Pith. sign in

REVIEW 4 major objections 6 minor 30 references

A Hybrid Classical-Quantum Approach for Multi-Constrained Location Optimization Problem

T0 review · 4 major / 6 minor · reviewed 2026-08-02 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read Combining unbalanced penalization, a linear ramp parameter schedule, and warm starting yields the best QAOA performance on the maximal covering location problem for the instances tested.

desk verdict Systematic first test of UP+LR+WS-QAOA on MCLP, but the QUBO encoding's ground state is unverified—infeasible solutions can score lower than the true optimum. read the letter →

arxiv 2607.16277 v1 pith:ENVRMNBN submitted 2026-07-08 quant-ph

Jorge Saavedra-Benavides , J. Alejandro Montanez-Barrera , Alberto Maldonado-Romo , Daniel Sierra-Sosa This is my paper · ORCID
classification quant-ph MSC 90C2790C1081P68 PACS 03.67.Ac
keywords MaximalCoveringLocationProblemQUBOUnbalancedPenalizationQAOAWarm-StartingLinearRampFacilityQuantumoptimization
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper claims that the maximal covering location problem (MCLP), an NP-hard facility-siting problem with both equality and inequality constraints, can be solved more accurately by QAOA when three techniques are combined: Unbalanced Penalization (UP) to encode inequality constraints without extra qubits, a linear ramp (LR) parameter schedule that reduces the variational parameters to two, and warm-starting (WS-QAOA) with a classically relaxed solution. The authors test four QAOA configurations on five small grid sizes and report that the full combination, UP+LR+WS, achieves the highest approximation ratio, probability of sampling the optimal solution, and feasibility ratio, while using fewer optimizer calls than configurations without LR. A sympathetic reader would care because MCLP is practically relevant and multi-constrained, and the paper offers evidence that encoding choice and classical subroutines matter as much as circuit depth for near-term quantum optimization.

What carries the argument

The load-bearing mechanism is the Unbalanced Penalization (UP) encoding of inequality constraints, in which a violation h(x) < 0 pushes an exponential penalty e^{-h(x)} upward; a second-order Taylor expansion converts that penalty into a quadratic QUBO term, leaving the qubit count unchanged (no slack variables). On top of this, the Linear Ramp (LR) schedule fixes the QAOA angles as linear functions of layer index, reducing the optimization space to two parameters, and WS-QAOA prepares the initial state by rotating each qubit according to a classically relaxed solution, replacing the uniform superposition. Together they define a search that starts near a good solution, stays feasible via the

What would settle it

Enumerate every feasible and infeasible binary string for one of the 3x4 instances (18 qubits, 262,144 strings) and compare the minimizer of the penalized QUBO, using the paper's lambda0 = P and lambda1 = lambda2 = mean demand, against the MCLP optimum from a classical solver. If any instance has a QUBO ground state that is not the MCLP optimum, the encoding premise fails.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central discovery is that the way constraints are embedded into a QUBO and the way QAOA's parameters and initial state are set are mutually reinforcing. The UP encoding replaces slack variables with a penalty built from a quadratic expansion of e^{-h(x)}, halving the qubit count for the MCLP instances studied; the linear ramp schedule cuts the number of variational parameters from 2p to 2; and the warm start biases the initial state toward a solution of the continuous relaxation. The reported experiments, on grids from 2x2 to 3x4 with ten instances each, show the triple combination reaching average approximation ratios and feasibility ratios near 1.0 and probabi

Load-bearing premise

Everything rests on the claim that the constructed QUBO, with the UP penalties and the chosen coefficients, has its ground state at the true MCLP optimum; the paper verifies this energy ordering for one 3x3 instance via a ranked energy landscape, but does not prove it for all instances, and the Taylor expansion of the exponential penalty is only approximate.

Editorial extensions

If this is right

  • For MCLP instances of the sizes tested, practitioners can expect UP+LR+WS-QAOA to outperform plain QAOA and the other three configurations on all three quality metrics at a given circuit depth p.
  • The UP encoding removes the need for slack variables, so any constrained QUBO problem whose inequality constraints fit the form h(x) >= 0 can be embedded with roughly half the qubits of the slack-variable method.
  • With LR, the number of classical optimization parameters stays at two regardless of circuit depth, which the paper ties to substantially fewer function evaluations; this makes deeper circuits more practical.
  • Because WS-QAOA's benefit traces to a continuous relaxation, the method inherits a sensitivity to that relaxation's quality, which the paper explicitly flags as the main limitation.
  • The results support the view that, for this class of problems, encoding and initialization choices dominate the benefit from increasing p, since UP_LR_WS performs well even at small p.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The UP expansion is a second-order Taylor approximation of e^{-h(x)}, and binary violations are integer values, so for violations larger than 1 the approximation will drift from the true exponential penalty; on larger instances the penalty coefficients may need to grow or the expansion may need to be replaced, and the paper does not test this regime.
  • The choice lambda0 = P and lambda1 = lambda2 = mean demand is a heuristic tied to instance scale; a natural testable extension is an instance-adaptive penalty search that reuses the grid-search idea on every instance rather than a single 3x3 example.
  • The authors compare models under the same p=50 for size scaling, but the warm-started models degrade by about 10% on the largest (3x4) instances, suggesting a crossover point beyond which the relaxation quality is too poor to help; identifying that point would be a concrete follow-up.
  • If the LP relaxation of MCLP is near-integral, warm starting may be especially effective for this problem class; the same pipeline could be tried on problems with loose relaxations, where the warm start would be a random bias and performance should approach UP_LR.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 6 minor

Summary. The paper proposes a QUBO formulation of the Maximal Covering Location Problem using Unbalanced Penalization (UP) to encode inequality constraints without slack variables, and studies the effect of combining UP with a warm-started QAOA (WS-QAOA) and a linear ramp (LR) parameter schedule. Four model variants (UP, UP_LR, UP_WS, UP_LR_WS) are compared on small randomly generated grid instances (up to 3x4) using CPLEX as a reference. The central empirical claim is that UP_LR_WS achieves the highest approximation ratio, probability of sampling the optimal solution, and feasibility ratio while using fewer classical optimizer evaluations, and that this advantage persists as instance size grows.

Significance. If verified, the paper would be a useful empirical contribution to hybrid quantum optimization for constrained facility-location problems: it demonstrates that UP can avoid the qubit overhead of slack variables, and that warm starting and a low-dimensional parameter schedule can improve QAOA in a multi-constrained setting. The paper is also careful in places: it explicitly notes that its approximation ratio is computed on the penalized Hamiltonian, and it uses CPLEX as an external reference for optimality. However, the significance is currently limited by the small instance sizes and, more importantly, by unverified preconditions about the QUBO encoding that all reported metrics depend on.

major comments (4)
  1. [Sec. 3.4.2, Eq. (22); Sec. 4.2-4.3] The penalty coefficients λ0=P and λ1=λ2=mean demand are selected by a grid search on the same 50 instances used to report all results. This is selection on the evaluation set: the reported values of r, P(x*), and FR are optimistic for new instances and do not provide an honest estimate of the method's generalization. Because the paper's main conclusion is that UP_LR_WS achieves high solution quality, this tuning protocol is load-bearing. The authors should either separate tuning from evaluation (e.g., a validation subset or a pre-registered rule) or report the sensitivity of all metrics to the penalty coefficients.
  2. [Sec. 3.1, Eq. (12); Sec. 3.4.2, Fig. 1; Eq. (15)-(16)] The manuscript does not establish that the ground state of the penalized QUBO Hamiltonian Eq. (15) coincides with the MCLP optimum. With λ0=P in Eq. (16), an infeasible solution with P+1 facilities can have lower energy than the true optimum whenever the additional facility covers more than P extra units of demand (e.g., demands drawn from {1,...,6} and P=1: if D'-D*=2, then E(S')-E(S*) = P - (D'-D*) = -1). The only evidence is the single 3x3 landscape in Fig. 1. Since the approximation ratio Eq. (23) is defined relative to the penalized Hamiltonian's eigenvalues, a low-energy infeasible state can inflate r, and the reported P(x*) and FR would then not measure actual MCLP solution quality. The authors must verify for every test instance that the CPLEX optimum is the unique ground state of Eq. (15), or at least provide a penalty upper bound that guarantees no infeasible state lies below i
  3. [Sec. 3.1, Eq. (12)] The second-order Taylor expansion e^{-h} ≈ 1 - h + h^2/2 is used to convert the exponential penalty into QUBO form, under the stated assumption of 'small constraint violations.' For MCLP, h(x) is integer-valued (e.g., h=-2 for a violation), and the expansion gives 5 instead of e^2 ≈ 7.39, i.e., it systematically underestimates the penalty for infeasible states. This compounds the ground-state problem in the previous comment. The authors should either justify the approximation for integer-valued h with concrete bounds, use an exact quadratic penalty for binary constraints, or empirically verify that the approximation does not change the ground state on all instances.
  4. [Sec. 5, Conclusions] The conclusion acknowledges that the heuristic rule for penalization coefficients 'remains a limitation,' but this limitation is not reflected in the paper's main claim, which states that the integration achieves high probabilities of obtaining the optimal solution. If the penalty coefficients are not valid for unseen instances, the central claim is only about the 50 tuned instances. The authors should either temper the conclusion accordingly or supply the missing validation.
minor comments (6)
  1. [Sec. 3.4.2, Eq. (14)] The sign convention in f_UP is unclear: for feasible h>0, the term -λ1 h is negative, which appears to reward slack in the inequality constraint. This should be clarified or corrected, since it affects the interpretation of the energy landscape.
  2. [Sec. 3.4.2] The sentence 'A grid search allowed us to determine the parameters that best adapted to each instance' is ambiguous: it is unclear whether the grid search was performed per instance or once to derive the formula in Eq. (22). Please state the exact procedure and whether the evaluation instances were seen during the search.
  3. [Sec. 4.1, Fig. 3] The statement that SV requires 'approximately twice as many variables' should be made precise: the exact qubit count formula for the SV embedding should be given in the text, not only inferred from the figure.
  4. [Sec. 3.4.4, Eq. (23)] The definition of r uses emax of the penalized Hamiltonian. For a minimization problem, a state with energy above emax would give negative r; it may be useful to clarify the normalization, though this is a minor presentation issue.
  5. [General] No code or data are provided, which makes it difficult to reproduce Figs. 4-6 and to check the ground-state claim for all 50 instances. A reproducibility statement with data and code would strengthen the paper.
  6. [Abstract and Sec. 5] The phrase 'maintaining approximation of low-energy states' is awkward; consider 'while maintaining approximation ratios close to the optimal low-energy state.' Also, the conclusion should more explicitly separate the two claims: (1) UP_LR_WS outperforms other models on the tested penalized Hamiltonian, and (2) the tested penalized Hamiltonian faithfully represents MCLP.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity; the evaluation is anchored to external CPLEX optima and the claimed limitations are correctness concerns, not circular reductions.

full rationale

The derivation chain is: MCLP (Eqs. 1–5) → QUBO with UP penalties (Eqs. 12–16, 22) → Ising Hamiltonian (Eq. 7) → QAOA/WS-QAOA/LR circuits (Eqs. 9, 17–21) → metrics (Eqs. 23–25). The anchor to the original problem is external: CPLEX provides both the relaxed solution used by WS and the optimal solution x* used as reference (§3.4.3). The optimality claim is therefore not defined circularly in terms of the QUBO's ground state; if the penalized ground state failed to match the CPLEX optimum, P(x*) would be low and the paper's conclusions would fail. The approximation ratio is explicitly computed against the penalized Hamiltonian (Eq. 23 and §3.4.4), so high r is a statement about the QAOA state relative to that Hamiltonian, not a disguised fit of the MCLP objective. The penalty coefficients are chosen by grid search and the paper itself calls this 'a limitation' (§5) and notes that r depends on the penalization coefficients (§3.4.4); this is an overfitting/correctness concern, not a circular reduction, because the coefficients do not directly set r, P(x*), or FR, and the CPLEX reference is independent. Self-citations [15,20] introduce UP and LR as published methods rather than as theorems that force the conclusions; the novelty is empirical integration. Overall, no load-bearing step reduces to its own input.

Assumptions & free parameters 3 free parameters · 6 assumptions · 0 invented entities

The central claim depends on a handful of heuristic choices: the UP Taylor approximation, the grid-searched penalty coefficients, and the WS regularization parameter. No new physical entities are introduced. The methods are borrowed from prior work, two of which are self-cited, but the main burden is the unproven fidelity of the penalized Hamiltonian's ground state.

free parameters (3)
  • λ0 (equality penalty coefficient) = λ0 = P (number of facilities)
    Set equal to P per instance; chosen via a grid-search motivated heuristic (§3.4.2), not derived.
  • λ1 = λ2 (inequality penalty coefficients) = λ1 = λ2 = (1/|I|)Σ_i a_i
    Selected by grid search to 'best adapt' to each instance; the same instances are used for evaluation, so this is fitting to the test data (§3.4.2).
  • ϵ (WS-QAOA regularization) = 0.001
    Fixed hyperparameter for all WS models (§3.4.3); chosen without sensitivity analysis.
assumptions (6)
  • ad hoc to paper The second-order Taylor expansion e^{-h(x)} ≈ 1 - h(x) + h(x)^2/2 is accurate enough to encode inequality constraints in QUBO, despite violations being integer-sized.
    Eq. 12 in §3.1; binary constraint violations are at least 1, so the 'small violations' assumption is questionable.
  • domain assumption The penalized Hamiltonian's ground state matches the original MCLP optimum for the selected λ coefficients.
    Verified only for one 3×3 instance (Fig. 1); no proof that this holds across all instances and sizes (§3.4.2).
  • domain assumption UP (Eq. 14) and its extension to ≤ constraints correctly handle the MCLP inequality constraints without extra variables.
    Taken from ref [15]; treated as a black box.
  • domain assumption WS-QAOA initial state from continuous relaxation (Eq. 18-21) and LR schedule (Eq. 17) are applied as published without modification.
    From refs [19,20]; no re-derivation.
  • standard math The QAOA variational form and Ising mapping (Eqs. 6-9) are valid.
    Standard textbook material for QUBO-to-Ising mapping and QAOA.
  • domain assumption The coverage relation N_i and demand values a_i are representative of MCLP instances.
    Instance generation in §3.4.1; only 10 random instances per size, sizes ≤18 qubits.

how reviews work

0 comments
Cite this review

Pith. "Pith review of A Hybrid Classical-Quantum Approach for Multi-Constrained Location Optimization Problem." pith.science (2026). https://pith.science/paper/ENVRMNBN

@misc{pith2026260716277,
  author       = {Pith},
  title        = {Pith review of: A Hybrid Classical-Quantum Approach for Multi-Constrained Location Optimization Problem},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ENVRMNBN}},
  note         = {Machine review of arXiv:2607.16277}
}
abstract

The Maximal Covering Location Problem (MCLP) is an NP-hard Combinatorial Optimization Problem (COP) that aims to determine the optimal facility placements that maximize total coverage. It is characterized by both equality and inequality constraints, which ensure correct coverage but significantly increase the complexity of exploring the solution space as instance size grows. Hybrid quantum-classical approaches might offer a promising alternative to classical optimization methods by enabling the exploration of complex energy landscapes through quantum superposition and probabilistic sampling. In this work, the MCLP is formulated as a Quadratic Unconstrained Binary Optimization (QUBO) model, where constraint embedding plays a critical role in solution quality. In particular, Unbalanced Penalization (UP) is employed as an alternative to the Slack Variables (SV) for handling inequality constraints without increasing the number of variables. This study focuses on QAOA and one of its variants, the WS-QAOA, which leverages a biased initial state derived from a continuous relaxation of the problem. Additionally, a linear ramp (LR) parameter schedule is incorporated to reduce optimization complexity. The performance of these techniques is evaluated both individually and in combination, as a function of circuit depth $p$ and problem size. Results show that the combined approach of UP, LR, and WS-QAOA consistently improves solution quality and feasibility metrics, while maintaining robust performance as the problem size increases, highlighting its potential within hybrid quantum-classical optimization frameworks.

Figures

Figures reproduced from arXiv: 2607.16277 by the authors.

Figure 1
Figure 1. Ranked energy landscape of a 3 × 3 MCLP instance. • Approximation ratio r: r(ψ) = ⟨ψ|HˆC |ψ⟩ − emax emin − emax , (23) where emin and emax denote the minimum and maximum eigenvalues of the cost Hamiltonian, respectively. • Probability of obtaining the optimal solution P(x ∗ ): P(x ∗ ) = |⟨ψ|x ∗ ⟩|2 , (24) where x ∗ ∈ {0, 1} n denotes the optimal solution. • Feasibility ratio F R: F R(ψ) = Number of feasible samples … view at source ↗
Figure 2
Figure 2. Experimental workflow of the integration WS-QAOA and QAOA with the proposed integrations. [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 6
Figure 6. shows the average results obtained by the models across different performance metrics as a function of the size of the instances. All models were evaluated with p = 50 to ensure equal conditions. In agreement with the results presented in [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
Figures from the paper (4 more)
Figure 3
Figure 3. Figure 3: Comparison of the number of qubits required for SV and UP across MCLP instances with different grid sizes. [PITH_FULL_IMAGE:figures/full_fig_p009_3.png]
Figure 4
Figure 4. Figure 4: Average values and standard deviation of [PITH_FULL_IMAGE:figures/full_fig_p010_4.png]
Figure 5
Figure 5. Figure 5: Average values and standard deviation of [PITH_FULL_IMAGE:figures/full_fig_p011_5.png]
Figure 6
Figure 6. Figure 6: Average values and standard deviation of [PITH_FULL_IMAGE:figures/full_fig_p012_6.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

30 extracted references · 6 canonical work pages

  1. [1]

    Transit facility allocation: Hybrid quantum-classical optimization.PLOS ONE, 17(9):e0274632, September 2022

    Einar Gabbassov. Transit facility allocation: Hybrid quantum-classical optimization.PLOS ONE, 17(9):e0274632, September 2022. ISSN 1932-6203. doi:10.1371/journal.pone.0274632. URL https://dx.plos.org/10. 1371/journal.pone.0274632. /uni00000013/uni00000011/uni0000001a/uni00000013 /uni00000013/uni00000011/uni0000001a/uni00000018 /uni00000013/uni00000011/uni...

    work page doi:10.1371/journal.pone.0274632 2022

  2. [2]

    Solving a real-world package delivery routing problem using quantum annealers.Scientific Reports, 14(1):24791, October 2024

    Eneko Osaba, Esther Villar-Rodriguez, and Antón Asla. Solving a real-world package delivery routing problem using quantum annealers.Scientific Reports, 14(1):24791, October 2024. ISSN 2045-2322. doi:10.1038/s41598- 024-75572-1. URLhttps://www.nature.com/articles/s41598-024-75572-1

    doi:10.1038/s41598- 2024

  3. [3]

    Quantum annealing for the two- level facility location problem.Future Generation Computer Systems, 174:107961, January 2026

    Alessia Ciacco, Francesca Guerriero, and Francesco Paolo Saccomanno. Quantum annealing for the two- level facility location problem.Future Generation Computer Systems, 174:107961, January 2026. ISSN 0167739X. doi:10.1016/j.future.2025.107961. URL https://linkinghub.elsevier.com/retrieve/pii/ S0167739X25002560

    arXiv 2026

  4. [4]

    MAXIMAL COVERING LOCATION PROBLEMS FOR HEALTHCARE SYSTEMS: A SYS- TEMATIC REVIEW.Pesquisa Operacional, 45:e287992, 2025

    Maressa Nunes Ribeiro Tavares, Ricardo Saraiva De Camargo, and Fátima Machado De Souza Lima. MAXIMAL COVERING LOCATION PROBLEMS FOR HEALTHCARE SYSTEMS: A SYS- TEMATIC REVIEW.Pesquisa Operacional, 45:e287992, 2025. ISSN 1678-5142, 0101-7438. doi:10.1590/0101-7438.2025.045.00287992. URL http://www.scielo.br/scielo.php?script=sci_ arttext&pid=S0101-743820250...

    arXiv 2025

  5. [5]

    Moncayo-Martínez and Naihui He

    Luis A. Moncayo-Martínez and Naihui He. Quantum optimisation for supply chain: QUBO formulations and QAOA solutions for facility location and load balancing.Results in Engineering, 29:108373, March 2026. ISSN 25901230. doi:10.1016/j.rineng.2025.108373. URL https://linkinghub.elsevier.com/retrieve/pii/ S2590123025044172

    arXiv 2026

  6. [6]

    The maximal covering location problem.Papers of the Regional Science Association, 32(1):101–118, December 1974

    Richard Church and Charles ReVelle. The maximal covering location problem.Papers of the Regional Science Association, 32(1):101–118, December 1974. ISSN 1056-8190, 1435-5957. doi:10.1007/BF01942293. URL 11 Hybrid Classical-Quantum MCLP OptimizationPREPRINT /uni00000013/uni00000011/uni00000019/uni00000018 /uni00000013/uni00000011/uni0000001a/uni00000013 /u...

    doi:10.1007/bf01942293 1974

  7. [7]

    Louis Hakimi

    Nimrod Megiddo, Eitan Zemel, and S. Louis Hakimi. The Maximum Coverage Location Problem.SIAM Journal on Algebraic Discrete Methods, 4(2):253–261, June 1983. ISSN 0196-5212, 2168-345X. doi:10.1137/0604028. URLhttps://epubs.siam.org/doi/10.1137/0604028

    work page doi:10.1137/0604028 1983

  8. [8]

    Rodríguez-Chía

    Marta Baldomero-Naranjo, Jörg Kalcsics, and Antonio M. Rodríguez-Chía. On the complexity of the upgrading version of the maximal covering location problem.Networks, 83(4):627–641, June 2024. ISSN 0028-3045, 1097-0037. doi:10.1002/net.22207. URLhttps://onlinelibrary.wiley.com/doi/10.1002/net.22207

    work page doi:10.1002/net.22207 2024

Show all 30 references
  1. [9]

    Facility siting and integer-friendly programming.European Journal of Operational Research, 65 (2):147–158, March 1993

    Charles ReVelle. Facility siting and integer-friendly programming.European Journal of Operational Research, 65 (2):147–158, March 1993. ISSN 03772217. doi:10.1016/0377-2217(93)90329-L. URL https://linkinghub. elsevier.com/retrieve/pii/037722179390329L

    1993

  2. [10]

    Love, Alán Aspuru- Guzik, and Jeremy L

    Alberto Peruzzo, Jarrod McClean, Peter Shadbolt, Man-Hong Yung, Xiao-Qi Zhou, Peter J. Love, Alán Aspuru- Guzik, and Jeremy L. O’Brien. A variational eigenvalue solver on a photonic quantum processor.Nature Communications, 5(1):4213, July 2014. ISSN 2041-1723. doi:10.1038/ncom...

    2014 doi

  3. [11]

    Booth, and Jonathan Tennyson

    Jules Tilly, Hongxiang Chen, Shuxiang Cao, Dario Picozzi, Kanav Setia, Ying Li, Edward Grant, Leonard Wossnig, Ivan Rungger, George H. Booth, and Jonathan Tennyson. The Variational Quantum Eigen- solver: A review of methods and best practices.Physics Reports, 986:1–128, Novemb...

    2022 doi

  4. [12]

    A Quantum Approximate Optimization Algorithm, 2014

    Edward Farhi, Jeffrey Goldstone, and Sam Gutmann. A Quantum Approximate Optimization Algorithm, 2014. URLhttps://arxiv.org/abs/1411.4028. Version Number: 1

    2014 arXiv

  5. [13]

    Investigating the effect of circuit cutting in QAOA for the MaxCut problem on NISQ devices.Quantum Science and Technology, 8(4):045022, October 2023

    Marvin Bechtold, Johanna Barzen, Frank Leymann, Alexander Mandl, Julian Obst, Felix Truger, and Benjamin Weder. Investigating the effect of circuit cutting in QAOA for the MaxCut problem on NISQ devices.Quantum Science and Technology, 8(4):045022, October 2023. ISSN 2058-9565....

    2023 doi

  6. [14]

    Quantum bridge analytics I: a tutorial on for- mulating and using QUBO models.Annals of Operations Research, 314(1):141–183, July 2022

    Fred Glover, Gary Kochenberger, Rick Hennig, and Yu Du. Quantum bridge analytics I: a tutorial on for- mulating and using QUBO models.Annals of Operations Research, 314(1):141–183, July 2022. ISSN 0254-5330, 1572-9338. doi:10.1007/s10479-022-04634-2. URL https://link.springer....

    2022 doi

  7. [15]

    Unbalanced penalization: a new approach to encode inequality constraints of combinatorial problems for quantum optimization algorithms

    J A Montañez-Barrera, Dennis Willsch, A Maldonado-Romo, and Kristel Michielsen. Unbalanced penalization: a new approach to encode inequality constraints of combinatorial problems for quantum optimization algorithms. Quantum Science and Technology, 9(2):025022, April 2024. ISSN...

    2024 doi

  8. [16]

    Lalinde-Pulido, Juan C

    Alejandro Giraldo-Quintero, Juan G. Lalinde-Pulido, Juan C. Duque, and Daniel Sierra-Sosa. Using quantum computing to solve the maximal covering location problem.Computational Urban Science, 2(1):43, December

  9. [17]

    A review on Quantum Approximate Optimization Algorithm and its variants.Physics Reports, 1068: 1–66, June 2024

    Kostas Blekos, Dean Brand, Andrea Ceschini, Chiao-Hui Chou, Rui-Hao Li, Komal Pandya, and Alessandro Summer. A review on Quantum Approximate Optimization Algorithm and its variants.Physics Reports, 1068: 1–66, June 2024. ISSN 03701573. doi:10.1016/j.physrep.2024.03.002. URL ht...

    2024 doi

  10. [18]

    Quantum Alternating Operator Ansatz for Solving the Minimum Exact Cover Problem.Physica A: Statistical Mechanics and its Applications, 626: 129089, September 2023

    Sha-Sha Wang, Hai-Ling Liu, Su-Juan Qin, Fei Gao, and Qiao-Yan Wen. Quantum Alternating Operator Ansatz for Solving the Minimum Exact Cover Problem.Physica A: Statistical Mechanics and its Applications, 626: 129089, September 2023. ISSN 03784371. doi:10.1016/j.physa.2023.12908...

    2023

  11. [19]

    Egger, Jakub Mareˇcek, and Stefan Woerner

    Daniel J. Egger, Jakub Mareˇcek, and Stefan Woerner. Warm-starting quantum optimization.Quantum, 5:479, June

  12. [20]

    J. A. Montanez-Barrera and Kristel Michielsen. Towards a Linear-Ramp QAOA protocol: Evidence of a scaling advantage in solving some combinatorial optimization problems.npj Quantum Information, 11(1):131, August

  13. [21]

    Church and Alan Murray.Location Covering Models: History, Applications and Advance- ments

    Richard L. Church and Alan Murray.Location Covering Models: History, Applications and Advance- ments. Advances in Spatial Science. Springer International Publishing, Cham, 2018. ISBN 978-3-319- 99845-9 978-3-319-99846-6. doi:10.1007/978-3-319-99846-6. URL http://link.springer....

    2018 doi

  14. [22]

    Ising formulations of many NP problems.Frontiers in Physics, 2, 2014

    Andrew Lucas. Ising formulations of many NP problems.Frontiers in Physics, 2, 2014. ISSN 2296-424X. doi:10.3389/fphy.2014.00005. URL http://journal.frontiersin.org/article/10.3389/fphy.2014. 00005/abstract

    2014

  15. [23]

    Grant and Travis S

    Erica K. Grant and Travis S. Humble. Adiabatic Quantum Computing and Quantum Annealing. In Oxford Research Encyclopedia of Physics. Oxford University Press, July 2020. ISBN 978-0-19-087199-

    2020

  16. [24]

    Warm-Starting and Quantum Computing: A Systematic Mapping Study.ACM Computing Surveys, 56 (9):1–31, October 2024

    Felix Truger, Johanna Barzen, Marvin Bechtold, Martin Beisel, Frank Leymann, Alexander Mandl, and Vladimir Yussupov. Warm-Starting and Quantum Computing: A Systematic Mapping Study.ACM Computing Surveys, 56 (9):1–31, October 2024. ISSN 0360-0300, 1557-7341. doi:10.1145/3652510...

    2024

  17. [25]

    URL https://www.ibm.com/docs/en/icos/22.1

    IBM ILOG CPLEX Optimization Studio, August 2025. URL https://www.ibm.com/docs/en/icos/22.1. 2?topic=optimizers-users-manual-cplex

    2025

  18. [26]

    Okada, Hirofumi Nishi, Taichi Kosugi, and Yu-ichiro Matsushita

    Ken N. Okada, Hirofumi Nishi, Taichi Kosugi, and Yu-ichiro Matsushita. Systematic study on the dependence of the warm-start quantum approximate optimization algorithm on approximate solutions.Scientific Reports, 14(1): 13 Hybrid Classical-Quantum MCLP OptimizationPREPRINT 1167...

    2024 doi

  19. [27]

    URL https://oxfordre.com/physics/view/10.1093/ acrefore/9780190871994.001.0001/acrefore-9780190871994-e-32

    doi:10.1093/acrefore/9780190871994.013.32. URL https://oxfordre.com/physics/view/10.1093/ acrefore/9780190871994.001.0001/acrefore-9780190871994-e-32

  20. [2021]

    doi:10.22331/q-2021-06-17-479

    ISSN 2521-327X. doi:10.22331/q-2021-06-17-479. URL https://quantum-journal.org/papers/ q-2021-06-17-479/

    2021 doi

  21. [2022]

    doi:10.1007/s43762-022-00070-x

    ISSN 2730-6852. doi:10.1007/s43762-022-00070-x. URL https://link.springer.com/10.1007/ s43762-022-00070-x

    doi

  22. [2025]

    doi:10.1038/s41534-025-01082-1

    ISSN 2056-6387. doi:10.1038/s41534-025-01082-1. URL http://arxiv.org/abs/2405.09169. arXiv:2405.09169 [quant-ph]

    arXiv

Pith tools

Reviewed August 2, 2026 · model on record in the stance chip above.