Adiabatic optimization without local minima

Several previous works have investigated the circumstances under which quantum adiabatic optimization algorithms can tunnel out of local energy minima that trap simulated annealing or other classical local search algorithms. Here we investigate the even more basic question of whether adiabatic optimization algorithms always succeed in polynomial time for trivial optimization problems in which there are no local energy minima other than the global minimum. Surprisingly, we find a counterexample in which the potential is a single basin on a graph, but the eigenvalue gap is exponentially small as a function of the number of vertices. In this counterexample, the ground state wavefunction consists of two "lobes" separated by a region of exponentially small amplitude. Conversely, we prove if the ground state wavefunction is single-peaked then the eigenvalue gap scales at worst as one over the square of the number of vertices.Comment: 20 pages, 1 figure. Journal versio

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

Academic Dishonesty and Testing: How Student Beliefs and Test Settings Impact Decisions to Cheat

Research shows that academic dishonesty in post-secondary education runs particularly high among students in the specific disciplines of engineering, business, and nursing. The authors were interested in how student attitudes towards specific environments for testing might contribute to the prevalence or likelihood of cheating on tests and exams. It was hypothesized that while there would be no difference in their beliefs or attitudes regarding the acceptability of cheating behaviors in unproctored versus proctored settings, students would be more likely to engage in cheating behavior in an unproctored setting. Technology continues to transform the world around us at a rapid pace, allowing faculty to incorporate more technology into the classroom and to educate more students remotely via hybrid and online classes. While these opportunities have their benefits, they also present new challenges. The opportunity for cheating on tests increases, especially when exams are delivered in unproctored environments. An instrument was created to investigate the attitudes and behaviors of first- and second-year undergraduate engineering students while taking tests in both proctored and unproctored environments. In all, 734 students were surveyed from four different institutions of higher education. Students provided both qualitative and quantitative responses to questions related to their beliefs and attitudes toward cheating in today’s socially shareable society. Results indicated that both students’ attitudes and behaviors vary as a result of tests being delivered in a proctored versus unproctored environment