Hybrid Quantum Branch-and-Bound Method for Quadratic Unconstrained Binary Optimization

Daniel de Roux; David E. Bernal Neira; Zedong Peng

REVIEW 3 major objections 5 minor 2 cited by

Hybrid Quantum Branch-and-Bound Method for Quadratic Unconstrained Binary Optimization

T0 review · 3 major / 5 minor · reviewed 2026-08-04 · deepseek-v4-flash

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

Pith's one-line read This paper claims that a hybrid quantum-classical branch-and-bound framework can accelerate exact QUBO solving, with a graph-degree branching rule alone cutting solve time by 11% and node count by 17% on a filtered 1,454-instance benchmark.

desk verdict The headline speedup is real but classical: degree-based branching, not the quantum warm-start, drives the 11%/17% gain, and the benchmark filter plus XORSAT-only instances make the result conditional. read the letter →

arxiv 2509.11040 v1 pith:J3P4F3W7 submitted 2025-09-14 math.OC

Zedong Peng , Daniel de Roux , David E. Bernal Neira This is my paper

classification math.OC MSC 90C2090C5790C5981P68

keywords QUBObranch-and-boundquantumannealingIsingsolverbranchingruleexactoptimizationheuristicwarm-startXORSAT

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

This paper argues that exact QUBO solvers can be accelerated by hybridizing classical branch-and-bound with Ising/quantum heuristics, while preserving optimality certificates. On a filtered set of 1,454 benchmark instances, its graph-degree branching rule alone reduces the number of explored nodes by 17.3% and wall-clock time by 11.1% relative to the default commercial solver. Warm-starting the root node with solutions from a quantum annealer or classical heuristics gives smaller, roughly 3–10% runtime gains, and invoking heuristics at every internal node is typically counterproductive. The paper concludes that the practical value of the hybrid framework currently lies more in problem-structure-aware branching than in the quantum oracle itself.

What carries the argument

The load-bearing mechanism is a branching-priority rule derived from the QUBO's quadratic coefficient matrix Q: build the graph whose edges are nonzero off-diagonal entries and set each variable's priority to its degree in that graph. Branching first on high-degree variables is intended to shrink the remaining subproblem's active variable set, making it easier to embed into quantum hardware and reducing the branch-and-bound tree. The framework wraps a commercial branch-and-bound solver with two integration points—warm-start at the root node and heuristic callbacks at internal nodes—so that any Ising-style solver (quantum annealer, simulated annealer, or classical heuristic) can be plugged in

What would settle it

Run the same branching-priority rule on an unfiltered, diverse QUBO corpus (including dense and small instances) and compare node counts; if the 17% node reduction disappears or reverses on easy or dense instances, the headline gains are artifacts of the instance filter.

Watch

Extended reading notes

Core claim

The central empirical claim is that a branching priority computed from the interaction graph of the QUBO—branching first on variables that appear in many quadratic terms—reduces the size of subproblems and speeds up exact search. Tested across 1,454 QUBO instances, this priority rule alone gives a 17.3% reduction in branch-and-bound nodes and an 11.1% reduction in runtime compared with the out-of-the-box commercial solver. Injecting heuristic solutions at the root via warm starts yields roughly 3–10% runtime improvements, with little difference between quantum annealing, simulated annealing, and classical heuristic methods; combining warm starts with the branching rule does not beat the bran

Load-bearing premise

The claimed speedups are computed on a filtered subset of benchmark instances—those that take longer than 10 seconds with the default solver and are solved by at least one method within the time limit—so the gains may only hold for mid-difficulty instances of this type.

Editorial extensions

If this is right

Exact QUBO solvers can be accelerated without modifying solver internals, by supplying a graph-derived branching priority through existing solver interfaces.
Warm-started solutions from quantum or classical Ising heuristics yield modest consistent runtime improvements, but they do not stack additively with the branching rule.
Node-level heuristic injection is too costly in practice; precomputed solution pools at the root are a better delivery mechanism.
The gap between current warm-start gains (~10%) and the best-solution upper bound (~83%) indicates that improving heuristic solution quality, not the integration, is the main lever for future speedups.
Structured XORSAT-style QUBO instances may respond differently than dense or differently structured QUBOs; performance on other benchmark families is not established.

Reading between the lines

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

The speedups reported on the filtered 1,454-instance set may not generalize: the filter excludes easy instances and unsolved hard instances, and degree-based branching might help precisely on the mid-difficulty XORSAT instances.
The quantum annealing results are comparable to or slightly worse than classical simulated annealing and classical heuristics, suggesting the 'quantum' component is not the source of the speedup; a purely classical implementation of the same branching rule would likely match the headline numbers.
A testable extension: apply the degree-based branching priority to general mixed-integer quadratic programs with sparse quadratic terms; if the mechanism is structural, similar node reductions should appear beyond QUBO.
The best-solution upper bound implies that if oracle quality reaches near-optimal quickly, hybrid branch-and-bound could approach those gains; benchmarking stronger classical heuristics in this framework would gauge how close current methods are.

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.

Desk Editor's Note

read the letter

Punchline: the 11% time / 17% node improvement is genuine but comes from a classical degree-based branching rule, not from the quantum components. The quantum warm-starts add only 3–8% on the same filtered benchmark. That distinction is buried in the abstract, and it matters for how you read the paper.

What the paper does well: this is a clean, large-scale empirical study with public code and a new benchmark (QUBOLib.jl, 5,807 instances). It systematically tests 16 MQLib heuristics, simulated annealing, and D-Wave quantum annealing, injected via MIPStart and heuristic callbacks, against default Gurobi. The main finding — a simple graph-degree branch priority beats quantum warm-starts — is a useful reality check. The paper also documents that node-level callback injection is too expensive, which is a fair negative result. The comparison across 1,454 filtered instances is more thorough than anything else I've seen in this niche.

Soft spots, in proportion:

1. The benchmark filter (baseline >10s and solved by at least one method within 900s) is reasonable but introduces selection bias, and the SGM10 metric amplifies improvements for instances just above the 10s threshold. The 11%/17% number is specific to this filtered XORSAT-heavy set, not to QUBOs in general. The abstract should say so.

2. The 'Embedding' variant in Table 2 is never actually described. The intro mentions edge-contraction preprocessing, but the method section only shows a toy embedding diagram. That's a reproducibility gap.

3. The test set is almost entirely planted 3-XORSAT and 5-XORSAT instances. No evidence the degree-based branching rule transfers to denser or differently structured QUBOs.

4. The small deltas between warm-start variants (e.g., 7.8% vs 2.9% runtime) are presented without significance tests. Some of these differences are probably noise.

None of these flaws invalidate the central claim: a degree-based branching priority accelerates exact Gurobi on these hard XORSAT instances, and quantum warm-starts help slightly. The paper is honest in its conclusion, even if the abstract oversells the quantum part.

Who is this for? Researchers working on hybrid quantum-classical optimization or exact QUBO solvers. It's worth a serious referee — the benchmark and the systematic comparison justify the review. I'd ask the authors to clarify the embedding method, qualify the benchmark filter, and add some uncertainty quantification on the deltas. For my own work, I'd cite the benchmark and the negative result on callbacks.

Recommendation: engage with it, but read the abstract as referring to the classical branch priority, not the quantum hybrid.

Referee Report

3 major / 5 minor

Summary. The paper proposes a hybrid quantum-classical branch-and-bound (B&B) framework for exactly solving QUBOs. It injects solutions from Ising-type heuristics (MQLib, simulated annealing, D-Wave quantum annealing) into Gurobi via MIP starts and heuristic callbacks, and introduces a degree-based branching priority derived from the QUBO interaction graph. Experiments on 5,807 QUBOLib instances (mostly planted 3-XORSAT and 5-XORSAT), filtered to 1,454 hard instances, report that the degree-based branching priority alone reduces shifted-geometric-mean node count by 17.3% and runtime by 11.1% versus default Gurobi, while quantum/ML warm starts yield smaller improvements and node-level callbacks are generally harmful. The paper concludes that the classical priority rule is the main driver of the observed speedup, with quantum warm-starts giving only modest additional gains.

Significance. If the effects are robust, the paper provides a useful practical data point: a simple QUBO-aware branching rule can accelerate an exact commercial solver, while quantum and classical heuristic warm-starts give smaller improvements and node-wise callbacks are counterproductive. The open-source implementation and the release of a 5,000+ instance benchmark are concrete assets, and the paper is honest in its conclusions about the limited role of the quantum oracle. However, the headline numbers are not attributable to the hybrid quantum mechanism, and the benchmark-filter plus SGM10 metric choices need scrutiny before the speedup claim is accepted at face value. The work is more a careful empirical evaluation of heuristic injection and branching rules on XORSAT-derived QUBOs than a demonstration that quantum hardware accelerates exact QUBO solving.

major comments (3)

[Abstract; §1; Table 2] The headline 'up to 11% less solution time and 17% fewer nodes' corresponds to the 'Branch Priority' row of Table 2, a purely classical variant with no Ising solver involved. The quantum warm-start rows show 2.9–7.8% runtime reductions and 9.8–12.9% node reductions; adding branch priority to quantum starts does not beat priority alone (10.9% vs 11.1% for MQLib). The abstract and the contribution bullet attribute the gain to 'hybrid quantum-classical strategies,' which is not supported by the table. Please separate the classical branch-priority effect from the incremental quantum contribution, or adjust the headline claim accordingly.
[§4, Table 2] All SGM10 numbers are computed on the filtered 1,454 instances selected by '(i) take more than 10 seconds to solve using default Gurobi, and (ii) can be solved to optimality by at least one of the tested methods.' This filter, combined with the 10-second shift, inflates improvements for instances whose baseline is just above the threshold: reducing 11 s to 1 s changes the SGM10 contribution by about 48%, whereas the same 10 s reduction from 100 s changes it by about 9%. In addition, 389 baseline runs and 377 branch-priority runs are censored at 900 s, and setting unsolved runs to the time limit mixes caps with genuine solve times. Please report solve rates, distribution summaries, and SGM with several shifts (e.g., 1, 10, 100, 1000) or paired per-instance ratios.
[§4, Table 1; §1] The benchmark is composed entirely of planted 3-regular 3-XORSAT and 5-regular 5-XORSAT instances. The degree-based branching rule is motivated by the sparse interaction graph and may not transfer to dense or differently structured QUBOs. The phrase 'thousands of diverse QUBO instances' at the end of §1 and the broad scope implied by the title overstate the evidence. Either add experiments on other QUBO families (e.g., random dense QUBOs, MaxCut instances) or explicitly frame the result as valid for the QUBOLib/XORSAT benchmark class.

minor comments (5)

[§1; §4] The contribution bullet says 'a median 17% node reduction and 11% wall-clock speed-up,' but Table 2 reports shifted geometric means, not medians. The numerical summary should consistently refer to SGM10 or report actual medians.
[§4] The text twice refers to 'Table 4' for the performance summary, but the table is labeled Table 2. Please correct the cross-references.
[§3.3, Figures 1–2] Figures 1 and 2 contain slide-deck artifacts: '© David E. Bernal Neira, 2024', 'Oct 21, 2024 QBB 8', 'Benchmark Results – Branch Priority', and an unresolved citation placeholder '[?]'. These should be cleaned before publication.
[§4, Table 2] The label 'MIP Start + Embedding DWave QA' is not defined before the table. Clarify what 'Embedding' refers to (likely minor-embedding overhead) and how it is measured.
[Abstract; §1] The abstract says 'hundreds of QUBO instances,' while the contribution bullet says 'more than a thousand instances.' Use one consistent count, since the filtered benchmark has 1,454 instances.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the paper's claims are empirical comparisons on an external benchmark, with no fitted quantity renamed as a prediction and no load-bearing self-citation.

full rationale

The central claims are measured speedups and node reductions from Table 2 (e.g., Branch Priority: -17.3% nodes, -11.1% runtime vs. default Gurobi on 1,454 QUBOLib instances). These are experimental results, not derivations from fitted parameters. The branch-priority rule is defined directly from each instance's Q-matrix graph (degree of the graph induced by Q), not tuned to the benchmark outcomes; it is a fixed heuristic tested against Gurobi. Warm-start injections (MQLib, SA, QA) are external heuristics compared on the same instances. The only self-citation is [XRA+23] for the QUBO.jl/QUBOTools.jl packaging used to load instances; the benchmark instances themselves come from previously published external datasets [KAHL22, Hen19], so the packaging is not load-bearing for the speedup claims. No uniqueness theorem from the authors' prior work is invoked, no ansatz is smuggled in via citation, and no known result is merely renamed. The benchmark filter (instances taking >10 s with default Gurobi and solvable by at least one method) and the use of SGM10 are methodological choices that could affect generalization or interpretation, but they do not make the comparison circular: the same filtered set is used for baseline and proposed methods, and the branch-priority rule contains no benchmark-derived fitted parameter. The paper is self-contained as an empirical study against default Gurobi, so circularity score is 0.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The central results depend on a few hand-chosen experimental settings (branch priority rule, TOP-k counts, benchmark filter) rather than fitted mathematical models. These choices are transparent but should be seen as free parameters when interpreting the speedups.

free parameters (3)

Branch priority rule (vertex degree) = degree of each variable in the QUBO interaction graph
The branching order is set to variables with most quadratic interactions; chosen by hand as a heuristic, not fitted to data.
TOP-k solution injection count = 1, 10, 30, 100 (scanned)
The number of warm-start solutions injected from SA/QA is scanned over four values; it is a tuning parameter, not estimated.
Benchmark filter thresholds = >10 s default Gurobi time, solvable by at least one method
The 1,454-instance test set is defined by these hand-chosen thresholds, which affect all reported SGM10 improvements.

assumptions (4)

domain assumption Gurobi 11.0.0 with NonConvex=2 solves QUBO instances to global optimality and reports correct bounds when terminated.
The paper relies on Gurobi's B&B as the exact solver and on its optimality certificates (Section 4).
domain assumption D-Wave Advantage 4.1 sampling returns samples from the Ising model corresponding to the input QUBO.
The D-Wave QA warm-start results presuppose the annealer's samples are legitimate feasible solutions of the QUBO (Section 4).
domain assumption MIPStart and heuristic callbacks inject feasible solutions into Gurobi without corrupting optimality guarantees.
The framework relies on these documented Gurobi interfaces working as specified (Sections 3.1, 3.2).
domain assumption The XORSAT planted-solution instances from QUBOLib are representative of practically occurring QUBOs.
The benchmark conclusions generalize only if these structured instances are a fair proxy (Section 4).

how reviews work

0 comments

Cite this review

Pith. "Pith review of Hybrid Quantum Branch-and-Bound Method for Quadratic Unconstrained Binary Optimization." pith.science (2026). https://pith.science/paper/J3P4F3W7

@misc{pith2026250911040,
  author       = {Pith},
  title        = {Pith review of: Hybrid Quantum Branch-and-Bound Method for Quadratic Unconstrained Binary Optimization},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/J3P4F3W7}},
  note         = {Machine review of arXiv:2509.11040}
}

read the original abstract

Quantum algorithms have shown promise in solving Quadratic Unconstrained Binary Optimization (QUBO) problems, benefiting from their connection to the transverse field Ising model. Various Ising solvers, both classical and quantum, have emerged to tackle such problems efficiently but lack global optimality guarantees and often suffer from hardware limitations such as limited qubit availability. In this work, we propose a hybrid branch-and-bound (B&B) framework that integrates Ising solvers as heuristics within a classical B&B algorithm. Unlike prior theoretical studies, our work presents a practical implementation, available as open-source on GitHub. We explore when and where to apply Ising solvers in the search tree and introduce a custom branching rule optimized QUBO embedding. Our method is evaluated on hundreds of QUBO instances from QUBOLib.jl using Gurobi and the D-Wave quantum annealer. Our results show up to 11% less solution time and 17% fewer nodes compared to default Gurobi, an off-the-shelf commercial optimization solver. These findings demonstrate the value of hybrid quantum-classical strategies for enhancing exact optimization.

Figures

Figures reproduced from arXiv: 2509.11040 by the authors.

Discussion (0). Sign in to comment.

Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Geometric Characteristics of Subproblems in Ising-Machine-Assisted Large Neighborhood Search
cond-mat.stat-mech 2026-07 conditional novelty 6.0 of 10

When subproblem binary-variable counts are matched, route-based LNS-K beats QUBO-structure-based LNS-Q on a 400-customer VRP and shifts its selected customers toward spatially localized sets.
Ising-Machine-Assisted Large Neighborhood Search with Flexibly Tunable Subproblem Size
cond-mat.stat-mech 2026-07 conditional novelty 5.0 of 10

Introducing a segment-length parameter into Ising-machine-assisted large neighborhood search for VRP yields ~10% better solutions than the prior method by enabling finer subproblem-size control.

Reference graph

Works this paper leans on

13 extracted references · 8 linked inside Pith · cited by 2 Pith papers

[1]

sufficiently

Hybrid Quantum Branch-and-Bound Method for Quadratic Unconstrained Binary Optimization Zedong Peng Purdue University 610 Purdue Mall 47907, West Lafayette, Indiana, USA peng372@purdue.edu Daniel de Roux Carnegie Mellon University* 5000 Forbes Ave 15213, Pittsburgh, Pennsylvania, USA dderoux@andrew.cmu.edu *now at Google. David E. Bernal Neira Purdue Unive...

arXiv 2025
[2]

Invoking heuristic solvers at every node can be prohibitively expensive and may significantly in- crease the overall computation time

However, these calls must be handled with care, as we now discuss. Invoking heuristic solvers at every node can be prohibitively expensive and may significantly in- crease the overall computation time. We propose the following strategy to mitigate this issue. Since QUBO does not have constraints, a feasible solution for one node in the tree is feasible fo...

2024
[3]

https://docs.dwavesys.com/docs/latest/c_gs_7.html#triangle x2 -1 -1 -1 2 2 2 Triangular graph of QUBO QPU T opology Embedding Intuition: Fix the most connected variable, and the size of the resulting embedded subproblem will be smaller. ➢Branch Priority=the degree of the graph induced by matrix Q y1 y2 y3 y4 y2 y1 y3 y4 Figure 1: Example of embedding a 3-...

2024
[12]

Branch- and-bound digitized counterdiabatic quantum optimization.arXiv preprint arXiv:2504.15367,

[SRC+25] Anton Simen, Sebastián V Romero, Ale- jandro Gomez Cadavid, Enrique Solano, and Narendra N Hegade. Branch- and-bound digitized counterdiabatic quantum optimization.arXiv preprint arXiv:2504.15367,

arXiv
[13]

[XRA+23] Pedro Maciel Xavier, Pedro Ripper, Tiago Andrade, Joaquim Dias Garcia, Nelson Maculan, and David E Bernal Neira. Qubo. jl: A julia ecosystem for quadratic unconstrained binary optimization.arXiv preprint arXiv:2307.02577, 2023

arXiv 2023
[1999]

Ef- ficient Internal Strategies in Quantum Re- laxation based Branch-and-Bound.arXiv preprint arXiv:2405.00935,

[MHNY24] Hiromichi Matsuyama, Wei-hao Huang, Kohji Nishimura, and Yu Yamashiro. Ef- ficient Internal Strategies in Quantum Re- laxation based Branch-and-Bound.arXiv preprint arXiv:2405.00935,

arXiv
[2000]

Solv- ing QUBOs with a quantum-amenable branch and bound method.arXiv preprint arXiv:2407.20185,

[HBBZ24] Thomas Häner, Kyle EC Booth, Sima E Borujeni, and Elton Yechao Zhu. Solv- ing QUBOs with a quantum-amenable branch and bound method.arXiv preprint arXiv:2407.20185,

arXiv
[2004]

Adiabatic quantum optimization fails to solve the knapsack problem

[PND08] L Pusey-Nazzaro and P Date. Adiabatic quantum optimization fails to solve the knapsack problem. arXiv 2020.arXiv preprint arXiv:2008.07456,

arXiv 2020

Show all 13 references

[2005]

A quantum approximate optimization algorithm.arXiv preprint arXiv:1411.4028,

[FGG14] Edward Farhi, Jeffrey Goldstone, and Sam Gutmann. A quantum approximate optimization algorithm.arXiv preprint arXiv:1411.4028,

arXiv
[2006]

A brief history of linear and mixed-integer programming computa- tion.Documenta Mathematica, 2012:107– 121,

[Bix12] Robert E Bixby. A brief history of linear and mixed-integer programming computa- tion.Documenta Mathematica, 2012:107– 121,

2012
[2014]

Universal quantum speedup for branch-and-bound, branch-and-cut, and tree-search algorithms.arXiv preprint arXiv:2210.03210,

[CMYP22] Shouvanik Chakrabarti, Pierre Minssen, Romina Yalovetzky, and Marco Pis- toia. Universal quantum speedup for branch-and-bound, branch-and-cut, and tree-search algorithms.arXiv preprint arXiv:2210.03210,

arXiv
[2019]

Progress in mathematical programming solvers from 2001 to 2020.EURO Journal on Compu- tational Optimization, 10:100031,

[KBPV22] Thorsten Koch, Timo Berthold, Jaap Ped- ersen, and Charlie Vanaret. Progress in mathematical programming solvers from 2001 to 2020.EURO Journal on Compu- tational Optimization, 10:100031,

2001
[2020]

Improving solutions by em- bedding larger subproblems in a D-Wave quantum annealer.Scientific reports, 9(1):2098,

[OOTT19] Shuntaro Okada, Masayuki Ohzeki, Masayoshi Terabe, and Shinichiro Taguchi. Improving solutions by em- bedding larger subproblems in a D-Wave quantum annealer.Scientific reports, 9(1):2098,

Pith tools

Reviewed August 4, 2026 · model on record in the stance chip above.

[1] [1]

sufficiently

Hybrid Quantum Branch-and-Bound Method for Quadratic Unconstrained Binary Optimization Zedong Peng Purdue University 610 Purdue Mall 47907, West Lafayette, Indiana, USA peng372@purdue.edu Daniel de Roux Carnegie Mellon University* 5000 Forbes Ave 15213, Pittsburgh, Pennsylvania, USA dderoux@andrew.cmu.edu *now at Google. David E. Bernal Neira Purdue Unive...

arXiv 2025

[2] [2]

Invoking heuristic solvers at every node can be prohibitively expensive and may significantly in- crease the overall computation time

However, these calls must be handled with care, as we now discuss. Invoking heuristic solvers at every node can be prohibitively expensive and may significantly in- crease the overall computation time. We propose the following strategy to mitigate this issue. Since QUBO does not have constraints, a feasible solution for one node in the tree is feasible fo...

2024

[3] [3]

https://docs.dwavesys.com/docs/latest/c_gs_7.html#triangle x2 -1 -1 -1 2 2 2 Triangular graph of QUBO QPU T opology Embedding Intuition: Fix the most connected variable, and the size of the resulting embedded subproblem will be smaller. ➢Branch Priority=the degree of the graph induced by matrix Q y1 y2 y3 y4 y2 y1 y3 y4 Figure 1: Example of embedding a 3-...

2024

[4] [12]

Branch- and-bound digitized counterdiabatic quantum optimization.arXiv preprint arXiv:2504.15367,

[SRC+25] Anton Simen, Sebastián V Romero, Ale- jandro Gomez Cadavid, Enrique Solano, and Narendra N Hegade. Branch- and-bound digitized counterdiabatic quantum optimization.arXiv preprint arXiv:2504.15367,

arXiv

[5] [13]

[XRA+23] Pedro Maciel Xavier, Pedro Ripper, Tiago Andrade, Joaquim Dias Garcia, Nelson Maculan, and David E Bernal Neira. Qubo. jl: A julia ecosystem for quadratic unconstrained binary optimization.arXiv preprint arXiv:2307.02577, 2023

arXiv 2023

[6] [1999]

Ef- ficient Internal Strategies in Quantum Re- laxation based Branch-and-Bound.arXiv preprint arXiv:2405.00935,

[MHNY24] Hiromichi Matsuyama, Wei-hao Huang, Kohji Nishimura, and Yu Yamashiro. Ef- ficient Internal Strategies in Quantum Re- laxation based Branch-and-Bound.arXiv preprint arXiv:2405.00935,

arXiv

[7] [2000]

Solv- ing QUBOs with a quantum-amenable branch and bound method.arXiv preprint arXiv:2407.20185,

[HBBZ24] Thomas Häner, Kyle EC Booth, Sima E Borujeni, and Elton Yechao Zhu. Solv- ing QUBOs with a quantum-amenable branch and bound method.arXiv preprint arXiv:2407.20185,

arXiv

[8] [2004]

Adiabatic quantum optimization fails to solve the knapsack problem

[PND08] L Pusey-Nazzaro and P Date. Adiabatic quantum optimization fails to solve the knapsack problem. arXiv 2020.arXiv preprint arXiv:2008.07456,

arXiv 2020