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

Polymorphisms in NFkB, PXR, LXR and risk of colorectal cancer in a prospective study of Danes

<p>Abstract</p> <p>Background</p> <p>Transcription factors and nuclear receptors constitute a link between exposure to heterocyclic amines and polycyclic aromatic hydrocarbons from meat and tobacco smoke and colorectal cancer (CRC) risk. The aim of this study was to investigate if polymorphisms in nuclear factor kappa-B, pregnane X receptor, and liver X receptor were associated with risk of CRC, and to investigate possible interactions with lifestyle factors such as smoking, meat consumption, and NSAID use.</p> <p>Methods</p> <p>The polymorphisms nuclear factor kappa-B (<it>NFkB, NFKB1) </it>-94 insertion/deletion ATTG (rs28362491), pregnane X receptor (<it>PXR, NR1I2) </it>A-24381C (rs1523127), C8055T (rs2276707), A7635G (rs6785049), liver X receptor (<it>LXR-β, NR1H3) </it>C-rs1405655T, T-rs2695121C were assessed together with lifestyle factors in a nested case-cohort study of 378 CRC cases and 756 random participants from the Danish prospective Diet, Cancer and Health study of 57,053 persons.</p> <p>Results</p> <p>Carriers of <it>NFkB </it>-94deletion were at 1.45-fold higher risk of CRC than homozygous carriers of the insertion allele (incidence rate ratio (IRR) = 1.45, 95% confidence interval (95% CI): 1.10-1.92). There was interaction between this polymorphism and intake of red and processed meat in relation to CRC risk. Carriers of <it>NFkB </it>-94deletion were at 3% increased risk pr 25 gram meat per day (95% CI: 0.98-1.09) whereas homozygous carriers of the insertion were not at increased risk (p for interaction = 0.03). <it>PXR </it>and <it>LXR </it>polymorphisms were not associated with CRC risk. There was no interaction between use of nonsteroid antiinflammatory drugs (NSAID) or smoking status and <it>NFkB</it>, <it>PXR </it>or <it>LXR </it>polymorphisms.</p> <p>Conclusions</p> <p>A polymorphism in <it>NFkB </it>was associated with CRC risk and there was interaction between this polymorphism and meat intake in relation to CRC risk. This study suggests a role for NFkB in CRC aetiology.</p