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arXiv:quant-ph/0504166

Some Open Problems in Quantum Information Theory

Olaf Krueger, Reinhard F. Werner

Published Apr 21, 2005• 36 citations
arXivHTMLPDF

Abstract

This article is a snap-shot of a web site, which has been collecting open problems in quantum information for several years, and documenting the progress made on these problems. By posting it we make the complete collection available in one printout. We also hope to draw more attention to this project, inviting every researcher in the field to raise to the challenges, but also to suggest new problems.

DOI
10.48550/arxiv.quant-ph/0504166

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This article is a snap-shot of a web site, which has been collecting open problems in quantum information for several years, and documenting the progress made on these problems. By posting it we make the complete collection available in one printout. We also hope to draw more attention to this project, inviting every researcher in the field to raise to the challenges, but also to suggest new problems.
On the basis of its unrivalled potential to solve factorization problems and further application in cryptography, quantum computing is considered as one of the most promising computational models for the future. It provides a new angle for thinking of computation and a new approach for attack various computationally difficult problems. In this article, we give a comprehensive survey of developments in the last twenty years on quantum algorithms, quantum complexity, quantum programming theory, quantum circuits, and quantum cryptography that we hope will serve as references for researchers in related fields. We also outline various research directions and open problems in this area, with the hope of prompting further progress or even solutions.
Formulating gauge theories on a lattice offers a genuinely non-perturbative way of studying quantum field theories, and has led to impressive achievements. In particular, it significantly deepened our understanding of quantum chromodynamics. Yet, some very relevant problems remain inherently challenging, such as real time evolution, or the presence of a chemical potential, cases in which Monte Carlo simulations are hindered by a sign problem. In the last few years, a number of possible alternatives have been put forward, based on quantum information ideas, which could potentially open the access to areas of research that have so far eluded more standard methods. They include tensor network calculations, quantum simulations with different physical platforms and quantum computations, and constitute nowadays a vibrant research area. Experts from different fields, including experimental and theoretical high energy physics, condensed matter, and quantum information, are turning their attention to these interdisciplinary possibilities, and driving the progress of the field. The aim of this article is to review the status and perspectives of these new avenues for the exploration of lattice gauge theories.
The development and use of quantum computers has the potential for revolutionary impact on the waycomputing supports chemical applications. Quantum computation for chemical applications has received enormous attention in recent years with rapid progress in both theoretical and experimental fronts. The development of quantum algorithms for quantum chemistry is stimulated by the greater availability of more capable quantum computing devices. But major challenges remain with one key example the development of quantum algorithms for solving chemical problems thought to be intractable for classical computers. Other challenges include understanding the role of quantum entanglement, coherence, and superposition in complex chemical processes such as photosynthesis.Theoretical chemists have encountered and analyzed quantum effects in physical chemistry for decades.Combining the results of the chemical physics community with insights from the quantum informationcommunity can lead to a fresh understanding of important chemical processes and the emergence of thenovel many-body formulations amenable for quantum computing. This Research Topic will invite leading scientists from all over the world who work in the fields of quantum information and computation to report their recent research results.