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Cited by 270Quantum Computing Algorithms and ArchitectureComplexity and Algorithms in GraphsAdvanced Optimization Algorithms Research

The DOI matches its Crossref record; 122 of the 122 references it cites were found in a registry or an index.

Warm-starting quantum optimization

Open access
Egger, Daniel J., Mareček, Jakub, Woerner, Stefan·2021·Quantum
DOI 10.22331/q-2021-06-17-479
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Abstract

There is an increasing interest in quantum algorithms for problems of integer programming and combinatorial optimization. Classical solvers for such problems employ relaxations, which replace binary variables with continuous ones, for instance in the form of higher-dimensional matrix-valued problems (semidefinite programming). Under the Unique Games Conjecture, these relaxations often provide the best performance ratios available classically in polynomial time. Here, we discuss how to warm-start quantum optimization with an initial state corresponding to the solution of a relaxation of a combinatorial optimization problem and how to analyze properties of the associated quantum algorithms. In particular, this allows the quantum algorithm to inherit the performance guarantees of the classical algorithm. We illustrate this in the context of portfolio optimization, where our results indicate that warm-starting the Quantum Approximate Optimization Algorithm (QAOA) is particularly beneficial at low depth. Likewise, Recursive QAOA for MAXCUT problems shows a systematic increase in the size of the obtained cut for fully connected graphs with random weights, when Goemans-Williamson randomized rounding is utilized in a warm start. It is straightforward to apply the same ideas to other randomized-rounding schemes and optimization problems.

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Research works printed but not linked: 4

  1. Edward Farhi, Jeffrey Goldstone, and Sam Gutmann. A quantum approximate optimization algorithm, 2014a. URL https://arxiv.org/abs/1411.4028. · arXiv
  2. Michael Juenger, Elisabeth Lobe, Petra Mutzel, Gerhard Reinelt, Franz Rendl, Giovanni Rinaldi, and Tobias Stollenwerk. Performance of a quantum annealer for Ising ground state computations on chimera graphs, 2019. URL https://arxiv.org/abs/1904.11965. · arXiv
  3. Sergey Bravyi, Alexander Kliesch, Robert Koenig, and Eugene Tang. Hybrid quantum-classical algorithms for approximate graph coloring, 2020b. URL https://arxiv.org/abs/2011.13420. · arXiv
  4. Michael Mitzenmacher and Eli Upfal. Probability and computing: Randomization and probabilistic techniques in algorithms and data analysis. Cambridge university press, 2017.

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Metadata

Authors
Egger, D. J., Mareček, J., & Woerner, S.
Affiliations
  • IBM Research - Zurich (CH)
  • Czech Technical University in Prague (CZ)
ORCID
Venue
Quantum
Publisher
Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften
Published
2021-06-17
Volume
5
Pages
479
ISSN
2521-327X (ISSN-L)
DOI
10.22331/q-2021-06-17-479
OpenAlex
W3088409280
Cited by
269
References
122
Citations by year
2026: 44 · 2025: 61 · 2024: 57 · 2023: 56 · 2022: 34 · 2021: 16
FWCI
14.35
Type
journal article
Language
en
Open access
Licence
Locations
  • Quantum (publishedVersion, cc-by)
  • arXiv (Cornell University) (submittedVersion)
  • DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
  • arXiv (Cornell University) (cc-by)
  • Bulletin of the American Physical Society
Funders
OP RDE project Research Center for Informatic (CZ.02.1.01/0.0/0.0/16_019/0000765)
Topics
  • Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
  • Physical Sciences › Computer Science › Computational Theory and Mathematics › Complexity and Algorithms in Graphs
  • Physical Sciences › Mathematics › Numerical Analysis › Advanced Optimization Algorithms Research
Keywords
warm start, quantum optimization, quantum approximate optimization algorithm, MaxCut, portfolio optimization, semidefinite relaxation, Unique Games Conjecture, randomized rounding, integer programming, combinatorial optimization, performance guarantees

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