scholarly journals Reachability Deficits in Quantum Approximate Optimization of Graph Problems

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 532
Author(s):  
V. Akshay ◽  
H. Philathong ◽  
I. Zacharov ◽  
J. Biamonte
Keyword(s):  
Performance Indicator ◽  
Experimental Realization ◽  
Approximate Optimization ◽  
Graph Problems ◽  
Approximation Quality ◽  
Rapid Fall ◽  
Problem Instances ◽  
Reported Data ◽  
Quantum Optimization ◽  
Intermediate Density

The quantum approximate optimization algorithm (QAOA) has become a cornerstone of contemporary quantum applications development. Here we show that the density of problem constraints versus problem variables acts as a performance indicator. Density is found to correlate strongly with approximation inefficiency for fixed depth QAOA applied to random graph minimization problem instances. Further, the required depth for accurate QAOA solution to graph problem instances scales critically with density. Motivated by Google's recent experimental realization of QAOA, we preform a reanalysis of the reported data reproduced in an ideal noiseless setting. We found that the reported capabilities of instances addressed experimentally by Google, approach a rapid fall-off region in approximation quality experienced beyond intermediate-density. Our findings offer new insight into performance analysis of contemporary quantum optimization algorithms and contradict recent speculation regarding low-depth QAOA performance benefits.

scholarly journals New graph algorithms via polyhedral techniques

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Jakub Tarnawski
Keyword(s):  
Linear Programming ◽  
Perfect Matching ◽  
Traveling Salesman ◽  
Benchmark Problem ◽  
Matching Problem ◽  
Graph Problems ◽  
Weighted Directed Graph ◽  
Asymmetric Traveling Salesman Problem ◽  
Problem Instances ◽  
New Algorithms

Abstract This article gives a short overview of my dissertation, where new algorithms are given for two fundamental graph problems. We develop novel ways of using linear programming formulations, even exponential-sized ones, to extract structure from problem instances and to guide algorithms in making progress. The first part of the dissertation addresses a benchmark problem in combinatorial optimization: the asymmetric traveling salesman problem (ATSP). It consists in finding the shortest tour that visits all vertices of a given edge-weighted directed graph. A ρ-approximation algorithm for ATSP is one that runs in polynomial time and always produces a tour at most ρ times longer than the shortest tour. Finding such an algorithm with constant ρ had been a long-standing open problem. Here we give such an algorithm. The second part of the dissertation addresses the perfect matching problem. We have known since the 1980s that it has efficient parallel algorithms if the use of randomness is allowed. However, we do not know if randomness is necessary – that is, whether the matching problem is in the class NC. We show that it is in the class quasi-NC. That is, we give a deterministic parallel algorithm that runs in poly-logarithmic time on quasi-polynomially many processors.

scholarly journals Quantum approximate optimization of non-planar graph problems on a planar superconducting processor

2021 ◽  
Author(s):  
Matthew P. Harrigan ◽  
Kevin J. Sung ◽  
Matthew Neeley ◽  
Kevin J. Satzinger ◽  
Frank Arute ◽  
...  
Keyword(s):  
Planar Graph ◽  
Approximate Optimization ◽  
Graph Problems

scholarly journals Bang-bang control as a design principle for classical and quantum optimization algorithms

2019 ◽  
Vol 19 (5&6) ◽  
pp. 424-446
Author(s):  
Aniruddha Bapat ◽  
Stephen Jordan
Keyword(s):  
Simulated Annealing ◽  
Optimization Algorithm ◽  
Control Strategy ◽  
Design Principle ◽  
Quantum Algorithms ◽  
Optimization Algorithms ◽  
Successful Control ◽  
Problem Instances ◽  
Quantum Optimization ◽  
Bang Bang Control

Physically motivated classical heuristic optimization algorithms such as simulated annealing (SA) treat the objective function as an energy landscape, and allow walkers to escape local minima. It has been argued that quantum properties such as tunneling may give quantum algorithms advantage in finding ground states of vast, rugged cost landscapes. Indeed, the Quantum Adiabatic Algorithm (QAO) and the recent Quantum Approximate Optimization Algorithm (QAOA) have shown promising results on various problem instances that are considered classically hard. Here, building on previous observations from \cite{mcclean2016, Yang2017}, we argue that the type of control strategy used by the optimization algorithm may be crucial to its success. Along with SA, QAO, and QAOA, we define a new, bang-bang version of simulated annealing, BBSA, and study the performance of these algorithms on two well-studied problem instances from the literature. Both classically and quantumly, the successful control strategy is found to be bang-bang, exponentially outperforming the quasistatic analogues on the same instances. Lastly, we construct O(1)-depth QAOA protocols for a class of symmetric cost functions, and provide an accompanying physical picture.

Outcomes: Promoting Reflective Practice Using Performance Indicator Questionnaires

2010 ◽  
Vol 20 (2) ◽  
pp. 64-70 ◽  
Author(s):  
Mary Pat McCarthy
Keyword(s):  
Clinical Education ◽  
Performance Indicator ◽  
Clinical Skills ◽  
Self Assessment ◽  
Clinical Practicum ◽  
Self Reflection ◽  
Healthcare Settings ◽  
Language Pathology ◽  
Traditional Performance ◽  
The University

This article details the process of self-reflection applied to the use of traditional performance indicator questionnaires. The study followed eight speech-language pathology graduate students enrolled in clinical practicum in the university, school, and healthcare settings over a period of two semesters. Results indicated when reflection was focused on students' own clinical skills, modifications to practice were implemented. Results further concluded self-assessment using performance indicators paired with written reflections can be a viable form of instruction in clinical education.

Enhancing Spatial Ability Through Sport Practice

2012 ◽  
Vol 33 (2) ◽  
pp. 83-88 ◽  
Author(s):  
David Moreau ◽  
Jérome Clerc ◽  
Annie Mansy-Dannay ◽  
Alain Guerrien
Keyword(s):  
Mental Rotation ◽  
Spatial Representations ◽  
Mental Rotation Test ◽  
Sport Training ◽  
Sport Practice ◽  
Undergraduate University Students ◽  
Before And After ◽  
Cognitive Plasticity ◽  
Reported Data ◽  
The Relationship

This experiment investigated the relationship between mental rotation and sport training. Undergraduate university students (n = 62) completed the Mental Rotation Test ( Vandenberg & Kuse, 1978 ), before and after a 10-month training in two different sports, which either involved extensive mental rotation ability (wrestling group) or did not (running group). Both groups showed comparable results in the pretest, but the wrestling group outperformed the running group in the posttest. As expected from previous studies, males outperformed women in the pretest and the posttest. Besides, self-reported data gathered after both sessions indicated an increase in adaptive strategies following training in wrestling, but not subsequent to training in running. These findings demonstrate the significant effect of training in particular sports on mental rotation performance, thus showing consistency with the notion of cognitive plasticity induced from motor training involving manipulation of spatial representations. They are discussed within an embodied cognition framework.

Relative Importance of Leader Influences for Subordinates’ Proactive Behaviors, Prosocial Behaviors, and Task Performance

2014 ◽  
Vol 13 (2) ◽  
pp. 70-86 ◽  
Author(s):  
Dan S. Chiaburu ◽  
Troy A. Smith ◽  
Jiexin Wang ◽  
Ryan D. Zimmerman
Keyword(s):  
Task Performance ◽  
Transformational Change ◽  
Future Research ◽  
Contingent Reward ◽  
Work Effectiveness ◽  
Leader Influence ◽  
Member Exchange ◽  
Proactive Behaviors ◽  
Reported Data ◽  
Transactional Leader

We meta-analytically examine the relationships between three forms of leader influence, contingent reward (transactional), leader-member exchange (LMX; relational), and transformational (change-oriented) on subordinates’ proactive behaviors. Using non-self-reported data from a combined sample of more than 9,000 employees, we confirm positive relationships between leader influences and employee proactive outcomes. We examine the extent to which one leadership influence is stronger than the others in promoting subordinate proactivity. By combining our new meta-analytic data with existing meta-analytic correlations, we further investigate the extent to which various leadership predictors are differentially related to proactive and prosocial contextual performance, and to task performance. For all outcomes, there are only minimal differences between the contingent reward, LMX, and transformational leadership predictors. Using our results, we propose future research directions for the relationship between leader influences and subordinate work effectiveness.

Dual parameterization and parameterized approximability of subset graph problems

2017 ◽  
Vol 51 (1) ◽  
pp. 261-266 ◽  
Author(s):  
Édouard Bonnet ◽  
Vangelis Th. Paschos
Keyword(s):  
Graph Problems

Changes Occurring During Coagulation in Glass. I. Normal Human Blood

1960 ◽  
Vol 4 (01) ◽  
pp. 001-016
Author(s):  
Jessica H. Lewis ◽  
Paul Didisheim ◽  
John H. Ferguson ◽  
Kenichi Hattori
Keyword(s):  
Coagulation Factors ◽  
Factor Ix ◽  
Factor Vii ◽  
Sodium Oxalate ◽  
Factor V ◽  
Rapid Rise ◽  
Rapid Fall ◽  
Glass Tubes ◽  
Normal Human ◽  
The Individual

SummaryNormal whole blood was allowed to stand in glass tubes at 37° C, and the clotting process stopped at various intervals by the addition of sodium oxalate. During the first 15 minutes a marked acceleration of clotting activity was found. Study of the individual coagulation factors showed the following changes: a sustained and rapid fall in platelet count, a sustained and rapid rise in PTC (factor IX), a steady fall in fibrinogen, a more gradual fall in AHF (factor VIII), a rapid rise and subsequent fall in proaccelerin (factor V) activity, a somewhat lesser and slower rise and fall in proconvertin (factor VII) activity, and a slow fall in prothrombin concentration. No changes were noted in Hageman factor or PTA activities.

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