Discrete-query quantum algorithm for NAND trees

Recently, Farhi, Goldstone, and Gutmann gave a quantum algorithm for evaluating NAND trees that runs in time O(sqrt(N log N)) in the Hamiltonian query model. In this note, we point out that their algorithm can be converted into an algorithm using O(N^{1/2 + epsilon}) queries in the conventional quantum query model, for any fixed epsilon > 0.Comment: 2 pages. v2: updated name of one autho

Efficient discrete-time simulations of continuous-time quantum query algorithms

The continuous-time query model is a variant of the discrete query model in which queries can be interleaved with known operations (called "driving operations") continuously in time. Interesting algorithms have been discovered in this model, such as an algorithm for evaluating nand trees more efficiently than any classical algorithm. Subsequent work has shown that there also exists an efficient algorithm for nand trees in the discrete query model; however, there is no efficient conversion known for continuous-time query algorithms for arbitrary problems. We show that any quantum algorithm in the continuous-time query model whose total query time is T can be simulated by a quantum algorithm in the discrete query model that makes O[T log(T) / log(log(T))] queries. This is the first upper bound that is independent of the driving operations (i.e., it holds even if the norm of the driving Hamiltonian is very large). A corollary is that any lower bound of T queries for a problem in the discrete-time query model immediately carries over to a lower bound of \Omega[T log(log(T))/log (T)] in the continuous-time query model.Comment: 12 pages, 6 fig

Discrete-Query Quantum Algorithm for NAND Trees

This is a comment on the article “A Quantum Algorithm for the Hamiltonian NAND Tree” by Edward Farhi, Jeffrey Goldstone, and Sam Gutmann, Theory of Computing 4 (2008) 169--190. That paper gave a quantum algorithm for evaluating NAND trees with running time O(√N) in the Hamiltonian query model. In this note, we point out that their algorithm can be converted into an algorithm using N^[1/2 + o(1)] queries in the conventional (discrete) quantum query model

Solid state differentiation of plasma thiols using a centrifugally activated mercaptobenzothiazole disulfide exchange indicator

The solid state interaction of mono and macromolecular thiols at a disulphide heterocycle is shown to provide a versatile pathway for their speciation

“Tales and Adventures”: G.A. Henty’s Union Jack and the Competitive World of Publishing for Boys in the 1880s’

In the competitive publishing environment of the late nineteenth century, writers and magazines had to distinguish themselves carefully from potential rivals. This article examines how G.A. Henty’s quality boys’ weekly, Union Jack (1880-83), attempted to secure a niche in the juvenile publishing market by deliberately distinguishing itself from other papers as a literary, imperialist and “healthy” publication. The article explores the design and marketing techniques of the magazine, its status as a fiction paper, the high calibre of its contributors, and its aggressive rhetoric in targeting an exclusively masculine audience. It argues that while Union Jack was marketed as a niche publication, it eventually failed to distinguish itself sufficiently to survive in an extremely competitive environment

Approximating Fractional Time Quantum Evolution

An algorithm is presented for approximating arbitrary powers of a black box unitary operation, $\mathcal{U}^t$, where $t$ is a real number, and $\mathcal{U}$ is a black box implementing an unknown unitary. The complexity of this algorithm is calculated in terms of the number of calls to the black box, the errors in the approximation, and a certain `gap' parameter. For general $\mathcal{U}$ and large $t$, one should apply $\mathcal{U}$ a total of $\lfloor t \rfloor$ times followed by our procedure for approximating the fractional power $\mathcal{U}^{t-\lfloor t \rfloor}$. An example is also given where for large integers $t$ this method is more efficient than direct application of $t$ copies of $\mathcal{U}$. Further applications and related algorithms are also discussed.Comment: 13 pages, 2 figure

Examining Biased Assimilation of Brand-related Online Reviews

This paper examines the impact of pre-existing brand attitudes on consumer processing of electronic word-of-mouth (eWOM). This topic is particularly important for brands that simultaneously possess strongly pronounced proponents as well as opponents. Two experimental studies using univalent (study 1, N = 538) and mixed (study 2, N = 262) sets of online reviews find indications for biased assimilation effects of eWOM processing. Consumers perceive positive (negative) arguments in online reviews as more (less) persuasive when having a positive (negative) attitude towards the brand. Perceived persuasiveness in turn influences behavioral intentions and acts as a mediator on the relationship between attitude and behavioral intentions. We examine two moderators of this effect. When priming individuals to focus on other consumers (vs. a self-focus prime), the biased assimilation effect is weaker (study 3a, N = 131). In contrast, we show that biased assimilation becomes stronger under conditions of high (vs. low) cognitive impairment (study 3b, N = 124). Our findings contribute to the literature on the relationship between eWOM and brands and advance our understanding of potential outcomes of brand polarization