Related papers: Quantum Complexity of Integration
Identifying computational tasks suitable for (future) quantum computers is an active field of research. Here we explore utilizing quantum computers for the purpose of solving differential equations. We consider two approaches: (i) basis…
The simulation of large-scale classical systems in exponentially small space on quantum computers has gained attention. The prior work demonstrated that a quantum algorithm offers an exponential speedup over any classical algorithm in…
Many recent investigations conclude, based on asymptotic complexity analyses, that quantum computers could accelerate combinatorial optimization (CO) tasks relative to a purely classical computer. However, asymptotic analysis alone cannot…
Quantum computing is a new model of computation, based on quantum physics. Quantum computers can be exponentially faster than conventional computers for problems such as factoring. Besides full-scale quantum computers, more restricted…
Partial differential equations frequently appear in the natural sciences and related disciplines. Solving them is often challenging, particularly in high dimensions, due to the "curse of dimensionality". In this work, we explore the…
Security for machine learning has begun to become a serious issue for present day applications. An important question remaining is whether emerging quantum technologies will help or hinder the security of machine learning. Here we discuss a…
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…
Quantum computation appears to offer significant advantages over classical computation and this has generated a tremendous interest in the field. In this thesis we consider the application of quantum computers to scientific computing and…
Quantum computers use quantum mechanical phenomena to perform conventionally intractable calculations for specific problems. Despite being universal machines, quantum computers are not expected to replace classical computers, but rather, to…
Quantum computation holds promise for the solution of many intractable problems. However, since many quantum algorithms are stochastic in nature they can only find the solution of hard problems probabilistically. Thus the efficiency of the…
Quantum computation and quantum information are of great current interest in computer science, mathematics, physical sciences and engineering. They will likely lead to a new wave of technological innovations in communication, computation…
Recently developed quantum algorithms suggest that quantum computers can solve certain problems and perform certain tasks more efficiently than conventional computers. Among other reasons, this is due to the possibility of creating…
The standard setting of quantum computation for continuous problems uses deterministic queries and the only source of randomness for quantum algorithms is through measurement. This setting is related to the worst case setting on a classical…
Quantum computers promise to enhance machine learning for practical applications. Quantum machine learning for real-world data has to handle extensive amounts of high-dimensional data. However, conventional methods for measuring quantum…
We show that a separation between the class of all problems that can efficiently be solved on a quantum computer and those solvable using probabilistic classical algorithms in polynomial time implies the generalized contextuality of quantum…
Quantum computing and quantum Monte Carlo (QMC) are respectively the state-of-the-art quantum and classical computing methods for understanding many-body quantum systems. Here, we propose a hybrid quantum-classical algorithm that integrates…
Linear differential equations are ubiquitous in science and engineering. Quantum computers can simulate quantum systems, which are described by a restricted type of linear differential equations. Here we extend quantum simulation algorithms…
In the field of quantum information, classical optimizers play an important role. From experimentalists optimizing their physical devices to theorists exploring variational quantum algorithms, many aspects of quantum information require the…
Quantum random sampling is the leading proposal for demonstrating a computational advantage of quantum computers over classical computers. Recently, first large-scale implementations of quantum random sampling have arguably surpassed the…
In this study, we give an extension of Montanaro's arXiv/archive:1504.06987 quantum Monte Carlo method, tailored for computing expected values of random variables that exhibit infinite variance. This addresses a challenge in analyzing…