MARC details
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04475ntm a22003737a 4500 |
| 003 - CONTROL NUMBER IDENTIFIER |
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AT-ISTA |
| 005 - DATE AND TIME OF LATEST TRANSACTION |
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20250915130516.0 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
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250915s2024 au ||||| m||| 00| 0 eng d |
| 040 ## - CATALOGING SOURCE |
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| Transcribing agency |
ISTA |
| 100 ## - MAIN ENTRY--PERSONAL NAME |
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| Personal name |
Medina Ramos, Raimel A. |
| 9 (RLIN) |
1084228 |
| 245 ## - TITLE STATEMENT |
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| Title |
Exploring the optimization landscape of variational quantum algorithms |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) |
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| Name of publisher, distributor, etc. |
Institute of Science and Technology Austria |
| Date of publication, distribution, etc. |
2024 |
| 500 ## - GENERAL NOTE |
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| General note |
Thesis |
| 505 ## - FORMATTED CONTENTS NOTE |
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| Formatted contents note |
Abstract |
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Acknowledgements |
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About the Author |
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List of Collaborators and Publications |
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Table of Contents |
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| Formatted contents note |
List of Figures |
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List of Algorithms |
| 505 ## - FORMATTED CONTENTS NOTE |
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1 Introduction |
| 505 ## - FORMATTED CONTENTS NOTE |
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2 Duality approach to quantum annealing of the 3-XORSAT problem |
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3 Avoiding Barren Plateaus Using Classical Shadows |
| 505 ## - FORMATTED CONTENTS NOTE |
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4 Recursive greedy initialization of the QAOA with guaranteed improvement |
| 505 ## - FORMATTED CONTENTS NOTE |
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5 A Recursive Lower Bound on the Energy Improvement of the Quantum Approximate Optimization Algorithm |
| 505 ## - FORMATTED CONTENTS NOTE |
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A Appendices to Chapter 2 |
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B Appendices to Chapter 2 |
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C Appendices to Chapter 3 |
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D Appendices to Chapter 4 |
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| Formatted contents note |
Bibliography |
| 520 ## - SUMMARY, ETC. |
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| Summary, etc. |
Can current quantum computers provide a speedup over their classical counterparts for some kinds of problems? In this thesis, with a focus on ground state search/preparation, we address some of the challenges that both quantum annealing and variational quantum algorithms suffer from, hindering any possible practical speedup in comparison to the best classical counterparts. In the first part of the thesis, we study the performance of quantum annealing for solving a particular combinatorial optimization problem called 3-XOR satisfability (3-XORSAT). The classical problem is mapped into a ground state search of a 3-local classical Hamiltonian $H_C$. We consider how modifying the initial problem, by adding more interaction terms to the corresponding Hamiltonian, leads to the emergence of a first-order phase transition during the annealing process. This phenomenon causes the total annealing duration, $T$, required to prepare the ground state of $H_C$ with a high probability to increase exponentially with the size of the problem. Our findings indicate that with the growing complexity of problem instances, the likelihood of encountering first-order phase transitions also increases, making quantum annealing an impractical solution for these types of combinatorial optimization problems. In the second part, we focus on the problem of barren plateaus in generic variational quantum algorithms. Barren plateaus correspond to flat regions in the parameter space where the gradient of the cost function is zero in expectation, and with the variance decaying exponentially with the system size, thus obstructing an efficient parameter optimization. We propose an algorithm to circumvent Barren Plateaus by monitoring the entanglement entropy of k-local reduced density matrices, alongside a method for estimating entanglement entropy via classical shadow tomography. We illustrate the approach with the paradigmatic example of the variational quantum eigensolver, and show that our algorithm effectively avoids barren plateaus in the initialization as well as during the optimization stage. Lastly, in the last two Chapters of this thesis, we focus on the quantum approximate optimization algorithm (QAOA), originally introduced as an algorithm for solving generic combinatorial optimization problems in near-term quantum devices. Specifically, we focus on how to develop rigorous initialization strategies with guarantee improvement. Our motivation for this study lies in that for random initialization, the optimization typically leads to local minima with poor performance. Our main result corresponds to the analytical construction of index-1 saddle points or transition states, stationary points with a single direction of descent, as a tool for systematically exploring the QAOA optimization landscape. This leads us to propose a novel greedy parameter initialization strategy that guarantees for the energy to decrease with an increasing number of circuit layers. Furthermore, with precise estimates for the negative Hessian eigenvalue and its eigenvector, we establish a lower bound for energy improvement following a QAOA iteration. |
| 856 ## - ELECTRONIC LOCATION AND ACCESS |
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| Uniform Resource Identifier |
<a href="https://doi.org/10.15479/at:ista:17208">https://doi.org/10.15479/at:ista:17208</a> |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) |
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| Source of classification or shelving scheme |
Dewey Decimal Classification |