Realizable Quantum Adiabatic Search

Grover's unstructured search algorithm is one of the best examples to date for the superiority of quantum algorithms over classical ones. Its applicability, however, has been questioned by many due to its oracular nature. We propose a mechanism to carry out a quantum adiabatic variant of Grover's search algorithm using a single bosonic particle placed in an optical lattice. By studying the scaling of the gap and relevant matrix element in various spatial dimensions, we show that a quantum speedup can already be gained in three dimensions. We argue that the suggested scheme is realizable with present-day experimental capabilities.Comment: 6 pages, 4 figure

Continuous-Time Quantum Algorithms for Unstructured Problems

We consider a family of unstructured problems, for which we propose a method for constructing analog, continuous-time quantum algorithms that are more efficient than their classical counterparts. In this family of problems, which we refer to as `scrambled output' problems, one has to find a minimum-cost configuration of a given integer-valued n-bit function whose output values have been scrambled in some arbitrary way. Special cases within this set of problems are Grover's search problem of finding a marked item in an unstructured database, certain random energy models, and the functions of the Deutsch-Josza problem. We consider a couple of examples in detail. In the first, we provide a deterministic analog quantum algorithm to solve the seminal problem of Deutsch and Josza, in which one has to determine whether an n-bit boolean function is constant (gives 0 on all inputs or 1 on all inputs) or balanced (returns 0 on half the input states and 1 on the other half). We also study one variant of the random energy model, and show that, as one might expect, its minimum energy configuration can be found quadratically faster with a quantum adiabatic algorithm than with classical algorithms.Comment: 8 pages, 4 figure

Tradition, Authority and Dialogue: Arendt and Alexander on Education

In this paper I discuss two attempts to challenge mainstream liberal education, by Hannah Arendt and by contemporary Israeli philosopher Hanan Alexander. Arendt and Alexander both identify problems in liberal-secular modern politics and present alternatives based on reconnecting politics and education to tradition. I analyze their positions and bring them into a dialogue that suggests a complex conception of education that avoids many of the pitfalls of modern liberal thought. First, I outline Arendt and Alexander’s educational views and discuss their similarities, arguing that both may be understood as opposed to the modern attempt to adopt a «view from nowhere» at the world. Next, I suggest that Alexander’s view may benefit from adopting Arendt’s conceptions of tradition and authority. In the consecutive section, I argue that Alexander sheds light on significant problems in Arendt’s approach to education, problems his understanding of critical dialogue can help solve. The succeeding section joins the two views together to form an approach I call «critical traditionalism», and examines it against prevailing approaches to political education. I conclude by pointing to an important point overlooked by both Arendt and Alexander, namely the need for internal political struggle within each tradition

Period Finding with Adiabatic Quantum Computation

We outline an efficient quantum-adiabatic algorithm that solves Simon's problem, in which one has to determine the `period', or xor-mask, of a given black-box function. We show that the proposed algorithm is exponentially faster than its classical counterpart and has the same complexity as the corresponding circuit-based algorithm. Together with other related studies, this result supports a conjecture that the complexity of adiabatic quantum computation is equivalent to the circuit-based computational model in a stronger sense than the well-known, proven polynomial equivalence between the two paradigms. We also discuss the importance of the algorithm and its theoretical and experimental implications for the existence of an adiabatic version of Shor's integer factorization algorithm that would have the same complexity as the original algorithm.Comment: 6 page

Social Networks and Unraveling in Labor Markets

This paper studies the phenomenon of early hiring in entry-level labor markets (e.g. the market for gastroenterology fellowships and the market for judicial clerks) in the presence of social networks. We o¤er a two-stage model in which workers in training institutions reveal information on their own ability over time. In the early stage, workers receive a noisy signal about their own ability. The early information is ?soft?and non-veri?able, and workers can convey the information credibly only to ? rms that are connected to them (potentially via their mentors). At the second stage, ? hard? veri?able (and accurate) information is revealed to the workers and can be credibly transmitted to all ?rms. We characterize the e¤ects of changes to the network structure on the unraveling of the market towards early hiring. Moreover, we show that an e¢ cient design of the matching procedure can prevent unraveling.Networks; market design; unraveling; entry-level labor markets; early hiring