QED driven QAOA for network-flow optimization
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We present a general framework for modifying quantum approximate optimization algorithms (QAOA) to solve constrained network flow problems. By exploiting an analogy between flow-constraints and Gauss' law for electromagnetism, we design lattice quantum electrodynamics (QED)- inspired mixing Hamiltonians that preserve flow constraints throughout the QAOA process. This results in an exponential reduction in the size of the configuration space that needs to be explored, which we show through numerical simulations, yields higher quality approximate solutions compared to the original QAOA routine. We outline a specific implementation for edge-disjoint path (EDP) problems related to traffic congestion minimization, numerically analyze the effect of initial state choice, and explore trade-offs between circuit complexity and qubit resources via a particle-vortex duality mapping. Comparing the effect of initial states reveals that starting with an ergodic (unbiased) superposition of solutions yields better performance than beginning with the mixer ground-state, suggesting a departure from the ``short-cut to adiabaticity" mechanism often used to motivate QAOA.
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Several other approaches have been identified where ansatz adaptations happen as a secondary effect.
“Several other approaches have been identified where the ansatz adaptations happen as a secondary effect, e.g., References [36, 48, 82, 131, 153].”
From Quantum Combinatorial Optimization in the NISQ Era: A Systematic Mapping Study (2024) · cites this paper as [153]
Zhang et al. proposed an approach for network flow optimization problems similar to the Quantum Alternating Operator Ansatz but inspired by quantum electrodynamics.
“An approach for network flow optimization problems like, e.g., routing problems, which is similar to the Quantum Alternating Operator Ansatz but inspired by quantum electrodynamics, has been proposed by Zhang et al. [153].”
From Quantum Combinatorial Optimization in the NISQ Era: A Systematic Mapping Study (2024) · cites this paper as [153]
Zhang et al. also provide an advanced, restricted version of their method that additionally avoids physically irrelevant solutions.
“They also provide an advanced, restricted version of their method that additionally avoids physically irrelevant solutions.”
From Quantum Combinatorial Optimization in the NISQ Era: A Systematic Mapping Study (2024) · cites this paper as [153]
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- Authors
- Zhang, Y., Zhang, R., & Potter, A. C.
- Affiliations
- The University of Texas at Austin (US)
- ORCID
- Potter, Andrew C.
- Venue
- Quantum
- Published
- 2021-07-27
- Volume
- 5
- Pages
- 510
- ISSN
- 2521-327X (ISSN-L)
- OpenAlex
- W3036910907
- Cited by
- 19
- References
- 19
- Citations by year
- 2026: 6 · 2025: 2 · 2024: 3 · 2023: 3 · 2022: 3 · 2021: 1 · 2020: 1
- FWCI
- 0.88
- 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)
- Funders
- National Science Foundation (DMR-1653007, CCF1648712)
- 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 › Computer Science › Artificial Intelligence › Metaheuristic Optimization Algorithms Research
- Keywords
- quantum approximate optimization algorithm, network flow optimization, constrained optimization, edge-disjoint paths, particle-vortex duality, circuit complexity
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