---
OA_place: publisher
_id: '17208'
abstract:
- lang: eng
  text: "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. \r\n\r\nIn 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.\r\n\r\nIn 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. \r\n\r\nLastly, 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."
acknowledged_ssus:
- _id: ScienComp
alternative_title:
- ISTA Thesis
article_processing_charge: No
author:
- first_name: Raimel A
  full_name: Medina Ramos, Raimel A
  id: CE680B90-D85A-11E9-B684-C920E6697425
  last_name: Medina Ramos
  orcid: 0000-0002-5383-2869
citation:
  ama: Medina Ramos RA. Exploring the optimization landscape of variational quantum
    algorithms. 2024. doi:<a href="https://doi.org/10.15479/at:ista:17208">10.15479/at:ista:17208</a>
  apa: Medina Ramos, R. A. (2024). <i>Exploring the optimization landscape of variational
    quantum algorithms</i>. Institute of Science and Technology Austria. <a href="https://doi.org/10.15479/at:ista:17208">https://doi.org/10.15479/at:ista:17208</a>
  chicago: Medina Ramos, Raimel A. “Exploring the Optimization Landscape of Variational
    Quantum Algorithms.” Institute of Science and Technology Austria, 2024. <a href="https://doi.org/10.15479/at:ista:17208">https://doi.org/10.15479/at:ista:17208</a>.
  ieee: R. A. Medina Ramos, “Exploring the optimization landscape of variational quantum
    algorithms,” Institute of Science and Technology Austria, 2024.
  ista: Medina Ramos RA. 2024. Exploring the optimization landscape of variational
    quantum algorithms. Institute of Science and Technology Austria.
  mla: Medina Ramos, Raimel A. <i>Exploring the Optimization Landscape of Variational
    Quantum Algorithms</i>. Institute of Science and Technology Austria, 2024, doi:<a
    href="https://doi.org/10.15479/at:ista:17208">10.15479/at:ista:17208</a>.
  short: R.A. Medina Ramos, Exploring the Optimization Landscape of Variational Quantum
    Algorithms, Institute of Science and Technology Austria, 2024.
corr_author: '1'
date_created: 2024-07-09T09:14:24Z
date_published: 2024-07-09T00:00:00Z
date_updated: 2026-04-07T12:43:22Z
day: '09'
ddc:
- '539'
degree_awarded: PhD
department:
- _id: GradSch
- _id: MaSe
doi: 10.15479/at:ista:17208
ec_funded: 1
file:
- access_level: closed
  checksum: 6f45273d04f4418bc2adc018baed0525
  content_type: application/zip
  creator: rmedinar
  date_created: 2024-07-09T09:21:44Z
  date_updated: 2024-07-10T11:34:09Z
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  file_size: '14218691'
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  content_type: application/pdf
  creator: rmedinar
  date_created: 2024-07-17T09:23:24Z
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  success: 1
file_date_updated: 2024-07-17T09:23:24Z
fulldoi: https://doi.org/10.15479/at:ista:17208
has_accepted_license: '1'
keyword:
- Quantum computing
- Variational Quantum Algorithms
- Optimization
language:
- iso: eng
month: '07'
oa: 1
oa_version: Published Version
page: '133'
project:
- _id: 23841C26-32DE-11EA-91FC-C7463DDC885E
  call_identifier: H2020
  grant_number: '850899'
  name: 'Non-Ergodic Quantum Matter: Universality, Dynamics and Control'
publication_identifier:
  issn:
  - 2663-337X
publication_status: published
publisher: Institute of Science and Technology Austria
related_material:
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  - id: '10545'
    relation: part_of_dissertation
    status: public
  - id: '10067'
    relation: part_of_dissertation
    status: public
  - id: '17222'
    relation: part_of_dissertation
    status: public
  - id: '13125'
    relation: part_of_dissertation
    status: public
  - id: '11471'
    relation: part_of_dissertation
    status: public
status: public
supervisor:
- first_name: Maksym
  full_name: Serbyn, Maksym
  id: 47809E7E-F248-11E8-B48F-1D18A9856A87
  last_name: Serbyn
  orcid: 0000-0002-2399-5827
title: Exploring the optimization landscape of variational quantum algorithms
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: dissertation
user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd
year: '2024'
...