different methods based on so-called random or randomized measurements.…
Finite-sum optimization has wide applications in machine learning, covering important problems such as support vector machines, regression, etc. In this paper, we initiate the study of solving finite-sum optimization problems by quantum…
Quantum computers use the quantum interference of different computational paths to enhance correct outcomes and suppress erroneous outcomes of computations. A common pattern underpinning quantum algorithms can be identified when quantum…
Quantum kernel methods are a promising branch of quantum machine learning, yet their effectiveness on diverse, high-dimensional, real-world data remains unverified. Current research has largely been limited to low-dimensional or synthetic…
We study the impact of quantum computation on the fundamental problem of testing the property of distributions. In particular, we focus on testing whether two unknown classical distributions are close or far enough, and propose the…
Operating quantum sensors and quantum computers would make data in the form of quantum states available for purely quantum processing, opening new avenues for studying physical processes and certifying quantum technologies. In this…
We describe the construction of a spherical wavelet analysis through the inverse stereographic projection of the Euclidean planar wavelet framework, introduced originally by Antoine and Vandergheynst and developed further by Wiaux et al.…
Computational methods are the most effective tools we have besides scientific experiments to explore the properties of complex biological systems. Progress is slowing because digital silicon computers have reached their limits in terms of…
Machine learning is a fascinating and exciting field within computer science. Recently, this excitement has been transferred to the quantum information realm. Currently, all proposals for the quantum version of machine learning utilize the…
We address the problem of sensing the curvature of a manifold by performing measurements on a particle constrained to the manifold itself. In particular, we consider situations where the dynamics of the particle is quantum mechanical and…
Qubit-resolved operations and measurements are required for most current quantum information processing schemes. However, these operations can be experimentally costly due to the need for local addressing, demanding significant classical…
Eigenvalue transformations appear ubiquitously in scientific computation, ranging from matrix polynomials to differential equations, and are beyond the reach of the quantum singular value transformation framework. In this work, we study the…