Quantum Sampling Problems, BosonSampling and Quantum Supremacy

There is a large body of evidence for the potential of greater computational power using information carriers that are quantum mechanical over those governed by the laws of classical mechanics. But the question of the exact nature of the power contributed by quantum mechanics remains only partially answered. Furthermore, there exists doubt over the practicality of achieving a large enough quantum computation that definitively demonstrates quantum supremacy. Recently the study of computational problems that produce samples from probability distributions has added to both our understanding of the power of quantum algorithms and lowered the requirements for demonstration of fast quantum algorithms. The proposed quantum sampling problems do not require a quantum computer capable of universal operations and also permit physically realistic errors in their operation. This is an encouraging step towards an experimental demonstration of quantum algorithmic supremacy. In this paper, we will review sampling problems and the arguments that have been used to deduce when sampling problems are hard for classical computers to simulate. Two classes of quantum sampling problems that demonstrate the supremacy of quantum algorithms are BosonSampling and IQP Sampling. We will present the details of these classes and recent experimental progress towards demonstrating quantum supremacy in BosonSampling.Comment: Survey paper first submitted for publication in October 2016. 10 pages, 4 figures, 1 tabl

A patient preference study that evaluated fluticasone furoate and mometasone furoate nasal sprays for allergic rhinitis

Background: Corticosteroid nasal sprays are the mainstay of treatment for allergic rhinitis. These sprays have sensory attributes such as scent and/or odor, taste and aftertaste, and run down the throat and/or the nose, which, when unpleasant, can affect patient preference for, and compliance with, treatment. Objective: This study examined patient preference for fluticasone furoate nasal spray (FFNS) or mometasone furoate nasal spray (MFNS) based on their sensory attributes after administration in patients with allergic rhinitis. Methods: This was a multicenter, randomized, double-blind, cross-over study. Patient preferences were determined by using three questionnaires (Overall Preference, Immediate Attributes, and Delayed Attributes). Results: Overall, 56% of patients stated a preference for FFNS versus 32% for MFNS (p _ 0.001); the remaining 12% stated no preference. More patients stated a preference for FFNS versus MFNS for the attributes of “less drip down the throat” (p _ 0.001), “less run out of the nose” (p _ 0.05), “more soothing” (p _ 0.05), and “less irritating” (p _ 0.001). More patients responded in favor of FFNS versus MFNS for the immediate attributes, “run down the throat” (p _ 0.001), and “run out of the nose” (p _ 0.001), and, in the delayed attributes, “run down the throat” (p _ 0.001), “run out of the nose” (p _ 0.01), “presence of aftertaste” (p _ 0.01), and “no nasal irritation” (p _ 0.001). Conclusion: Patients with allergic rhinitis preferred FFNS versus MFNS overall and based on a number of individual attributes, including “less drip down the throat,” “less run out of the nose,” and “less irritating.” Greater preference may improve patient adherence and thereby improve symptom management of the patient’s allergic rhinitis

Commuting Quantum Circuits with Few Outputs are Unlikely to be Classically Simulatable

We study the classical simulatability of commuting quantum circuits with n input qubits and O(log n) output qubits, where a quantum circuit is classically simulatable if its output probability distribution can be sampled up to an exponentially small additive error in classical polynomial time. First, we show that there exists a commuting quantum circuit that is not classically simulatable unless the polynomial hierarchy collapses to the third level. This is the first formal evidence that a commuting quantum circuit is not classically simulatable even when the number of output qubits is exponentially small. Then, we consider a generalized version of the circuit and clarify the condition under which it is classically simulatable. Lastly, we apply the argument for the above evidence to Clifford circuits in a similar setting and provide evidence that such a circuit augmented by a depth-1 non-Clifford layer is not classically simulatable. These results reveal subtle differences between quantum and classical computation.Comment: 19 pages, 6 figures; v2: Theorems 1 and 3 improved, proofs modifie

Two-weight ternary codes and the equation y2 = 4 × 3a + 13

AbstractThis paper determines the parameters of all two-weight ternary codes C with the property that the minimum weight in the dual code C⊥ is at least 4. This yields a characterization of uniformly packed ternary [n, k, 4] codes. The proof rests on finding all integer solutions of the equation y2 = 4 × 3a + 13

Gift giving to children at Christmas and birthdays.

This paper explores gift giving of toys to children at Christmas and Birthdays and their perception of the gift giver. Three areas are discussed; gift giving, the methodological approach and the results and conclusions. Gift giving is an historical concept relating to exchanges of gifts representing many symbols and meanings. Toys are often given to children at birthdays and Christmas and the perception of the gift giver may be affected by many things. The long-term impact may alter the relationship between the child and parent. Miscommunication is often cited as being an influence on the level of disappointment that may occur. Four drawing sessions were conducted with preschool children from two nurseries. The aim of these sessions was to identify what the childrens favourite toy gift was at Christmas and birthday time, who had given it to them and what they thought of the giver. The pictorial results were coded and results concluded that almost all the children could identify their favourite toy gifts. A majority were satisfied with their gifts and most surprisingly identified Santa as the gift giver for Birthday toys as well as Christmas. Most children could not represent their feeling of the gift giver pictorially and interestingly enough mum was not mentioned once as a giver of gifts

And they say don't work with children.

This paper explores the role and method a researcher must consider when using children as research objects. Three areas are discussed; the researcher's role, children as research objects, and the results and conclusions. Researchers must consider an appropriate role when researching with children with the most advocated being the least adult role, as there are suggestions that children do not make good respondents. A suitable methodological approach has to be taken allowing children to be creative and to ensure effective responses. Doing artwork combined with questions provided creative responses. Four drawing sessions were conducted with preschool children from two nurseries. The aim of these sessions was to identify if the children could actually complete drawings, state who had given the gift to them and pictorially represent what they thought of the giver. The pictorial results were coded and the results identified that as all children produced a drawing doing artwork is an acceptable methodological approach for this group of respondents. A majority could remember who had given them a gift, but could not present their feelings of the gift giver pictorially suggesting that children may not be suitable respondents overall