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Warm-starting quantum optimization
Open accessAbstract
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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“Concerning the former, a preconditioning of the quantum algorithm for VQAs is provided by warm-starting with classical solvers for relaxed CO problems [42], e.g., an SDP solver [137].”
From Quantum Combinatorial Optimization in the NISQ Era: A Systematic Mapping Study (2024) · cites this paper as [42]
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“Recent work has argued in favor of using classical algorithms to generate initial states which are weighted in favor of likely good solutions [6, 7], and the effect of this”
MethodVariational quantum multiobjective optimization
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Low-depth Clifford circuits approximately solve MaxCut
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JuliQAOA: Fast, Flexible QAOA Simulation
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Metadata
- Authors
- Egger, D. J., Mareček, J., & Woerner, S.
- Affiliations
- IBM Research - Zurich (CH)
- Czech Technical University in Prague (CZ)
- Venue
- Quantum
- Published
- 2021-06-17
- Volume
- 5
- Pages
- 479
- ISSN
- 2521-327X (ISSN-L)
- 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
- gold
- doi.org
- 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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