On the Complexity of Random Quantum Computations and the Jones Polynomial

There is a natural relationship between Jones polynomials and quantum computation. We use this relationship to show that the complexity of evaluating relative-error approximations of Jones polynomials can be used to bound the classical complexity of approximately simulating random quantum computations. We prove that random quantum computations cannot be classically simulated up to a constant total variation distance, under the assumption that (1) the Polynomial Hierarchy does not collapse and (2) the average-case complexity of relative-error approximations of the Jones polynomial matches the worst-case complexity over a constant fraction of random links. Our results provide a straightforward relationship between the approximation of Jones polynomials and the complexity of random quantum computations.Comment: 8 pages, 4 figure

Survey and analysis of research on supersonic drag-due-to-lift minimization with recommendations for wing design

A survey of research on drag-due-to-lift minimization at supersonic speeds, including a study of the effectiveness of current design and analysis methods was conducted. The results show that a linearized theory analysis with estimated attainable thrust and vortex force effects can predict with reasonable accuracy the lifting efficiency of flat wings. Significantly better wing performance can be achieved through the use of twist and camber. Although linearized theory methods tend to overestimate the amount of twist and camber required for a given application and provide an overly optimistic performance prediction, these deficiencies can be overcome by implementation of recently developed empirical corrections. Numerous examples of the correlation of experiment and theory are presented to demonstrate the applicability and limitations of linearized theory methods with and without empirical corrections. The use of an Euler code for the estimation of aerodynamic characteristics of a twisted and cambered wing and its application to design by iteration are discussed

The Timing of Perfection of Security Interests Under the Uniform Commercial Code and the Bankruptcy Reform Act

This article will examine this new relationship as it applies to a specific problem created by the interaction between Article 9 and bankruptcy law: the timing of a transfer when a security interest is challenged as preferential in a bankruptcy proceeding. Resolution of this question is often critical for determining the secured party\u27s ability to recover assets pledged as collateral when the debtor goes into bankruptcy. The article will begin by explaining the timing of transfer problem as it arose under Article 9 and the Bankruptcy Act. Then it will describe and evaluate the new solution provided by the Bankruptcy Reform Act

The Reclaiming Seller Under the Bankruptcy Reform Act: Resolution or Renewal of an Old Conflict?

This Article will assess the impact of the Bankruptcy Reform Act upon the conflict of the Code cash and credit sellers with the trustee in bankruptcy. The article will begin by discussing the legal position of the reclaiming seller at common law, both because the new Act\u27s interaction with the Code cannot be understood without reference to such doctrines, and because these doctrines are often likely to be of continued applicability under the new Act. It will then examine the seller\u27s rights under the U.C.C., and will discuss his relations with certain bankruptcy-relevant Code third parties. Following this, the Article will examine the seller-trustee clash as it developed under the prior Bankruptcy Act. Finally, it will assess the position of the seller under the Bankruptcy Reform Act