Searches on star graphs and equivalent oracle problems

We examine a search on a graph among a number of different kinds of objects (vertices), one of which we want to find. In a standard graph search, all of the vertices are the same, except for one, the marked vertex, and that is the one we wish to find. We examine the case in which the unmarked vertices can be of different types, so the background against which the search is done is not uniform. We find that the search can still be successful, but the probability of success is lower than in the uniform background case, and that probability decreases with the number of types of unmarked vertices. We also show how the graph searches can be rephrased as equivalent oracle problems

Universal quantum computation using the discrete time quantum walk

A proof that continuous time quantum walks are universal for quantum computation, using unweighted graphs of low degree, has recently been presented by Childs [PRL 102 180501 (2009)]. We present a version based instead on the discrete time quantum walk. We show the discrete time quantum walk is able to implement the same universal gate set and thus both discrete and continuous time quantum walks are computational primitives. Additionally we give a set of components on which the discrete time quantum walk provides perfect state transfer.Comment: 9 pages, 10 figures. Updated after referee comments - Section V expanded and minor changes to other parts of the tex

Unambiguous discrimination among quantum operations

We address the problem of unambiguous discrimination among a given set of quantum operations. The necessary and sufficient condition for them to be unambiguously distinguishable is derived in the cases of single use and multiple uses respectively. For the latter case we explicitly construct the input states and corresponding measurements that accomplish the task. It is found that the introduction of entanglement can improve the discrimination.Comment: 5 pages, no figur

Architectures for a quantum random access memory

A random access memory, or RAM, is a device that, when interrogated, returns the content of a memory location in a memory array. A quantum RAM, or qRAM, allows one to access superpositions of memory sites, which may contain either quantum or classical information. RAMs and qRAMs with n-bit addresses can access 2^n memory sites. Any design for a RAM or qRAM then requires O(2^n) two-bit logic gates. At first sight this requirement might seem to make large scale quantum versions of such devices impractical, due to the difficulty of constructing and operating coherent devices with large numbers of quantum logic gates. Here we analyze two different RAM architectures (the conventional fanout and the "bucket brigade") and propose some proof-of-principle implementations which show that in principle only O(n) two-qubit physical interactions need take place during each qRAM call. That is, although a qRAM needs O(2^n) quantum logic gates, only O(n) need to be activated during a memory call. The resulting decrease in resources could give rise to the construction of large qRAMs that could operate without the need for extensive quantum error correction.Comment: 10 pages, 7 figures. Updated version includes the answers to the Refere

Improved quantum algorithms for the ordered search problem via semidefinite programming

One of the most basic computational problems is the task of finding a desired item in an ordered list of N items. While the best classical algorithm for this problem uses log_2 N queries to the list, a quantum computer can solve the problem using a constant factor fewer queries. However, the precise value of this constant is unknown. By characterizing a class of quantum query algorithms for ordered search in terms of a semidefinite program, we find new quantum algorithms for small instances of the ordered search problem. Extending these algorithms to arbitrarily large instances using recursion, we show that there is an exact quantum ordered search algorithm using 4 log_{605} N \approx 0.433 log_2 N queries, which improves upon the previously best known exact algorithm.Comment: 8 pages, 4 figure

Contextuality in Measurement-based Quantum Computation

We show, under natural assumptions for qubit systems, that measurement-based quantum computations (MBQCs) which compute a non-linear Boolean function with high probability are contextual. The class of contextual MBQCs includes an example which is of practical interest and has a super-polynomial speedup over the best known classical algorithm, namely the quantum algorithm that solves the Discrete Log problem.Comment: Version 3: probabilistic version of Theorem 1 adde

Distance measures to compare real and ideal quantum processes

With growing success in experimental implementations it is critical to identify a "gold standard" for quantum information processing, a single measure of distance that can be used to compare and contrast different experiments. We enumerate a set of criteria such a distance measure must satisfy to be both experimentally and theoretically meaningful. We then assess a wide range of possible measures against these criteria, before making a recommendation as to the best measures to use in characterizing quantum information processing.Comment: 15 pages; this version in line with published versio

A Quantum Random Walk Search Algorithm

Quantum random walks on graphs have been shown to display many interesting properties, including exponentially fast hitting times when compared with their classical counterparts. However, it is still unclear how to use these novel properties to gain an algorithmic speed-up over classical algorithms. In this paper, we present a quantum search algorithm based on the quantum random walk architecture that provides such a speed-up. It will be shown that this algorithm performs an oracle search on a database of $N$ items with $O(\sqrt{N})$ calls to the oracle, yielding a speed-up similar to other quantum search algorithms. It appears that the quantum random walk formulation has considerable flexibility, presenting interesting opportunities for development of other, possibly novel quantum algorithms.Comment: 13 pages, 3 figure

LGP2 plays a critical role in sensitizing mda-5 to activation by double-stranded RNA.

The DExD/H box RNA helicases retinoic acid-inducible gene-I (RIG-I) and melanoma differentiation associated gene-5 (mda-5) sense viral RNA in the cytoplasm of infected cells and activate signal transduction pathways that trigger the production of type I interferons (IFNs). Laboratory of genetics and physiology 2 (LGP2) is thought to influence IFN production by regulating the activity of RIG-I and mda-5, although its mechanism of action is not known and its function is controversial. Here we show that expression of LGP2 potentiates IFN induction by polyinosinic-polycytidylic acid [poly(I:C)], commonly used as a synthetic mimic of viral dsRNA, and that this is particularly significant at limited levels of the inducer. The observed enhancement is mediated through co-operation with mda-5, which depends upon LGP2 for maximal activation in response to poly(I:C). This co-operation is dependent upon dsRNA binding by LGP2, and the presence of helicase domain IV, both of which are required for LGP2 to interact with mda-5. In contrast, although RIG-I can also be activated by poly(I:C), LGP2 does not have the ability to enhance IFN induction by RIG-I, and instead acts as an inhibitor of RIG-I-dependent poly(I:C) signaling. Thus the level of LGP2 expression is a critical factor in determining the cellular sensitivity to induction by dsRNA, and this may be important for rapid activation of the IFN response at early times post-infection when the levels of inducer are low

Feminizing political parties: women’s party member organizations within European parliamentary parties

Party member women’s organizations were early features of party development. While some contemporary studies maintain these are important sites for the substantive representation of women, there is also a claim that they are in decline. Our primary purpose here is to establish the existence of party member women’s organizations – as one test of the first dimension of party feminization: the inclusion of women. We draw on new survey data of 17 European countries provided by Scarrow, Poguntke and Webb. We establish that almost half have a party member women’s organization. The new data also permits analysis of relationships between party member women’s organization and gender quotas for the top party leadership body (National Executive Committee (NEC)), women’s presence among the party leadership and candidate quota rules. Together we see these (i) as a means to establish whether women are marginalized within the party, thereby limiting descriptive representation and (ii) as surrogate measures for women’s substantive representation. We importantly find that the presence of a party member women’s organization does not come at the cost of women’s presence on the NEC. In the final section, we turn our attention to building a new comparative research agenda that more fully addresses substantive representation