Layer VQE: A Variational Approach for Combinatorial Optimization on Noisy Quantum Computers
Open accessAbstract
Combinatorial optimization on near-term quantum devices is a promising path to demonstrating quantum advantage. However, the capabilities of these devices are constrained by high noise or error rates. In this article, inspired by the variational quantum eigensolver (VQE), we propose an iterative layer VQE (L-VQE) approach. We present a large-scale numerical study, simulating circuits with up to 40 qubits and 352 parameters, that demonstrates the potential of the proposed approach. We evaluate quantum optimization heuristics on the problem of detecting multiple communities in networks, for which we introduce a novel qubit-frugal formulation. We numerically compare L-VQE with the quantum approximate optimization algorithm (QAOA) and demonstrate that QAOA achieves lower approximation ratios while requiring significantly deeper circuits. We show that L-VQE is more robust to finite sampling errors and has a higher chance of finding the solution as compared with standard VQE approaches. Our simulation results show that L-VQE performs well under realistic hardware noise.
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The Layer-VQE iteratively builds the quantum circuit by starting with a shallow ansatz, optimizing parameters, stopping before convergence, then iteratively adding a new layer and optimizing until a point prior to convergence.
“The basic idea behind Layer-VQE is to start with a shallow ansatz, then, optimize the parameters and stop the optimization before convergence is reached. Thereafter, the procedure of (i) adding a new layer to the ansatz and (ii) parameter optimization until a certain point prior to convergence is iteratively repeated.”
From Quantum Combinatorial Optimization in the NISQ Era: A Systematic Mapping Study (2024) · cites this paper as [89]
L-VQE uses a very expressive parameterized circuit that can in principle solve the problem exactly with no two-qubit gates, just by optimizing the parameters of the initial single-qubit-gate layer.
“L-VQE uses a very expressive parameterized circuit that can in principle solve the problem exactly with no two-qubit gates, just by optimizing the parameters of the initial single-qubit-gate layer .”
From Constrained quantum optimization for extractive summarization on a trapped-ion quantum computer (2022) · cites this paper as [24]
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- S. Wang et al., "Noise-induced barren plateaus in variational quan- tum algorithms," Nature Commun., vol. 12, 2021, Art. no. 6961, doi: 10.1038/s41467-021-27045-6. · DOI · Paper page
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- Authors
- Liu, X., Angone, A., Shaydulin, R., Safro, I., Alexeev, Y., & Cincio, L.
- Affiliations
- University of Delaware (US)
- Clemson University (US)
- Argonne National Laboratory (US)
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM, USA
- Venue
- IEEE Transactions on Quantum Engineering
- Published
- 2022
- Volume
- 3
- Pages
- 1-20
- ISSN
- 2689-1808 (ISSN-L)
- OpenAlex
- W3127043585
- Cited by
- 78
- References
- 85
- Citations by year
- 2026: 7 · 2025: 12 · 2024: 21 · 2023: 17 · 2022: 17 · 2021: 4
- FWCI
- 5.51
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Licence
- Locations
- IEEE Transactions on Quantum Engineering (publishedVersion, cc-by-nc-nd)
- arXiv (Cornell University) (submittedVersion)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
- OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Defense Advanced Research Projects Agency
- Laboratory Directed Research and Development
- Argonne National Laboratory
- Office of Science
- U.S. Department of Energy (DE-AC02-06CH11357)
- Office of Advanced Scientific Computing Research
- Accelerated Research for Quantum Computing program
- Laboratory Directed Research and Development program of Los Alamos National Laboratory (20200056DR)
- U.S. DOE
- Accelerated Research in Quantum Computing program
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Keywords
- variational quantum eigensolver, combinatorial optimization, noisy quantum computers, quantum approximate optimization algorithm, community detection, sampling error, circuit depth, device noise
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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