Classical simulation of Yang-Baxter gates

A unitary operator that satisfies the constant Yang-Baxter equation immediately yields a unitary representation of the braid group B n for every $n \ge 2$. If we view such an operator as a quantum-computational gate, then topological braiding corresponds to a quantum circuit. A basic question is when such a representation affords universal quantum computation. In this work, we show how to classically simulate these circuits when the gate in question belongs to certain families of solutions to the Yang-Baxter equation. These include all of the qubit (i.e., $d = 2$) solutions, and some simple families that include solutions for arbitrary $d \ge 2$. Our main tool is a probabilistic classical algorithm for efficient simulation of a more general class of quantum circuits. This algorithm may be of use outside the present setting.Comment: 17 pages. Corrected error in proof of Theorem

Yang-Baxter operators need quantum entanglement to distinguish knots

Any solution to the Yang-Baxter equation yields a family of representations of braid groups. Under certain conditions, identified by Turaev, the appropriately normalized trace of these representations yields a link invariant. Any Yang-Baxter solution can be interpreted as a two-qudit quantum gate. Here we show that if this gate is non-entangling, then the resulting invariant of knots is trivial. We thus obtain a general connection between topological entanglement and quantum entanglement, as suggested by Kauffman et al.Comment: 12 pages, 2 figure

Partial-indistinguishability obfuscation using braids

An obfuscator is an algorithm that translates circuits into functionally-equivalent similarly-sized circuits that are hard to understand. Efficient obfuscators would have many applications in cryptography. Until recently, theoretical progress has mainly been limited to no-go results. Recent works have proposed the first efficient obfuscation algorithms for classical logic circuits, based on a notion of indistinguishability against polynomial-time adversaries. In this work, we propose a new notion of obfuscation, which we call partial-indistinguishability. This notion is based on computationally universal groups with efficiently computable normal forms, and appears to be incomparable with existing definitions. We describe universal gate sets for both classical and quantum computation, in which our definition of obfuscation can be met by polynomial-time algorithms. We also discuss some potential applications to testing quantum computers. We stress that the cryptographic security of these obfuscators, especially when composed with translation from other gate sets, remains an open question.Comment: 21 pages,Proceedings of TQC 201

An Analysis of the Causal Relationship Between Transportation and GDP: A Time-Series Approach for the United States

Time-series analysis using monthly data from January 2000 to December 2015 is used to investigate the relationship between transportation and real GDP, controlling for the price of diesel, the amount of money invested in infrastructure, the inflation rate, and the real effective exchange rate. Transportation is proxied with the freight Transportation Services Index. Using Granger-causality, I find that changes in transportation Granger cause changes in real GDP, but not vice versa. It is a one-directional relationship where past values of transportation lead changes in real GDP

From Kansas to Queensland: Global learning in preservice elementary teacher education

Communication of information between groups of humans has been extended through out history progressing from smoke signals, drum beats, message couriers, post, telegraph, telephone and now the ICT. The time between the utterance of a message and the reception of that message has progressively decreased. We are now able to communicate relatively cheaply, simultaneously sharing and responding to ideas and thoughts on a scale never previously possible. Although the technology exists to make possible easy access to people in all parts of the world, we still lack understandings of the aspirations and sensitivities of other cultures with whom we can communicate. This project supported pre-service elementary teachers in two countries – Australia and the United States – to engage in collaborative learning through Internet communications. The purpose of the project was to develop greater understanding of other’s cultures, and practices in teaching elementary students. Students attending an Australian preservice primary science methods course were matched with a cohort of undergraduate preservice elementary student teachers from a university in the United States studying an integrated mathematics science methods course. Over a six-week period the students engaged in the computer-mediated communication and were encouraged to learn about mutual cultural practices and primary/elementary science education in both countries. The outcomes demonstrated that students involved in the project benefited from an array of different and enriching learning experiences. Students benefited through enhanced understanding of the teaching of science and an appreciation of the common problems confronting science education in both countries. However, there was little engagement in debate or discussion of individual differences and the cultural context of each other’s country even when opportunities presented themselves. Nevertheless, the on-line tasks provided the pre-service teachers with the experience and confidence to engage their own students in similar global learning initiatives when they become teachers

THE HISTORY OF A LOTTERY GAME THAT WAS SELDOM WON

Lotto Extra was offered as part of the United Kingdom National Lottery’s portfolio of games between 2000 and 2006. A demand model for the game is estimated and used to illustrate a discussion of why sales of the game fell steadily to the point where it was no longer viable. Emphasis is placed on the lack of minor prizes and the long sequences of weeks when no one won the jackpot (and only) prize