Showing papers by "National Security Agency published in 2017"

Fast optimization algorithms and the cosmological constant

Abstract: Denef and Douglas have observed that in certain landscape models the problem of finding small values of the cosmological constant is a large instance of a problem that is hard for the complexity class NP (Nondeterministic Polynomial-time). The number of elementary operations (quantum gates) needed to solve this problem by brute force search exceeds the estimated computational capacity of the observable Universe. Here we describe a way out of this puzzling circumstance: despite being NP-hard, the problem of finding a small cosmological constant can be attacked by more sophisticated algorithms whose performance vastly exceeds brute force search. In fact, in some parameter regimes the average-case complexity is polynomial. We demonstrate this by explicitly finding a cosmological constant of order 10^(-120) in a randomly generated 10^9-dimensional Arkani-Hamed–Dimopoulos–Kachru landscape.

Graphing trillions of triangles.

Abstract: The increasing size of Big Data is often heralded but how data are transformed and represented is also profoundly important to knowledge discovery, and this is exemplified in Big Graph analytics. Much attention has been placed on the scale of the input graph but the product of a graph algorithm can be many times larger than the input. This is true for many graph problems, such as listing all triangles in a graph. Enabling scalable graph exploration for Big Graphs requires new approaches to algorithms, architectures, and visual analytics. A brief tutorial is given to aid the argument for thoughtful representation of data in the context of graph analysis. Then a new algebraic method to reduce the arithmetic operations in counting and listing triangles in graphs is introduced. Additionally, a scalable triangle listing algorithm in the MapReduce model will be presented followed by a description of the experiments with that algorithm that led to the current largest and fastest triangle listing benchmarks to date. Finally, a method for identifying triangles in new visual graph exploration technologies is proposed.

Cartan Subalgebras for Quantum Symmetric Pair Coideals

Abstract: There is renewed interest in the coideal subalgebras used to form quantum symmetric pairs because of recent discoveries showing that they play a fundamental role in the representation theory of quantized enveloping algebras However, there is still no general theory of finite-dimensional modules for these coideals In this paper, we establish an important step in this direction: we show that every quantum symmetric pair coideal subalgebra admits a quantum Cartan subalgebra which is a polynomial ring that specializes to its classical counterpart The construction builds on Kostant and Sugiura's classification of Cartan subalgebras for real semisimple Lie algebras via strongly orthogonal systems of positive roots We show that these quantum Cartan subalgebras act semisimply on finite-dimensional unitary modules and identify particularly nice generators of the quantum Cartan subalgebra for a family of examples

Low-noise, ultra-low temperature dissipative devices

Abstract: A dissipative device has a planar configuration with one or more resistor elements formed on an insulating substrate. Conductors are formed on the insulating substrate and are coupled to the resistor element(s) to transmit signals to/from the resistor element(s). The geometry of and materials for the dissipative device allow the conductors to act as heat sinks, which conduct heat generated in the resistor element(s) to the substrate (and on to a coupled housing) and cool hot electrons generated by the resistor element(s) via electron-phonon coupling. The dissipative device can be used in cooling a signal to a qubit, a cavity system of a quantum superconducting qubit, or any other cryogenic device sensitive to thermal noise.

Readiness of Quantum Optimization Machines for Industrial Applications

Abstract: There have been multiple attempts to demonstrate that quantum annealing and, in particular, quantum annealing on quantum annealing machines, has the potential to outperform current classical optimization algorithms implemented on CMOS technologies. The benchmarking of these devices has been controversial. Initially, random spin-glass problems were used, however, these were quickly shown to be not well suited to detect any quantum speedup. Subsequently, benchmarking shifted to carefully crafted synthetic problems designed to highlight the quantum nature of the hardware while (often) ensuring that classical optimization techniques do not perform well on them. Even worse, to date a true sign of improved scaling with the number of problem variables remains elusive when compared to classical optimization techniques. Here, we analyze the readiness of quantum annealing machines for real-world application problems. These are typically not random and have an underlying structure that is hard to capture in synthetic benchmarks, thus posing unexpected challenges for optimization techniques, both classical and quantum alike. We present a comprehensive computational scaling analysis of fault diagnosis in digital circuits, considering architectures beyond D-wave quantum annealers. We find that the instances generated from real data in multiplier circuits are harder than other representative random spin-glass benchmarks with a comparable number of variables. Although our results show that transverse-field quantum annealing is outperformed by state-of-the-art classical optimization algorithms, these benchmark instances are hard and small in the size of the input, therefore representing the first industrial application ideally suited for testing near-term quantum annealers and other quantum algorithmic strategies for optimization problems.

New Wilson-like theorems arising from Dickson polynomials

Abstract: Wilson's Theorem states that the product of all nonzero elements of a finite field ${\mathbb F}_q$ is $-1$. In this article, we define some natural subsets $S \subset {\mathbb F}_q^\times$ and find formulas for the product of the elements of $S$, denoted $\prod S$. These new formulas are appealing for the simple, natural description of the sets $S$, and for the simplicity of the product. An example is $\prod\left\{ a \in {\mathbb F}_q^\times : \text{$1-a$ and $3+a$ are nonsquares} \right\} = 2$ if $q \equiv \pm 1 \pmod{12}$, or $-1$ otherwise.

Using Principal Component Scores to Enhance the Validity and Reliability of Big Five Personality Measures

Abstract: . Varimax rotated principal component scores (VRPCS) have previously been offered as a possible solution to the non-orthogonality of scores for the Big Five factors. However, few researchers have examined the reliability and validity of VRPCS. To address this gap, we use a lab study and a field study to investigate whether using VRPCS increase orthogonality, reliability, and criterion-related validity. Compared to the traditional unit-weighting scoring method, the use of VRPCS enhanced the reliability and discriminant validity of the Big Five factors, although there was little improvement in criterion-related validity. Results are discussed in terms of the benefit of using VRPCS instead of traditional unit-weighted sum scores.

Measuring ink stream deposition rate of an aerosol-jet printer

Abstract: A method is disclosed for calibrating a deposition rate in an aerosol jet printer. The method includes providing a substrate defining an array of wells, each defining a volume. The method also includes defining a toolpath such that a dispensing nozzle passes over the wells. The method also includes defining a dwell time such that the nozzle remains centered above each well for an amount of time equal to the dwell time, after which the nozzle follows the toolpath to be centered over the following well. The dwell time defines a deposition rate based on the volume of the wells. The method also includes causing the nozzle to move along the toolpath, depositing material into the wells. The method also includes observing one of overfilling and underfilling and adjusting dispensing parameters to effect a modified deposition rate, until the wells are being filled to within a tolerance of exactly full.