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

Characterization of a Chinese Hamster Mutant in Mitochondrial Gene Expression

Gal\u2732 is a Chinese hamster lung (CHL} cell mutant that is unable to grow in galactose due to a defect in mitochondria! protein synthesis, In this unique CHL mutant, the mitochondrially synthesized subunits of NADH dehydrogenase and cytochrome c oxidase are significantly reduced when compared to the wild-type levels, but not the ATPase subunits. In contrast to the protein levels, the mRNA levels as determined by Northern and slot blotting are elevated in the mutant compared to the wild type, Thus, the decreased levels of mitochondrially synthesized proteins in Gal 32 are the result of decreased translation of elevated mRNAs. To determine whether the differentially reduced protein synthesis in Gal\u2732 is at the level of translational initiation or elongation or sequestering of mRNA, the polysome profile of the Gal 32 mutant is compared to that of wild type. The polysome profile which is generated by centrifugation through a 1 5-30% sucrose gradient is analyzed by Northern blotting using cytochrome oxidase, NADH dehydrogenase, ATPase riboprobes and 16S and 12S DNA probes. The location and amount of the mRNAs and rRNAs are being examined to understand the molecular mechanism of decreased translation. Supported by NIH-MBRS S06-GM08016

BRCA1 mutations in African Americans

The breast cancer predisposing gene, BRCA1, was analyzed for germline mutations in 45 African American families at high-risk for hereditary breast cancer. Patients were considered high-risk if they had a family history of the disease, early onset breast cancer, bilateral breast cancer, or breast and ovarian cancer. The entire BRCA1 coding and flanking intron regions have been examined by single stranded conformation polymorphism analysis followed by sequencing of variant bands. Eleven different BRCA1 germline mutations/variations were identified in 7 patients from the 45 high-risk families. Two pathogenic, protein-truncating mutations were detected in exon 11. A ten base pair tandem duplication, 943ins10, was present in a woman with breast and ovarian cancer whose first-degree relatives had prostate cancer. A four base pair deletion, 3450de14, was detected in a breast cancer patient with five cases of breast cancer in the family; two of the proband\u27s sisters with breast cancer also carried the same mutation. Four amino acid substitutions (Lys1183Arg, Leu1564Pro, Gln1785His, and Glu1794Asp) and four nucleotide substitutions in intron 22 (IVS22+78 C/A, IVS22+67 T/C, IVS22+8 T/A and IVS22+7 T/C) were observed in patients and not in control subjects. One early onset breast cancer patient carried five distinct BRCA1 variations, two amino acid substitutions and three substitutions in intron 22. An amino acid substitution in exon 11, Ser1140Gly, was identified in 3 different unrelated patients and in 6 of 92 control samples. The latter probably represents a benign polymorphism

Open Quantum Random Walks

International audienceA new model of quantum random walks is introduced, on lattices as well as on nite graphs. These quantum random walks take into account the behavior of open quantum systems. They are the exact quantum analogue of classical Markov chains. We explore the \quantum trajectory" point of view on these quantum random walks, that is, we show that measuring the position of the particle after each time-step gives rise to a classical Markov chain, on the lattice times the state space of the particle. This quantum trajectory is a simulation of the master equation of the quantum random walk. The physical pertinence of such quantum random walks and the way they can be concretely realized is discussed. Connections and di erences with the already well-known quantum random walks, such as the Hadamard random walk, are established. We explore several examples and compute their limit behavior. We show that the typical behavior of Open Quantum Random Walks seems to be very di erent from Hadamard-type quantum random walks. Indeed, while being very quantum in their behavior, Open Quantum Random Walks tend to become more and more classical as time goes