Related papers: Quantum Algorithm For Estimating Eigenvalue
This PhD thesis explores the potential of quantum computing to address computational challenges in high-energy physics (HEP). As the Standard Model (SM) leaves key questions unanswered and no signs of new physics have emerged since the…
In this paper, we study quantum algorithms of matrix multiplication from the viewpoint of inputting quantum/classical data to outputting quantum/classical data. The main target is trying to overcome the input and output problem, which are…
The capacity for solving eigenstates with a quantum computer is key for ultimately simulating physical systems. Here we propose inverse iteration quantum eigensolvers, which exploit the power of quantum computing for the classical inverse…
Estimating the number of eigenvalues located in a given interval of a large sparse Hermitian matrix is an important problem in certain applications and it is a prerequisite of eigensolvers based on a divide-and-conquer paradigm. Often an…
Efficiently solving large-scale sparse linear systems poses a significant challenge in computational science, especially in fields such as physics, engineering, machine learning, and finance. Traditional classical algorithms face…
Quantum computers have an exponential speed-up advantage over classical computers. One of the most prominent utilities of quantum computers is their ability to study complex quantum systems in various fields using quantum computational…
Estimating the eigenvalues of a unitary transformation U by standard phase estimation requires the implementation of controlled-U-gates which are not available if U is only given as a black box. We show that a simple trick allows to measure…
Digital quantum computers provide a computational framework for solving the Schr\"{o}dinger equation for a variety of many-particle systems. Quantum computing algorithms for the quantum simulation of these systems have recently witnessed…
Making new methods for quantum problems often relies on using basic operations in linear algebra. Often these routines are hidden behind well-known libraries that have been optimized over decades. Attempting to improve on those basic…
We present classical and quantum algorithms based on spectral methods for a problem in tensor principal component analysis. The quantum algorithm achieves a quartic speedup while using exponentially smaller space than the fastest classical…
Classical algorithms for market equilibrium computation such as proportional response dynamics face scalability issues with Internet-based applications such as auctions, recommender systems, and fair division, despite having an almost…
Quantum mechanics is well known to accelerate statistical sampling processes over classical techniques. In quantitative finance, statistical samplings arise broadly in many use cases. Here we focus on a particular one of such use cases,…
In an extension of the Unconventional Noiseless Intermediate Quantum Emulator, this work introduces a classical emulation of the quantum Harrow-Hassidim-Lloyd algorithm for sampling from the solution space of linear systems. The emulated…
Quantum computing has the potential to solve many computational problems exponentially faster than classical computers. The high shares of renewables and the wide deployment of converter-interfaced resources require new tools that shall…
A central task in the field of quantum computing is to find applications where quantum computer could provide exponential speedup over any classical computer. Machine learning represents an important field with broad applications where…
Quantum computing can empower machine learning models by enabling kernel machines to leverage quantum kernels for representing similarity measures between data. Quantum kernels are able to capture relationships in the data that are not…
Applications related to artificial intelligence, machine learning, and system identification simulations essentially use eigenvectors. Calculating eigenvectors for very large matrices using conventional methods is compute-intensive and…
Leverage score sampling is crucial to the design of randomized algorithms for large-scale matrix problems, while the computation of leverage scores is a bottleneck of many applications. In this paper, we propose a quantum algorithm to…
Quantum computers can execute algorithms that sometimes dramatically outperform classical computation. Undoubtedly the best-known example of this is Shor's discovery of an efficient quantum algorithm for factoring integers, whereas the same…
Quantum algorithms for both differential equation solving and for machine learning potentially offer an exponential speedup over all known classical algorithms. However, there also exist obstacles to obtaining this potential speedup in…