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Adiabatic-Quantum-Computing-to-solve-the-MaxCut-graph-problem

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Adiabatic-Quantum-Computing-to-solve-the-MaxCut-graph-problem

Adiabatic Quantum Computing to solve the MaxCut graph problemFcnclla McAndrewSupervisors: Prof Kate Smith-Miles & Dr Charles HillThe University of Mel

Adiabatic-Quantum-Computing-to-solve-the-MaxCut-graph-problemlbourne School of Mathemat ics and StatisticsA t hesis submitted in part ial fulfilment of the requirements of t he degree of Master of Science (Mathe

matics and Statistics)44105AbstractMaxCut is an -NP hard graph theory problem which has been extensively researched by computer scientists, data scien Adiabatic-Quantum-Computing-to-solve-the-MaxCut-graph-problem

tists and mathematicians. As there are no polynomial time algorithms for NP Hard problems, there has been a great amount of research into approximatio

Adiabatic-Quantum-Computing-to-solve-the-MaxCut-graph-problem

n algorithms

Adiabatic Quantum Computing to solve the MaxCut graph problemFcnclla McAndrewSupervisors: Prof Kate Smith-Miles & Dr Charles HillThe University of Mel

Adiabatic-Quantum-Computing-to-solve-the-MaxCut-graph-problemblems.The main aim of this project Is to investigate if there exist any graph features that affect the performance of adiabatic quantum computing. By

identifying such features it is possible to gain insights into predicting the performance of the MaxCi t algorithm based off some prior feat ure extra Adiabatic-Quantum-Computing-to-solve-the-MaxCut-graph-problem

ction.AcknowledgementsFirst and foremost, I want to thank my supervisors Kate Smith-Miles and Charles Hill, who have been a great support, throughout

Adiabatic-Quantum-Computing-to-solve-the-MaxCut-graph-problem

this whole project.. The combination of Kate's mat hs insights and Charles’ physics knowledge as well as your pat ience and encouragement made this th

Adiabatic Quantum Computing to solve the MaxCut graph problemFcnclla McAndrewSupervisors: Prof Kate Smith-Miles & Dr Charles HillThe University of Mel

Adiabatic-Quantum-Computing-to-solve-the-MaxCut-graph-problems inside and outside of university, listening to me talk endlessly about MaxCut and quantum computing could not have been easy. Spec ial shout out to

my proofreaders DJ and Lukas.1 want to t hank my brot hers Angus, Edward, Will and Fin and my dad Alasdair. You all call me smart when 1 feel t he opp Adiabatic-Quantum-Computing-to-solve-the-MaxCut-graph-problem

osite and always put t ime aside for me when I need it. You’re all amazing and without you I’d be nowhere.Finally, 1 want to thank my mum Felicity, fo

Adiabatic-Quantum-Computing-to-solve-the-MaxCut-graph-problem

r being there in good times iUid bad times. Your love and our friendship has made this possible and I’m eternally grateful.iiContents1Introduction11.1

Adiabatic Quantum Computing to solve the MaxCut graph problemFcnclla McAndrewSupervisors: Prof Kate Smith-Miles & Dr Charles HillThe University of Mel

Adiabatic-Quantum-Computing-to-solve-the-MaxCut-graph-problemiew42.1MaxCut Graph Problem............................................ 42.1.1Problem Description...................................... 42.1.2Solution

Algorithms ..................................... 62.2Quantum Computing............................................... 82.2.1Overview ................ Adiabatic-Quantum-Computing-to-solve-the-MaxCut-graph-problem

................................ 82.2.2Adiabatic Quantum Computing............................. 112.3Mapping MaxCut to anAQC Problem..................

Adiabatic-Quantum-Computing-to-solve-the-MaxCut-graph-problem

............. 132.3.1Defining Initial Hamiltonian H/Ỉ........................ 132.3.2Defining Problem Hamiltonian Hp ........................ 153Metho

Adiabatic Quantum Computing to solve the MaxCut graph problemFcnclla McAndrewSupervisors: Prof Kate Smith-Miles & Dr Charles HillThe University of Mel

Adiabatic-Quantum-Computing-to-solve-the-MaxCut-graph-problemraph Features................................................. 233.4Simulating AQC ................................................ 25

Adiabatic Quantum Computing to solve the MaxCut graph problemFcnclla McAndrewSupervisors: Prof Kate Smith-Miles & Dr Charles HillThe University of Mel

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