Quantum walks: a comprehensive review

Quantum walks, the quantum mechanical counterpart of classical random walks, is an advanced tool for building quantum algorithms that has been recently shown to constitute a universal model of quantum computation. Quantum walks is now a solid field of research of quantum computation full of exciting open problems for physicists, computer scientists, mathematicians and engineers. In this paper we review theoretical advances on the foundations of both discrete- and continuous-time quantum walks, together with the role that randomness plays in quantum walks, the connections between the mathematical models of coined discrete quantum walks and continuous quantum walks, the quantumness of quantum walks, a summary of papers published on discrete quantum walks and entanglement as well as a succinct review of experimental proposals and realizations of discrete-time quantum walks. Furthermore, we have reviewed several algorithms based on both discrete- and continuous-time quantum walks as well as a most important result: the computational universality of both continuous- and discrete- time quantum walks.Comment: Paper accepted for publication in Quantum Information Processing Journa

Technical summary

The Working Group III (WGIII) contribution to the IPCC's Fifth Assessment Report (AR5) assesses literature on the scientific, technological, environmental, economic and social aspects of mitigation of climate change. It builds upon the WGIII contribution to the IPCC's Fourth Assessment Report (AR4), the Special Report on Renewable Energy Sources and Climate Change Mitigation (SRREN) and previous reports and incorporates subsequent new findings and research. Throughout, the focus is on the implications of its findings for policy, without being prescriptive about the particular policies that governments and other important participants in the policy process should adopt. In light of the IPCC's mandate, authors in WGIII were guided by several principles when assembling this assessment: (1) to be explicit about mitigation options, (2) to be explicit about their costs and about their risks and opportunities vis-a-vis other development priorities, (3) and to be explicit about the underlying criteria, concepts, and methods for evaluating alternative policies. This summary offers the main findings of the report

Mendelian randomization supports bidirectional causality between telomere length and clonal hematopoiesis of indeterminate potential

Human genetic studies support an inverse causal relationship between leukocyte telomere length (LTL) and coronary artery disease (CAD), but directionally mixed effects for LTL and diverse malignancies. Clonal hematopoiesis of indeterminate potential (CHIP), characterized by expansion of hematopoietic cells bearing leukemogenic mutations, predisposes both hematologic malignancy and CAD. TERT (which encodes telomerase reverse transcriptase) is the most significantly associated germline locus for CHIP in genome-wide association studies. Here, we investigated the relationship between CHIP, LTL, and CAD in the Trans-Omics for Precision Medicine (TOPMed) program (n = 63,302) and UK Biobank (n = 47,080). Bidirectional Mendelian randomization studies were consistent with longer genetically imputed LTL increasing propensity to develop CHIP, but CHIP then, in turn, hastens to shorten measured LTL (mLTL). We also demonstrated evidence of modest mediation between CHIP and CAD by mLTL. Our data promote an understanding of potential causal relationships across CHIP and LTL toward prevention of CAD