An Introduction to Quantum Computing for Non-Physicists

Richard Feynman's observation that quantum mechanical effects could not be simulated efficiently on a computer led to speculation that computation in general could be done more efficiently if it used quantum effects. This speculation appeared justified when Peter Shor described a polynomial time quantum algorithm for factoring integers. In quantum systems, the computational space increases exponentially with the size of the system which enables exponential parallelism. This parallelism could lead to exponentially faster quantum algorithms than possible classically. The catch is that accessing the results, which requires measurement, proves tricky and requires new non-traditional programming techniques. The aim of this paper is to guide computer scientists and other non-physicists through the conceptual and notational barriers that separate quantum computing from conventional computing. We introduce basic principles of quantum mechanics to explain where the power of quantum computers comes from and why it is difficult to harness. We describe quantum cryptography, teleportation, and dense coding. Various approaches to harnessing the power of quantum parallelism are explained, including Shor's algorithm, Grover's algorithm, and Hogg's algorithms. We conclude with a discussion of quantum error correction.Comment: 45 pages. To appear in ACM Computing Surveys. LATEX file. Exposition improved throughout thanks to reviewers' comment

Tools for Quantum Algorithms

We present efficient implementations of a number of operations for quantum computers. These include controlled phase adjustments of the amplitudes in a superposition, permutations, approximations of transformations and generalizations of the phase adjustments to block matrix transformations. These operations generalize those used in proposed quantum search algorithms.Comment: LATEX, 15 pages, Minor changes: one author's e-mail and one reference numbe

Towards a formal semantics for Ada 9X

The Ada 9X language precision team was formed during the revisions of Ada 83, with the goal of analyzing the proposed design, identifying problems, and suggesting improvements, through the use of mathematical models. This report defines a framework for formally describing Ada 9X, based on Kahn's 'natural semantics', and applies the framework to portions of the language. The proposals for exceptions and optimization freedoms are also analyzed, using a different technique

Observation of Bose-Einstein Condensation in a Strong Synthetic Magnetic Field

Extensions of Berry's phase and the quantum Hall effect have led to the discovery of new states of matter with topological properties. Traditionally, this has been achieved using gauge fields created by magnetic fields or spin orbit interactions which couple only to charged particles. For neutral ultracold atoms, synthetic magnetic fields have been created which are strong enough to realize the Harper-Hofstadter model. Despite many proposals and major experimental efforts, so far it has not been possible to prepare the ground state of this system. Here we report the observation of Bose-Einstein condensation for the Harper-Hofstadter Hamiltonian with one-half flux quantum per lattice unit cell. The diffraction pattern of the superfluid state directly shows the momentum distribution on the wavefuction, which is gauge-dependent. It reveals both the reduced symmetry of the vector potential and the twofold degeneracy of the ground state. We explore an adiabatic many-body state preparation protocol via the Mott insulating phase and observe the superfluid ground state in a three-dimensional lattice with strong interactions.Comment: 6 pages, 5 figures. Supplement: 6 pages, 4 figure

Meta-analysis of genome-wide association studies from the CHARGE consortium identifies common variants associated with carotid intima media thickness and plaque

Carotid intima media thickness (cIMT) and plaque determined by ultrasonography are established measures of subclinical atherosclerosis that each predicts future cardiovascular disease events. We conducted a meta-analysis of genome-wide association data in 31,211 participants of European ancestry from nine large studies in the setting of the Cohorts for Heart and Aging Research in Genomic Epidemiology (CHARGE) Consortium. We then sought additional evidence to support our findings among 11,273 individuals using data from seven additional studies. In the combined meta-analysis, we identified three genomic regions associated with common carotid intima media thickness and two different regions associated with the presence of carotid plaque (P < 5 × 10 -8). The associated SNPs mapped in or near genes related to cellular signaling, lipid metabolism and blood pressure homeostasis, and two of the regions were associated with coronary artery disease (P < 0.006) in the Coronary Artery Disease Genome-Wide Replication and Meta-Analysis (CARDIoGRAM) consortium. Our findings may provide new insight into pathways leading to subclinical atherosclerosis and subsequent cardiovascular events

Loci influencing blood pressure identified using a cardiovascular gene-centric array

Blood pressure (BP) is a heritable determinant of risk for cardiovascular disease (CVD). To investigate genetic associations with systolic BP (SBP), diastolic BP (DBP), mean arterial pressure (MAP) and pulse pressure (PP), we genotyped 50 000 single-nucleotide polymorphisms (SNPs) that capture variation in 2100 candidate genes for cardiovascular phenotypes in 61 619 individuals of European ancestry from cohort studies in the USA and Europe. We identified novel associations between rs347591 and SBP (chromosome 3p25.3, in an intron of HRH1) and between rs2169137 and DBP (chromosome1q32.1 in an intron of MDM4) and between rs2014408 and SBP (chromosome 11p15 in an intron of SOX6), previously reported to be associated with MAP. We also confirmed 10 previously known loci associated with SBP, DBP, MAP or PP (ADRB1, ATP2B1, SH2B3/ATXN2, CSK, CYP17A1, FURIN, HFE, LSP1, MTHFR, SOX6) at array-wide significance (P 2.4 10(6)). We then replicated these associations in an independent set of 65 886 individuals of European ancestry. The findings from expression QTL (eQTL) analysis showed associations of SNPs in the MDM4 region with MDM4 expression. We did not find any evidence of association of the two novel SNPs in MDM4 and HRH1 with sequelae of high BP including coronary artery disease (CAD), left ventricular hypertrophy (LVH) or stroke. In summary, we identified two novel loci associated with BP and confirmed multiple previously reported associations. Our findings extend our understanding of genes involved in BP regulation, some of which may eventually provide new targets for therapeutic intervention.</p

Common variants in Alzheimer’s disease and risk stratification by polygenic risk scores

Funder: Funder: Fundación bancaria ‘La Caixa’ Number: LCF/PR/PR16/51110003 Funder: Grifols SA Number: LCF/PR/PR16/51110003 Funder: European Union/EFPIA Innovative Medicines Initiative Joint Number: 115975 Funder: JPco-fuND FP-829-029 Number: 733051061Genetic discoveries of Alzheimer's disease are the drivers of our understanding, and together with polygenetic risk stratification can contribute towards planning of feasible and efficient preventive and curative clinical trials. We first perform a large genetic association study by merging all available case-control datasets and by-proxy study results (discovery n = 409,435 and validation size n = 58,190). Here, we add six variants associated with Alzheimer's disease risk (near APP, CHRNE, PRKD3/NDUFAF7, PLCG2 and two exonic variants in the SHARPIN gene). Assessment of the polygenic risk score and stratifying by APOE reveal a 4 to 5.5 years difference in median age at onset of Alzheimer's disease patients in APOE ɛ4 carriers. Because of this study, the underlying mechanisms of APP can be studied to refine the amyloid cascade and the polygenic risk score provides a tool to select individuals at high risk of Alzheimer's disease

Analysis of shared common genetic risk between amyotrophic lateral sclerosis and epilepsy

Because hyper-excitability has been shown to be a shared pathophysiological mechanism, we used the latest and largest genome-wide studies in amyotrophic lateral sclerosis (n = 36,052) and epilepsy (n = 38,349) to determine genetic overlap between these conditions. First, we showed no significant genetic correlation, also when binned on minor allele frequency. Second, we confirmed the absence of polygenic overlap using genomic risk score analysis. Finally, we did not identify pleiotropic variants in meta-analyses of the 2 diseases. Our findings indicate that amyotrophic lateral sclerosis and epilepsy do not share common genetic risk, showing that hyper-excitability in both disorders has distinct origins