---
DOAJ_listed: '1'
_id: '15122'
abstract:
- lang: eng
  text: Quantum computers are increasing in size and quality but are still very noisy.
    Error mitigation extends the size of the quantum circuits that noisy devices can
    meaningfully execute. However, state-of-the-art error mitigation methods are hard
    to implement and the limited qubit connectivity in superconducting qubit devices
    restricts most applications to the hardware's native topology. Here we show a
    quantum approximate optimization algorithm (QAOA) on nonplanar random regular
    graphs with up to 40 nodes enabled by a machine learning-based error mitigation.
    We use a swap network with careful decision-variable-to-qubit mapping and a feed-forward
    neural network to optimize a depth-two QAOA on up to 40 qubits. We observe a meaningful
    parameter optimization for the largest graph which requires running quantum circuits
    with 958 two-qubit gates. Our paper emphasizes the need to mitigate samples, and
    not only expectation values, in quantum approximate optimization. These results
    are a step towards executing quantum approximate optimization at a scale that
    is not classically simulable. Reaching such system sizes is key to properly understanding
    the true potential of heuristic algorithms like QAOA.
acknowledgement: S.H.S. acknowledges support from the IBM Ph.D. fellowship 2022 in
  quantum computing. The authors also thank M. Serbyn, R. Kueng, R. A. Medina, and
  S. Woerner for fruitful discussions.
article_number: '013223'
article_processing_charge: Yes
article_type: original
arxiv: 1
author:
- first_name: Stefan
  full_name: Sack, Stefan
  id: dd622248-f6e0-11ea-865d-ce382a1c81a5
  last_name: Sack
  orcid: 0000-0001-5400-8508
- first_name: Daniel J.
  full_name: Egger, Daniel J.
  last_name: Egger
citation:
  ama: Sack S, Egger DJ. Large-scale quantum approximate optimization on nonplanar
    graphs with machine learning noise mitigation. <i>Physical Review Research</i>.
    2024;6(1). doi:<a href="https://doi.org/10.1103/PhysRevResearch.6.013223">10.1103/PhysRevResearch.6.013223</a>
  apa: Sack, S., &#38; Egger, D. J. (2024). Large-scale quantum approximate optimization
    on nonplanar graphs with machine learning noise mitigation. <i>Physical Review
    Research</i>. American Physical Society. <a href="https://doi.org/10.1103/PhysRevResearch.6.013223">https://doi.org/10.1103/PhysRevResearch.6.013223</a>
  chicago: Sack, Stefan, and Daniel J. Egger. “Large-Scale Quantum Approximate Optimization
    on Nonplanar Graphs with Machine Learning Noise Mitigation.” <i>Physical Review
    Research</i>. American Physical Society, 2024. <a href="https://doi.org/10.1103/PhysRevResearch.6.013223">https://doi.org/10.1103/PhysRevResearch.6.013223</a>.
  ieee: S. Sack and D. J. Egger, “Large-scale quantum approximate optimization on
    nonplanar graphs with machine learning noise mitigation,” <i>Physical Review Research</i>,
    vol. 6, no. 1. American Physical Society, 2024.
  ista: Sack S, Egger DJ. 2024. Large-scale quantum approximate optimization on nonplanar
    graphs with machine learning noise mitigation. Physical Review Research. 6(1),
    013223.
  mla: Sack, Stefan, and Daniel J. Egger. “Large-Scale Quantum Approximate Optimization
    on Nonplanar Graphs with Machine Learning Noise Mitigation.” <i>Physical Review
    Research</i>, vol. 6, no. 1, 013223, American Physical Society, 2024, doi:<a href="https://doi.org/10.1103/PhysRevResearch.6.013223">10.1103/PhysRevResearch.6.013223</a>.
  short: S. Sack, D.J. Egger, Physical Review Research 6 (2024).
corr_author: '1'
date_created: 2024-03-17T23:00:59Z
date_published: 2024-03-01T00:00:00Z
date_updated: 2025-05-14T09:32:15Z
day: '01'
ddc:
- '530'
department:
- _id: MaSe
doi: 10.1103/PhysRevResearch.6.013223
external_id:
  arxiv:
  - '2307.14427'
file:
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has_accepted_license: '1'
intvolume: '         6'
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language:
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month: '03'
oa: 1
oa_version: Published Version
project:
- _id: bd660c93-d553-11ed-ba76-fb0fb6f49c0d
  name: IMB PhD Nomination Fellowship - Stefan Sack
publication: Physical Review Research
publication_identifier:
  eissn:
  - 2643-1564
publication_status: published
publisher: American Physical Society
quality_controlled: '1'
scopus_import: '1'
status: public
title: Large-scale quantum approximate optimization on nonplanar graphs with machine
  learning noise mitigation
tmp:
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  short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 6
year: '2024'
...
---
OA_place: publisher
_id: '14622'
abstract:
- lang: eng
  text: "This Ph.D. thesis presents a detailed investigation into Variational Quantum
    Algorithms\r\n(VQAs), a promising class of quantum algorithms that are well suited
    for near-term quantum\r\ncomputation due to their moderate hardware requirements
    and resilience to noise. Our\r\nprimary focus lies on two particular types of
    VQAs: the Quantum Approximate Optimization\r\nAlgorithm (QAOA), used for solving
    binary optimization problems, and the Variational Quantum\r\nEigensolver (VQE),
    utilized for finding ground states of quantum many-body systems.\r\nIn the first
    part of the thesis, we examine the issue of effective parameter initialization
    for\r\nthe QAOA. The work demonstrates that random initialization of the QAOA
    often leads to\r\nconvergence in local minima with sub-optimal performance. To
    mitigate this issue, we propose\r\nan initialization of QAOA parameters based
    on the Trotterized Quantum Annealing (TQA).\r\nWe show that TQA initialization
    leads to the same performance as the best of an exponentially\r\nscaling number
    of random initializations.\r\nThe second study introduces Transition States (TS),
    stationary points with a single direction\r\nof descent, as a tool for systematically
    exploring the QAOA optimization landscape. This\r\nleads us to propose a novel
    greedy parameter initialization strategy that guarantees for the\r\nenergy to
    decrease with increasing number of circuit layers.\r\nIn the third section, we
    extend the QAOA to qudit systems, which are higher-dimensional\r\ngeneralizations
    of qubits. This chapter provides theoretical insights and practical strategies
    for\r\nleveraging the increased computational power of qudits in the context of
    quantum optimization\r\nalgorithms and suggests a quantum circuit for implementing
    the algorithm on an ion trap\r\nquantum computer.\r\nFinally, we propose an algorithm
    to avoid “barren plateaus”, regions in parameter space with\r\nvanishing gradients
    that obstruct efficient parameter optimization. This novel approach relies\r\non
    defining a notion of weak barren plateaus based on the entropies of local reduced
    density\r\nmatrices and showcases how these can be efficiently quantified using
    shadow tomography.\r\nTo illustrate the approach we employ the strategy in the
    VQE and show that it allows to\r\nsuccessfully avoid barren plateaus in the initialization
    and throughout the optimization.\r\nTaken together, this thesis greatly enhances
    our understanding of parameter initialization and\r\noptimization in VQAs, expands
    the scope of QAOA to higher-dimensional quantum systems,\r\nand presents a method
    to address the challenge of barren plateaus using the VQE. These\r\ninsights are
    instrumental in advancing the field of near-term quantum computation."
alternative_title:
- ISTA Thesis
article_processing_charge: No
author:
- first_name: Stefan
  full_name: Sack, Stefan
  id: dd622248-f6e0-11ea-865d-ce382a1c81a5
  last_name: Sack
  orcid: 0000-0001-5400-8508
citation:
  ama: 'Sack S. Improving variational quantum algorithms : Innovative initialization
    techniques and extensions to qudit systems. 2023. doi:<a href="https://doi.org/10.15479/at:ista:14622">10.15479/at:ista:14622</a>'
  apa: 'Sack, S. (2023). <i>Improving variational quantum algorithms : Innovative
    initialization techniques and extensions to qudit systems</i>. Institute of Science
    and Technology Austria. <a href="https://doi.org/10.15479/at:ista:14622">https://doi.org/10.15479/at:ista:14622</a>'
  chicago: 'Sack, Stefan. “Improving Variational Quantum Algorithms : Innovative Initialization
    Techniques and Extensions to Qudit Systems.” Institute of Science and Technology
    Austria, 2023. <a href="https://doi.org/10.15479/at:ista:14622">https://doi.org/10.15479/at:ista:14622</a>.'
  ieee: 'S. Sack, “Improving variational quantum algorithms : Innovative initialization
    techniques and extensions to qudit systems,” Institute of Science and Technology
    Austria, 2023.'
  ista: 'Sack S. 2023. Improving variational quantum algorithms : Innovative initialization
    techniques and extensions to qudit systems. Institute of Science and Technology
    Austria.'
  mla: 'Sack, Stefan. <i>Improving Variational Quantum Algorithms : Innovative Initialization
    Techniques and Extensions to Qudit Systems</i>. Institute of Science and Technology
    Austria, 2023, doi:<a href="https://doi.org/10.15479/at:ista:14622">10.15479/at:ista:14622</a>.'
  short: 'S. Sack, Improving Variational Quantum Algorithms : Innovative Initialization
    Techniques and Extensions to Qudit Systems, Institute of Science and Technology
    Austria, 2023.'
corr_author: '1'
date_created: 2023-11-28T10:58:13Z
date_published: 2023-11-30T00:00:00Z
date_updated: 2026-04-07T13:53:47Z
day: '30'
ddc:
- '530'
degree_awarded: PhD
department:
- _id: GradSch
- _id: MaSe
doi: 10.15479/at:ista:14622
ec_funded: 1
file:
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  checksum: 068fd3570506ec42b2faa390de784bc4
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  creator: ssack
  date_created: 2023-11-30T15:53:10Z
  date_updated: 2024-11-30T23:30:03Z
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  date_updated: 2024-11-30T23:30:03Z
  embargo_to: open_access
  file_id: '14636'
  file_name: PhD Thesis (1).zip
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file_date_updated: 2024-11-30T23:30:03Z
has_accepted_license: '1'
language:
- iso: eng
month: '11'
oa: 1
oa_version: Published Version
page: '142'
project:
- _id: bd660c93-d553-11ed-ba76-fb0fb6f49c0d
  name: IMB PhD Nomination Fellowship - Stefan Sack
- _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:
  record:
  - id: '13125'
    relation: part_of_dissertation
    status: public
  - id: '11471'
    relation: part_of_dissertation
    status: public
  - id: '9760'
    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: 'Improving variational quantum algorithms : Innovative initialization techniques
  and extensions to qudit systems'
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  name: Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC
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  short: CC BY-NC-SA (4.0)
type: dissertation
user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd
year: '2023'
...