Prevalence of Helicobacter pylori in patients with gastro-oesophageal reflux disease : systematic review.

Objectives: To ascertain the prevalence of Helicobacter pylori in patients with gastro-oesophageal reflux disease and its association with the disease. Design: Systematic review of studies reporting the prevalence of H pylori in patients with and without gastro-oesophageal reflux disease. Data sources: Four electronic databases, searched to November 2001, experts, pharmaceutical companies, and journals. Main outcome measure: Odds ratio for prevalence of H pylori in patients with gastro-oesophageal reflux disease. Results: 20 studies were included. The pooled estimate of the odds ratio for prevalence of H pylori was 0.60 (95% confidence interval 0.47 to 0.78), indicating a lower prevalence in patients with gastro-oesophageal reflux disease. Substantial heterogeneity was observed between studies. Location seemed to be an important factor, with a much lower prevalence of H pylori in patients with gastro-oesophageal reflux disease in studies from the Far East, despite a higher overall prevalence of infection than western Europe and North America. Year of study was not a source of heterogeneity. Conclusion: The prevalence of H pylori infection was significantly lower in patients with than without gastro-oesophageal reflux, with geographical location being a strong contributor to the heterogeneity between studies. Patients from the Far East with reflux disease had a lower prevalence of H pylori infection than patients from western Europe and North America, despite a higher prevalence in the general population

Quantum rejection sampling

Rejection sampling is a well-known method to sample from a target distribution, given the ability to sample from a given distribution. The method has been first formalized by von Neumann (1951) and has many applications in classical computing. We define a quantum analogue of rejection sampling: given a black box producing a coherent superposition of (possibly unknown) quantum states with some amplitudes, the problem is to prepare a coherent superposition of the same states, albeit with different target amplitudes. The main result of this paper is a tight characterization of the query complexity of this quantum state generation problem. We exhibit an algorithm, which we call quantum rejection sampling, and analyze its cost using semidefinite programming. Our proof of a matching lower bound is based on the automorphism principle which allows to symmetrize any algorithm over the automorphism group of the problem. Our main technical innovation is an extension of the automorphism principle to continuous groups that arise for quantum state generation problems where the oracle encodes unknown quantum states, instead of just classical data. Furthermore, we illustrate how quantum rejection sampling may be used as a primitive in designing quantum algorithms, by providing three different applications. We first show that it was implicitly used in the quantum algorithm for linear systems of equations by Harrow, Hassidim and Lloyd. Secondly, we show that it can be used to speed up the main step in the quantum Metropolis sampling algorithm by Temme et al.. Finally, we derive a new quantum algorithm for the hidden shift problem of an arbitrary Boolean function and relate its query complexity to "water-filling" of the Fourier spectrum.Comment: 19 pages, 5 figures, minor changes and a more compact style (to appear in proceedings of ITCS 2012

Distinguishing n Hamiltonians on C^n by a single measurement

If an experimentalist wants to decide which one of n possible Hamiltonians acting on an n dimensional Hilbert space is present, he can conjugate the time evolution by an appropriate sequence of known unitary transformations in such a way that the different Hamiltonians result in mutual orthogonal final states. We present a general scheme providing such a sequence.Comment: 4 pages, Revte

Spatial search by quantum walk

Grover's quantum search algorithm provides a way to speed up combinatorial search, but is not directly applicable to searching a physical database. Nevertheless, Aaronson and Ambainis showed that a database of N items laid out in d spatial dimensions can be searched in time of order sqrt(N) for d>2, and in time of order sqrt(N) poly(log N) for d=2. We consider an alternative search algorithm based on a continuous time quantum walk on a graph. The case of the complete graph gives the continuous time search algorithm of Farhi and Gutmann, and other previously known results can be used to show that sqrt(N) speedup can also be achieved on the hypercube. We show that full sqrt(N) speedup can be achieved on a d-dimensional periodic lattice for d>4. In d=4, the quantum walk search algorithm takes time of order sqrt(N) poly(log N), and in d<4, the algorithm does not provide substantial speedup.Comment: v2: 12 pages, 4 figures; published version, with improved arguments for the cases where the algorithm fail

Quantum walk on a line for a trapped ion

We show that a multi-step quantum walk can be realized for a single trapped ion with interpolation between quantum and random walk achieved by randomizing the generalized Hadamard coin flip phase. The signature of the quantum walk is manifested not only in the ion's position but also its phonon number, which makes an ion trap implementation of the quantum walk feasible.Comment: 5 pages, 3 figure

Noise resistance of adiabatic quantum computation using random matrix theory

Besides the traditional circuit-based model of quantum computation, several quantum algorithms based on a continuous-time Hamiltonian evolution have recently been introduced, including for instance continuous-time quantum walk algorithms as well as adiabatic quantum algorithms. Unfortunately, very little is known today on the behavior of these Hamiltonian algorithms in the presence of noise. Here, we perform a fully analytical study of the resistance to noise of these algorithms using perturbation theory combined with a theoretical noise model based on random matrices drawn from the Gaussian Orthogonal Ensemble, whose elements vary in time and form a stationary random process.Comment: 9 pages, 3 figure

Scaling of running time of quantum adiabatic algorithm for propositional satisfiability

We numerically study quantum adiabatic algorithm for the propositional satisfiability. A new class of previously unknown hard instances is identified among random problems. We numerically find that the running time for such instances grows exponentially with their size. Worst case complexity of quantum adiabatic algorithm therefore seems to be exponential.Comment: 7 page

Quantum Optical Random Walk: Quantization Rules and Quantum Simulation of Asymptotics

Rules for quantizing the walker+coin parts of a classical random walk are provided by treating them as interacting quantum systems. A quantum optical random walk (QORW), is introduced by means of a new rule that treats quantum or classical noise affecting the coin's state, as sources of quantization. The long term asymptotic statistics of QORW walker's position that shows enhanced diffusion rates as compared to classical case, is exactly solved. A quantum optical cavity implementation of the walk provides the framework for quantum simulation of its asymptotic statistics. The simulation utilizes interacting two-level atoms and/or laser randomly pulsating fields with fluctuating parameters.Comment: 18 pages, 3 figure

A more representative chamber: representation and the House of Lords

Since 1997 there has been substantive reform of the House of Lords in an effort to make the chamber ‘more democratic and more representative’. Whilst the Labour government failed to press ahead with any of the proposed plans for further reform following the removal of the bulk of the hereditary peers in 1999, it remained committed to the notion that such reform must make the second chamber ‘more representative’. The coalition government's programme advocates a long-term aspiration for a House wholly or mainly elected on the basis of proportional representation, and a short-term approach based on additional appointments to ensure a balance of the parties. What is clear in all of these proposals for reform is a desire for the House of Lords to become more representative than it is at present. However, what is less clear is what is meant by ‘representative’ – who the House of Lords is supposed to represent, and what form representation will take. Moreover, in proposing to make the chamber more representative, either through appointment or election, little attention has been paid to how the current House of Lords provides representation. This article examines these questions in the context of Pitkin's classic conceptions of representation and peers' attitudes towards their own representative rol

Effects of Noise, Correlations and errors in the preparation of initial states in Quantum Simulations

In principle a quantum system could be used to simulate another quantum system. The purpose of such a simulation would be to obtain information about problems which cannot be simulated with a classical computer due to the exponential increase of the Hilbert space with the size of the system and which cannot be measured or controlled in an actual experiment. The system will interact with the surrounding environment, with the other particles in the system and be implemented using imperfect controls making it subject to noise. It has been suggested that noise does not need to be controlled to the same extent as it must be for general quantum computing. However the effects of noise in quantum simulations and how to treat them are not completely understood. In this paper we study an existing quantum algorithm for the one-dimensional Fano-Anderson model to be simulated using a liquid-state NMR device. We calculate the evolution of different initial states in the original model, and then we add interacting spins to simulate a more realistic situation. We find that states which are entangled with their environment, and sometimes correlated but not necessarily entangled have an evolution which is described by maps which are not completely positive. We discuss the conditions for this to occur and also the implications.Comment: Revtex 4-1, 14 pages, 21 figures, version 2 has typos corrected and acknowledgement adde