Quantum Arthur-Merlin Games

This paper studies quantum Arthur-Merlin games, which are Arthur-Merlin games in which Arthur and Merlin can perform quantum computations and Merlin can send Arthur quantum information. As in the classical case, messages from Arthur to Merlin are restricted to be strings of uniformly generated random bits. It is proved that for one-message quantum Arthur-Merlin games, which correspond to the complexity class QMA, completeness and soundness errors can be reduced exponentially without increasing the length of Merlin's message. Previous constructions for reducing error required a polynomial increase in the length of Merlin's message. Applications of this fact include a proof that logarithmic length quantum certificates yield no increase in power over BQP and a simple proof that QMA is contained in PP. Other facts that are proved include the equivalence of three (or more) message quantum Arthur-Merlin games with ordinary quantum interactive proof systems and some basic properties concerning two-message quantum Arthur-Merlin games.Comment: 22 page

Predicting fatigue crack growth rate in a welded butt joint: The role of effective R ratio in accounting for residual stress effect

A simple and efficient method is presented in this paper for predicting fatigue crack growth rate in welded butt joints. Three well-known empirical crack growth laws are employed using the material constants that were obtained from the base material coupon tests. Based on the superposition rule of the linear elastic fracture mechanics, welding residual stress effect is accounted for by replacing the nominal stress ratio (R) in the empirical laws by the effective stress intensity factor ratio (Reff). The key part of the analysis process is to calculate the stress intensity factor due to the initial residual stress field and also the stress relaxation and redistribution due to crack growth. The finite element method in conjunction with the modified virtual crack closure technique was used for this analysis. Fatigue crack growth rates were then calculated by the empirical laws and comparisons were made among these predictions as well as against published experimental tests, which were conducted under either constant amplitude load or constant stress intensity factor range. Test samples were M(T) geometry made of aluminium alloy 2024-T351 with a longitudinal weld by the variable polarity plasma arc welding process. Good agreement was achieved

Quantum Optimization Problems

Krentel [J. Comput. System. Sci., 36, pp.490--509] presented a framework for an NP optimization problem that searches an optimal value among exponentially-many outcomes of polynomial-time computations. This paper expands his framework to a quantum optimization problem using polynomial-time quantum computations and introduces the notion of an ``universal'' quantum optimization problem similar to a classical ``complete'' optimization problem. We exhibit a canonical quantum optimization problem that is universal for the class of polynomial-time quantum optimization problems. We show in a certain relativized world that all quantum optimization problems cannot be approximated closely by quantum polynomial-time computations. We also study the complexity of quantum optimization problems in connection to well-known complexity classes.Comment: date change