Related papers: Quantum Algorithms and Complexity for Continuous P…
Chemistry and materials science are widely regarded as potential killer application fields for quantum hardware. While the dream of unlocking unprecedented simulation capabilities remains compelling, quantum algorithm development must adapt…
Quantum computing uses the physical principles of very small systems to develop computing platforms which can solve problems that are intractable on conventional supercomputers. There are challenges not only in building the required…
Quantum algorithms can potentially solve a handful of problems more efficiently than their classical counterparts. In that context, it has been discussed that Markov chains problems could be solved significantly faster using quantum…
Quantum machine learning (QML) holds promise for accelerating pattern recognition, optimization, and data analysis, but the conditions under which it can truly outperform classical approaches remain unclear. Existing research often…
Genetic algorithms are heuristic optimization techniques inspired by Darwinian evolution. Quantum computation is a new computational paradigm which exploits quantum resources to speed up information processing tasks. Therefore, it is…
Motivated by notions of quantum heuristics and by average-case rather than worst-case algorithmic analysis, we define quantum computational advantage in terms of individual problem instances. Inspired by the classical notions of Kolmogorov…
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 computing promises to revolutionize several scientific and technological domains through fundamentally new ways of processing information. Among its most compelling applications is digital quantum simulation, where quantum computers…
Quantum algorithms can be analyzed in a query model to compute Boolean functions where input is given in a black box, but the aim is to compute function value for arbitrary input using as few queries as possible. In this paper we…
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 computing is gaining increased attention as a potential way to speed up simulations of physical systems, and it is also of interest to apply it to simulations of classical plasmas. However, quantum information science is…
Alongside the development of quantum algorithms and quantum complexity theory in recent years, quantum techniques have also proved instrumental in obtaining results in classical (non-quantum) areas. In this paper we survey these results and…
Quantum computing was so far mainly concerned with discrete problems. Recently, E. Novak and the author studied quantum algorithms for high dimensional integration and dealt with the question, which advantages quantum computing can bring…
Machine-learning tasks frequently involve problems of manipulating and classifying large numbers of vectors in high-dimensional spaces. Classical algorithms for solving such problems typically take time polynomial in the number of vectors…
The complexity is increasing rapidly in many areas of the automotive industry. The design of an automobile involves many different engineering disciplines, e. g., mechanical, electrical, and software engineering. The software of a vehicle…
Quantum computing could impact various industries, with the automotive industry with many computational challenges, from optimizing supply chains and manufacturing to vehicle engineering, being particularly promising. This chapter…
Quantum-inspired classical algorithms provide us with a new way to understand the computational power of quantum computers for practically-relevant problems, especially in machine learning. In the past several years, numerous efficient…
Hybrid quantum-classical algorithms are central to much of the current research in quantum computing, particularly when considering the noisy intermediate-scale quantum (NISQ) era, with a number of experimental demonstrations having already…
Quantum computation is a rapidly progressing field today. What are its principles? In what sense is it distinct from conventional computation? What are its advantages and disadvantages? What type of problems can it address? How practical is…
We introduce an algorithm for combinatorial search on quantum computers that is capable of significantly concentrating amplitude into solutions for some NP search problems, on average. This is done by exploiting the same aspects of problem…