Quantum adiabatic machine learning with zooming

Alexander Zlokapa; Alex Mott; Daniel Lidar; Jean-Roch Vlimant; Joshua Job; Maria Spiropulu

REVIEW 3 major objections 6 minor 1 cited by

Quantum adiabatic machine learning with zooming

T0 review · 3 major / 6 minor · reviewed 2026-08-14 · deepseek-v4-flash

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

Pith's one-line read QAML-Z, a zooming variant of quantum-annealing machine learning, matches optimized classical deep neural networks on small Higgs training sets and almost halves the large-set AUROC gap to the DNN.

desk verdict QAML-Z is a genuine algorithmic extension with reproducible benchmarks, but the augmented Hamiltonian omits cross-offset couplings and the quantum advantage disappears against SAE-Z. read the letter →

arxiv 1908.04480 v2 pith:PSQI3HW4 submitted 2019-08-13 quant-ph cs.LGhep-ph

Alexander Zlokapa , Alex Mott , Joshua Job , Jean-Roch Vlimant , Daniel Lidar , Maria Spiropulu This is my paper · ORCID

classification quant-phcs.LGhep-ph

keywords quantumannealingmachinelearningQAML-ZIsingmodelHiggsbosonclassificationweakclassifierscontinuousoptimizationROCcurve

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

QAML-Z is a proposed upgrade to quantum-annealing machine learning that replaces the binary on/off weights of weak classifiers with continuous weights found by repeatedly annealing inside a shrinking region of the energy landscape. On a Higgs-boson classification benchmark, the authors report that QAML-Z matches an optimized deep neural network at the smallest training-set sizes and reduces the area-under-the-ROC-curve (AUROC) gap between the earlier QAML algorithm and the DNN by 47% at the largest training-set size. The paper also shows that the zooming procedure drives the Ising energy down monotonically on the test set, and that a classical simulated-annealing version with excited states reproduces the quantum results to one standard deviation. The authors present these results as evidence that near-term quantum annealers can be competitive with classical machine learning in small-data regimes and that discrete annealers can be applied to continuous optimization.

What carries the argument

The load-bearing mechanism is the zooming Hamiltonian. Starting from the QAML objective, each weak classifier's contribution is shifted and scaled by the current weight $\mu_i(t)$ and the search breadth $\sigma(t)$, giving $H(t)=\sum_i(-C_i+\sum_j\mu_j(t)C_{ij})\sigma(t)s_i+\sum_{i<j}C_{ij}\sigma^2(t)s_i s_j$, up to constants. This turns one discrete optimization into a sequence of binary searches over the real-valued weight vector, with spin-up/spin-down outcomes moving each weight by an exponentially decaying step. The threshold-augmented classifier set provides the extra weak classifiers that make the continuous ensemble expressive.

What would settle it

Run QAML-Z on the exact, unpruned Ising model for the same Higgs data (in simulation, with all cross-terms and hundreds of logical qubits) and compare AUROC against the 5%-pruned version used on the annealer. If the full-model AUROC no longer matches the deep network at small training-set sizes, or no longer cuts the large-size gap by roughly half, then the claimed improvement is an artifact of the pruning rather than of the zooming algorithm.

Watch

Extended reading notes

Core claim

QAML-Z extends the QAML algorithm in two steps: it augments the weak-classifier set by threshold shifts $c_{il}(x_\tau) = \operatorname{sgn}(h_i(x_\tau)+\delta_l)/N$, and it turns each binary weight into a continuous weight by iterating the substitution $s_i c_i(x_\tau) \to \sigma(t)s_i c_i(x_\tau)+\mu_i(t)c_i(x_\tau)$ with shrinking breadth $\sigma(t)=b^t$. Each anneal updates $\mu_i(t+1)=\mu_i(t)+s_i\sigma(t+1)$, so the final classifier is a real-weighted ensemble. On the annealer, the authors report AUROC gains over QAML at every training-set size, parity with the DNN at small sizes, and a 47% reduction of the QAML-DNN gap at the largest size. Because only 33 fully connected logical qubits were available, the implemented Ising Hamiltonian kept only the largest 5% of cross-terms, and the authors also show that simulated annealing with zooming and excited states matches QAML-Z, which locates the algorithm's performance gain in the zooming procedure rather than to quantum dynamics specifically.

Load-bearing premise

The experimental result assumes that pruning the Ising Hamiltonian to the largest 5% of its cross-terms leaves the energy landscape close enough to the full QAML-Z objective that the zooming anneals still find essentially the same good classifiers; if pruning distorts which low-energy configurations are found, the reported AUROC numbers are for a different, truncated problem rather than for the algorithm being proposed.

Editorial extensions

If this is right

QAML-Z improves AUROC over the original QAML at every tested training-set size on the Higgs benchmark, so the zooming-plus-augmentation recipe is a working upgrade for this problem.
At training sets of order 1,000 examples, QAML-Z reaches deep-network-level AUROC, indicating that annealer-based classifiers can be competitive in small-data, online-learning settings.
At the largest training set, the AUROC gap between QAML and the deep network shrinks by 47%, meaning the quantum-classical performance margin is roughly halved.
The Ising energy on the test set decreases monotonically across zooming iterations, which the paper reads as evidence against overfitting during the repeated anneals.
Because simulated annealing with zooming and excited states matches QAML-Z within one standard deviation, the reported gain does not by itself demonstrate a quantum advantage over classical annealing.

Reading between the lines

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

My reading: the 5% cross-term pruning means the experimental numbers characterize a truncated Hamiltonian, so a natural check is to simulate the full QAML-Z objective on the same data and compare AUROC curves before attributing the gain to the algorithm.
My reading: zooming is a generic way to convert binary Ising optimization into continuous optimization, so the same shrinking-sigma schedule should transfer to other annealer tasks such as feature selection or regularized regression, not just classification.
My reading: since logistic regression on the augmented classifiers already matches the DNN, much of the power may come from the physics-based kinematic classifiers plus threshold augmentation; an extension would test whether zooming still helps when weak classifiers are generic stumps or random features.
My reading: the equivalence with SAE-Z implies that any future quantum-speedup or quantum-advantage claim for QAML-Z must be benchmarked against a classical counterpart with excited states, not against plain simulated annealing.

Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

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

The short version: this is a real algorithmic contribution with honest, reproducible benchmarks, but the derivation of the augmented Hamiltonian does not match the stated squared-error objective, and the authors' own classical baseline undercuts the quantum-specific claim. It deserves a serious referee, not a desk reject.

What's new: the zooming iteration—converting QAML's binary on/off weights into continuous weights via a binary search over the energy landscape—and the threshold-augmented weak classifiers are both genuine additions over the original QAML. The code and data links are provided, and the classical baselines (optimized DNN, XGBoost, logistic regression, and simulated annealing variants) are appropriate. The main empirical result, roughly a 47% reduction in the AUROC gap to a DNN at large training sizes and parity at small sizes, is internally consistent with the figures and given with error bars.

Now the soft spots, in increasing order of severity. Minor: the derivation of Eq. (7b) is compact and drops constants, but that part checks out. More serious: the D-Wave implementation prunes 95% of the Ising couplings, so the hardware runs on an approximation of the model; and excited states are selected by maximizing validation AUROC, which is a selection bias the paper acknowledges but does not quantify. Most serious: Eq. (9) only couples augmented classifiers within the same threshold offset. The squared-error objective for R = sum mu_il c_il includes cross-offset pair terms (i,l)-(j,l') for l != l', and those are absent from Eq. (9). So the Hamiltonian actually minimized on the annealer is not the Ising encoding of the QAML-Z objective derived in Sec. II B. This is a genuine mathematical gap, separate from the pruning. The public code can settle it quickly: if the code follows Eq. (9), the reported AUROC curves are for a different algorithm than the one claimed. The paper should either include the missing terms or explicitly state that cross-offset interactions are dropped as an approximation. Finally, the abstract and conclusion imply quantum annealing drives the improvement, but their own Figure 4 shows SAE-Z matches QAML-Z within one sigma. That claim should be reframed.

Who this is for: researchers in quantum annealing for machine learning, especially near-term quantum classifiers. They will want the zooming idea and the benchmark methodology, but they need to fix or acknowledge the Hamiltonian discrepancy and tone down the quantum claim. I'd engage with it, ask for a code check of Eq. (9) and a revised discussion of the SAE-Z comparison, and then likely accept it as a solid algorithmic contribution.

Referee Report

3 major / 6 minor

Summary. The paper proposes QAML-Z, an iterative extension of the QAML algorithm in which binary weak-classifier weights are replaced by continuous weights via a zooming search, and the weak-classifier set is augmented by threshold offsets. The algorithm is implemented on a D-Wave 2X quantum annealer and benchmarked on Higgs-boson classification, reporting AUROC values that match a deep neural network at small training-set sizes and reduce the QAML-to-DNN gap by about 47% at large training-set sizes. The authors also provide simulated-annealing and logistic-regression baselines, report error bars, and promise public source code and data.

Significance. If the reported AUROC results are trustworthy, the paper makes a useful contribution by showing that iterative zooming plus classifier augmentation materially improves QAML and brings quantum-annealing-based classification closer to classical benchmarks in a small-data regime. The manuscript has real strengths: it uses an independent simulated benchmark, compares against strong classical baselines whose hyperparameters were optimized, reports error bars, and promises reproducible code and data. It is also honest in reporting that simulated annealing with excited states (SAE-Z) reproduces QAML-Z performance to one standard deviation, which limits any claim of a quantum-specific advantage. The main caveats are that the implemented Hamiltonian deviates from the derived objective, the hardware results use a heavily pruned coupling graph, and the excited-state selection procedure uses validation-set labels in a way that may bias the comparison.

major comments (3)

[Section II B, Eq. (9)] Equation (9) does not correspond to the squared-error objective for the augmented classifier set. Expanding the objective with the augmented strong classifier R = sum_{i,l} mu_il c_il yields pairwise couplings C_{(i,l),(j,l')} = sum_tau c_il(x_tau)c_jl'(x_tau) for l != l', as well as linear cross terms involving mu_jl' C_{(i,l),(j,l')}. Equation (9) contains only same-offset couplings C_ijl and only for j > i, so the minimization solves a different optimization problem. Because c_il = sgn(h_i + delta_l)/N are highly correlated across offsets, the omitted cross-offset terms are not negligible. The authors should either derive the full Ising mapping for the augmented set or explicitly state and justify the approximation, and the supplied code should be checked against the derivation.
[Section III A] The D-Wave implementation retains only the largest 5% of Ising couplings, and every reported QAML-Z result on the quantum annealer is therefore obtained from a heavily truncated Hamiltonian. This means the comparison with DNN and XGBoost in Figure 2 is not a clean test of the QAML-Z objective defined in Section II B. The authors should quantify the effect of the pruning, for example by running SA-Z on both the full and the pruned Hamiltonian, or by reporting classical full-Hamiltonian QAML-Z results for a smaller problem size.
[Section II B and Section III A] The final classifier is not a single fixed ensemble but a per-threshold supremum over excited states selected on a validation set. This validation-set selection procedure is substantially more flexible than the validation-based hyperparameter tuning used for the DNN and XGBoost baselines, so the AUROC comparison in Figure 2 may be biased in favor of QAML-Z. The authors should report the number of excited states used, the selection criteria in detail, and compare with a fixed ensemble rule such as averaging over the selected excited states, to separate the benefit of the zooming algorithm from the benefit of validation-set model selection.

minor comments (6)

[Section III A] Please state the number N of weak classifiers and the total size of the augmented classifier set; with A = 3, the augmented set contains 7N classifiers, and it is unclear how the problem is embedded into the 33 fully connected logical qubits available on the D-Wave 2X.
[Section II B] The regularization schedules pf(t), qf(t) and the excited-state thresholds d and ne are described only as being specified in the supplementary code; these schedules should be given in the text or an appendix because they affect the reported results.
[Section III C, Figure 4] Because SAE-Z achieves statistically equivalent AUROC to QAML-Z, the abstract and conclusion should qualify the role of quantum annealing more carefully; the improvement over QAML appears to be driven substantially by zooming and by excited-state selection rather than by the quantum device.
[Section II B, Eqs. (7a)-(7b)] The derivation from Eq. (7a) to Eq. (7b) should explicitly show how self-interaction terms and constant terms are handled, and the spin encoding should be stated unambiguously for the zooming iterations.
[References [61,62]] The promised source code and data should include version or commit identifiers and persistent DOIs so that the reported experiments can be reproduced exactly.
[Section III B] The numerical AUROC values underlying Figure 2 should be given in a table with confidence intervals, since the small-training-set region appears to have large error bars and the claim of matching DNN performance should be supported by explicit numbers.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: QAML-Z is validated against external classical benchmarks on an independent test set, and no claimed prediction reduces to a fitted input.

full rationale

The derivation chain is self-contained in the relevant sense. QAML-Z is defined by the substitution s_i c_i -> σ(t) s_i c_i + μ_i(t) c_i, leading to the iterative Hamiltonian H(t) in Eqs. (7) and (9), with μ updated from spin readouts. The headline claim — matching DNN performance at small training-set sizes and reducing the QAML–DNN AUROC gap by about 47% at large sizes — is measured on a test set against classical DNN, XGBoost, and logistic regression baselines; it is not constructed from the target result. Hyperparameters (b=1/2, A=3, δ=0.0075, 8 iterations) are fixed before benchmarking, and the excited-state/validation selection is model selection rather than fitting the test AUROC. The original QAML baseline is cited from prior work by overlapping authors, but it functions as an external benchmark and the improvement is computed from measured AUROC values, so the self-citation is not load-bearing. The possible concern that Eq. (9) omits cross-offset couplings between augmented classifiers is a derivation-correctness issue, not circularity: even if the annealer minimizes a slightly different Hamiltonian, that does not make the reported result equal to the input by definition. No step reduces by construction to its own input.

Assumptions & free parameters 7 free parameters · 5 assumptions · 0 invented entities

The central empirical results depend on several hand-chosen hyperparameters (b, A, delta, T, pruning, regularization and excited-state selection schedules) and on assumptions about D-Wave sampling and the dataset. No new physical entities are introduced. The load-bearing approximation is the 5% coupling pruning.

free parameters (7)

Zoom breadth b = 1/2
Set in Section II B to 1/2 for a binary search. Controls how quickly the search window narrows and effectively fixes the number of useful iterations. Chosen by the authors, not optimized or derived.
Offset limit A = 3
Set in Section II B to 3, giving 7 threshold-shifted classifiers per base weak classifier. This expansion is central to the performance gain and was chosen by hand.
Threshold step size delta = 0.0075
Set in Section II B. Determines the granularity of decision-boundary shifts in the augmented classifier set; hand-picked.
Number of zooming iterations T = 8
Chosen because the marginal update decays exponentially with b=1/2; not selected by a principled criterion.
Regularization probabilities pf(t), qf(t) = Specified in supplementary code
Two-step random flip procedures are said to prevent overfitting, but the schedules are only present in code, not described or justified in the text.
Excited-state selection thresholds d and ne = Decayed by iteration in code
Used to select excited states to strengthen the classifier; the decay schedules are not specified in the text, only in code, and directly influence the ensemble.
Ising coupling pruning fraction = 5%
Only the largest 5% of cross-terms are kept so the problem fits on 33 logical qubits of D-Wave 2X. This is a major approximation to the QAML-Z Hamiltonian and is not varied or corrected for.

assumptions (5)

standard math Adiabatic theorem: a sufficiently slow evolution keeps the system in the instantaneous ground state.
Invoked in the Introduction to justify why annealing to the problem Hamiltonian yields the solution. The device is noisy, so the algorithm in practice relies on approximate adiabatic behavior plus post-selection.
domain assumption Samples returned by D-Wave 2X are representative low-energy states of the programmed Ising Hamiltonian.
The whole method treats annealer reads as spin configurations to update weights and select excited states. Analog errors and thermal excitations are acknowledged, so this is an assumption about hardware behavior.
domain assumption The simulated Higgs dataset from Mott et al. is a valid and adequate benchmark.
The paper explicitly notes the simulation is limited to gluon-fusion H to gamma gamma and excludes sub-leading contributions. Results are therefore specific to this simplified dataset.
ad hoc to paper Pruning the Ising Hamiltonian to the largest 5% of couplings preserves the optimization landscape relevant to classification performance.
Introduced specifically to fit the D-Wave 2X architecture; no analysis quantifies how the truncation changes minima or AUROC. This is load-bearing for all hardware results.
domain assumption Selecting excited states and hyperparameters on a validation set transfers to the test set.
The final classifier maximizes validation AUROC and takes suprema over excited states per ROC efficiency. This is standard model selection but assumes the validation set is not overfit.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Quantum adiabatic machine learning with zooming." pith.science (2026). https://pith.science/paper/PSQI3HW4

@misc{pith2026190804480,
  author       = {Pith},
  title        = {Pith review of: Quantum adiabatic machine learning with zooming},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/PSQI3HW4}},
  note         = {Machine review of arXiv:1908.04480}
}

read the original abstract

Recent work has shown that quantum annealing for machine learning, referred to as QAML, can perform comparably to state-of-the-art machine learning methods with a specific application to Higgs boson classification. We propose QAML-Z, a novel algorithm that iteratively zooms in on a region of the energy surface by mapping the problem to a continuous space and sequentially applying quantum annealing to an augmented set of weak classifiers. Results on a programmable quantum annealer show that QAML-Z matches classical deep neural network performance at small training set sizes and reduces the performance margin between QAML and classical deep neural networks by almost 50% at large training set sizes, as measured by area under the ROC curve. The significant improvement of quantum annealing algorithms for machine learning and the use of a discrete quantum algorithm on a continuous optimization problem both opens a new class of problems that can be solved by quantum annealers and suggests the approach in performance of near-term quantum machine learning towards classical benchmarks.

Figures

Figures reproduced from arXiv: 1908.04480 by the authors.

**Figure 3.** FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

**Figure 5.** FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗

Figures from the paper (1 more)

**Figure 4.** Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

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

Quantum Algorithms for Jet Clustering
hep-ph 2019-08 accept novelty 7.0 of 10

Thrust can be computed in O(N^2) time with a Grover-based quantum algorithm under a sequential data-loading model, and in O(N^2 log N) time classically with sorting, but the quantum advantage is only formal for very r...

Reference graph

Works this paper leans on

66 extracted references · 61 canonical work pages · cited by 1 Pith paper

[1]

Computa- tional methods in drug discovery,

Sumudu P Leelananda and Steﬀen Lindert, “Computa- tional methods in drug discovery,” Beilstein journal of organic chemistry 12, 2694–2718 (2016). 7

work page 2016
[2]

Machine learning and its applications to biology,

Adi L Tarca, Vincent J Carey, Xue-wen Chen, Roberto Romero, and Sorin Dr˘ aghici, “Machine learning and its applications to biology,” PLoS computational biology 3, e116 (2007)

work page 2007
[3]

William W Hsieh, Machine learning methods in the envi- ronmental sciences: Neural networks and kernels (Cam- bridge university press, 2009)

work page 2009
[4]

Machine learning phases of matter,

Juan Carrasquilla and Roger G Melko, “Machine learning phases of matter,” Nature Physics 13, 431 (2017)

work page 2017
[5]

Searching for exotic particles in high-energy physics with deep learning,

Pierre Baldi, Peter Sadowski, and Daniel Whiteson, “Searching for exotic particles in high-energy physics with deep learning,” Nature communications 5, 4308 (2014)

work page 2014
[6]

Machine learning at the energy and intensity fron- tiers of particle physics,

Alexander Radovic, Mike Williams, David Rousseau, Michael Kagan, Daniele Bonacorsi, Alexander Himmel, Adam Aurisano, Kazuhiro Terao, and Taritree Wongji- rad, “Machine learning at the energy and intensity fron- tiers of particle physics,” Nature 560, 41 (2018)

work page 2018
[7]

Quantum machine learning,

Jacob Biamonte, Peter Wittek, Nicola Pancotti, Patrick Rebentrost, Nathan Wiebe, and Seth Lloyd, “Quantum machine learning,” Nature 549, 195 (2017)

work page 2017
[8]

Quantum support vector machine for big data classiﬁ- cation,

Patrick Rebentrost, Masoud Mohseni, and Seth Lloyd, “Quantum support vector machine for big data classiﬁ- cation,” Physical review letters 113, 130503 (2014)

work page 2014

Show all 66 references

[9]

Quantum principal component analysis,

Seth Lloyd, Masoud Mohseni, and Patrick Reben- trost, “Quantum principal component analysis,” Nature Physics 10, 631 (2014)

2014
[10]

Quan- tum algorithm for data ﬁtting,

Nathan Wiebe, Daniel Braun, and Seth Lloyd, “Quan- tum algorithm for data ﬁtting,” Physical review letters 109, 050505 (2012)

2012
[11]

Prediction by linear regression on a quantum computer,

Maria Schuld, Ilya Sinayskiy, and Francesco Petruc- cione, “Prediction by linear regression on a quantum computer,” Physical Review A 94, 022342 (2016)

2016
[12]

Quantum algorithms for topological and geometric anal- ysis of data,

Seth Lloyd, Silvano Garnerone, and Paolo Zanardi, “Quantum algorithms for topological and geometric anal- ysis of data,” Nature communications 7, 10138 (2016)

2016
[13]

Quantum gra- dient descent and newton’s method for constrained poly- nomial optimization,

Patrick Rebentrost, Maria Schuld, Leonard Wossnig, Francesco Petruccione, and Seth Lloyd, “Quantum gra- dient descent and newton’s method for constrained poly- nomial optimization,” New Journal of Physics (2019)

2019
[14]

Read the ﬁne print,

Scott Aaronson, “Read the ﬁne print,” Nature Physics 11, 291 (2015)

2015
[15]

A quantum-inspired classical algorithm for recommendation systems,

Ewin Tang, “A quantum-inspired classical algorithm for recommendation systems,” in Proceedings of the 51st An- nual ACM SIGACT Symposium on Theory of Computing (2019) pp. 217–228

2019
[16]

On the robustness of bucket brigade quantum ram,

Srinivasan Arunachalam, Vlad Gheorghiu, Tomas Jochym-O’Connor, Michele Mosca, and Priyaa Varshi- nee Srinivasan, “On the robustness of bucket brigade quantum ram,” New Journal of Physics 17, 123010 (2015)

2015
[17]

Quantum annealing in the transverse ising model,

Tadashi Kadowaki and Hidetoshi Nishimori, “Quantum annealing in the transverse ising model,” Physical Review E 58, 5355 (1998)

1998
[18]

Test-driving 1000 qubits,

Joshua Job and Daniel Lidar, “Test-driving 1000 qubits,” Quantum Science and Technology 3, 030501 (2018)

2018
[19]

Per- spectives of quantum annealing: Methods and implemen- tations,

Philipp Hauke, Helmut G. Katzgraber, Wolfgang Lech- ner, Hidetoshi Nishimori, and William D. Oliver, “Per- spectives of quantum annealing: Methods and implemen- tations,” arXiv:1903.06559 (2019)

2019 arXiv
[20]

thesis, University of Southern California (2018)

Joshua Job, The Theory and Practice of Benchmarking Quantum Annealers, Ph.D. thesis, University of Southern California (2018)

2018
[21]

Training a binary classiﬁer with the quantum adiabatic algorithm,

Hartmut Neven, Vasil S Denchev, Geordie Rose, and William G Macready, “Training a binary classiﬁer with the quantum adiabatic algorithm,” arXiv preprint arXiv:0811.0416 (2008)

2008 arXiv
[22]

Quantum adia- batic machine learning,

Kristen L. Pudenz and Daniel A. Lidar, “Quantum adia- batic machine learning,” Quantum Information Process- ing 12, 2027–2070 (2013)

2013
[23]

Bayesian network structure learning using quantum annealing,

B. O’Gorman, R. Babbush, A. Perdomo-Ortiz, A. Aspuru-Guzik, and V. Smelyanskiy, “Bayesian network structure learning using quantum annealing,” The European Physical Journal Special Topics 224, 163–188 (2015)

2015
[24]

Quantum boltzmann machine,

Mohammad H. Amin, Evgeny Andriyash, Jason Rolfe, Bohdan Kulchytskyy, and Roger Melko, “Quantum boltzmann machine,” Physical Review X 8, 021050– (2018)

2018
[25]

A path towards quantum advantage in train- ing deep generative models with quantum annealers,

Walter Vinci, Lorenzo Buﬀoni, Hossein Sadeghi, Amir Khoshaman, Evgeny Andriyash, and Mohammad H. Amin, “A path towards quantum advantage in train- ing deep generative models with quantum annealers,” (2019), arXiv:1912.02119 [quant-ph]

2019 arXiv
[26]

Experimental investigation of an eight-qubit unit cell in a supercon- ducting optimization processor,

Richard Harris, Mark W Johnson, T Lanting, AJ Berkley, J Johansson, P Bunyk, E Tolkacheva, E Ladizinsky, N Ladizinsky, T Oh, et al. , “Experimental investigation of an eight-qubit unit cell in a supercon- ducting optimization processor,” Physical Review B 82, 024511 (2010)

2010
[27]

Quantum annealing with manufactured spins,

Mark W Johnson, Mohammad HS Amin, Suzanne Gildert, Trevor Lanting, Firas Hamze, Neil Dickson, Richard Harris, Andrew J Berkley, Jan Johansson, Paul Bunyk, et al. , “Quantum annealing with manufactured spins,” Nature 473, 194–198 (2011)

2011
[28]

Archi- tectural considerations in the design of a superconduct- ing quantum annealing processor,

P. I. Bunyk, E. M. Hoskinson, M. W. Johnson, E. Tolka- cheva, F. Altomare, A. J. Berkley, R. Harris, J. P. Hilton, T. Lanting, A. J. Przybysz, and J. Whittaker, “Archi- tectural considerations in the design of a superconduct- ing quantum annealing processor,” IEEE Transactions...

2014
[29]

Quantum annealing applied to de- conﬂicting optimal trajectories for air traﬃc manage- ment,

Tobias Stollenwerk, Bryan O’Gorman, Davide Ven- turelli, Salvatore Mandr` a, Olga Rodionova, Hokkwan Ng, Banavar Sridhar, Eleanor Gilbert Rieﬀel, and Rupak Biswas, “Quantum annealing applied to de- conﬂicting optimal trajectories for air traﬃc manage- ment,” IEEE transactions ...

2019
[30]

Find- ing low-energy conformations of lattice protein models by quantum annealing,

Alejandro Perdomo-Ortiz, Neil Dickson, Marshall Drew- Brook, Geordie Rose, and Al´ an Aspuru-Guzik, “Find- ing low-energy conformations of lattice protein models by quantum annealing,” Scientiﬁc reports 2, 571 (2012)

2012
[31]

Quantum annealing versus classical machine learning applied to a simpliﬁed computational biology problem,

Richard Y Li, Rosa Di Felice, Remo Rohs, and Daniel A Lidar, “Quantum annealing versus classical machine learning applied to a simpliﬁed computational biology problem,” NPJ quantum information 4, 14 (2018)

2018
[32]

Unconventional machine learning of genome-wide human cancer data,

Richard Y. Li, Sharvari Gujja, Sweta R. Bajaj, Omar E. Gamel, Nicholas Cilfone, Jeﬀrey R. Gulcher, Daniel A. Lidar, and Thomas W. Chittenden, “Unconventional machine learning of genome-wide human cancer data,” arXiv:1909.06206 (2019)

2019 arXiv
[33]

Solving a higgs optimization problem with quantum annealing for machine learning,

Alex Mott, Joshua Job, Jean-Roch Vlimant, Daniel Li- dar, and Maria Spiropulu, “Solving a higgs optimization problem with quantum annealing for machine learning,” Nature 550, 375 (2017)

2017
[34]

Charged particle tracking with quan- 8 tum annealing-inspired optimization,

Alexander Zlokapa, Abhishek Anand, Jean-Roch Vli- mant, Javier M Duarte, Joshua Job, Daniel Lidar, and Maria Spiropulu, “Charged particle tracking with quan- 8 tum annealing-inspired optimization,” arXiv preprint arXiv:1908.04475 (2019)

2019 arXiv
[35]

A pattern recognition algorithm for quantum anneal- ers,

Fr´ ed´ eric Bapst, Wahid Bhimji, Paolo Calaﬁura, Heather Gray, Wim Lavrijsen, Lucy Linder, and Alex Smith, “A pattern recognition algorithm for quantum anneal- ers,” Computing and Software for Big Science 4 (2019), 10.1007/s41781-019-0032-5

2019 doi
[36]

On the adiabatic theorem of quantum me- chanics,

Tosio Kato, “On the adiabatic theorem of quantum me- chanics,” Journal of the Physical Society of Japan5, 435– 439 (1950)

1950
[37]

Bounds for the adiabatic approximation with appli- cations to quantum computation,

Sabine Jansen, Mary-Beth Ruskai, and Ruedi Seiler, “Bounds for the adiabatic approximation with appli- cations to quantum computation,” J. Math. Phys. 48, 102111 (2007)

2007
[38]

Adiabatic approximation with exponential accuracy for many-body systems and quantum computation,

Daniel A. Lidar, Ali T. Rezakhani, and Alioscia Hamma, “Adiabatic approximation with exponential accuracy for many-body systems and quantum computation,” J. Math. Phys. 50, 102106 (2009)

2009
[39]

Quantum Computation by Adiabatic Evolution,

Edward Farhi, Jeﬀrey Goldstone, Sam Gutmann, and Michael Sipser, “Quantum Computation by Adiabatic Evolution,” arXiv:quant-ph/0001106 (2000)

2000 arXiv
[40]

Adiabatic quan- tum computation,

Tameem Albash and Daniel A Lidar, “Adiabatic quan- tum computation,” Reviews of Modern Physics 90, 015002 (2018)

2018
[41]

Robustness of adiabatic quantum computation,

Andrew M Childs, Edward Farhi, and John Preskill, “Robustness of adiabatic quantum computation,” Phys- ical Review A 65, 012322 (2001)

2001
[42]

Decoherence in adiabatic quantum computa- tion,

Mohammad HS Amin, Dmitri V Averin, and James A Nesteroﬀ, “Decoherence in adiabatic quantum computa- tion,” Physical Review A 79, 022107 (2009)

2009
[43]

Decoherence in adiabatic quantum computation,

Tameem Albash and Daniel A Lidar, “Decoherence in adiabatic quantum computation,” Physical Review A91, 062320 (2015)

2015
[44]

Minor-embedding in adiabatic quantum computation: I. the parameter setting problem,

Vicky Choi, “Minor-embedding in adiabatic quantum computation: I. the parameter setting problem,” Quan- tum Information Processing 7, 193–209 (2008)

2008
[45]

Minor-embedding in adiabatic quantum computation: Ii. minor-universal graph design,

Vicky Choi, “Minor-embedding in adiabatic quantum computation: Ii. minor-universal graph design,” Quan- tum Information Processing 10, 343–353 (2011)

2011
[46]

Adiabatic quantum programming: minor embed- ding with hard faults,

Christine Klymko, Blair D. Sullivan, and Travis S. Hum- ble, “Adiabatic quantum programming: minor embed- ding with hard faults,” Quant. Inf. Proc. 13, 709–729 (2014)

2014
[47]

A prac- tical heuristic for ﬁnding graph minors,

Jun Cai, William G. Macready, and Aidan Roy, “A prac- tical heuristic for ﬁnding graph minors,” arXiv:1406.2741 (2014)

2014 arXiv
[48]

Thermally assisted adiabatic quantum computation,

M. H. S. Amin, Peter J. Love, and C. J. S. Truncik, “Thermally assisted adiabatic quantum computation,” Phys. Rev. Lett. 100, 060503 (2008)

2008
[49]

Thermally assisted quantum annealing of a 16-qubit problem,

Neil G Dickson, MW Johnson, MH Amin, R Harris, F Altomare, AJ Berkley, P Bunyk, J Cai, EM Chapple, P Chavez, et al., “Thermally assisted quantum annealing of a 16-qubit problem,” Nature communications 4, 1–6 (2013)

2013
[50]

Relaxation ver- sus adiabatic quantum steady-state preparation,

Lorenzo Campos Venuti, Tameem Albash, Milad Mar- vian, Daniel Lidar, and Paolo Zanardi, “Relaxation ver- sus adiabatic quantum steady-state preparation,” Phys. Rev. A 95, 042302– (2017)

2017
[51]

Finite temperature quantum annealing solving expo- nentially small gap problem with non-monotonic success probability,

Anurag Mishra, Tameem Albash, and Daniel A. Lidar, “Finite temperature quantum annealing solving expo- nentially small gap problem with non-monotonic success probability,” Nature Communications 9, 2917 (2018)

2018
[52]

Deﬁning and detecting quantum speedup,

Troels F. Rønnow, Zhihui Wang, Joshua Job, Sergio Boixo, Sergei V. Isakov, David Wecker, John M. Mar- tinis, Daniel A. Lidar, and Matthias Troyer, “Deﬁning and detecting quantum speedup,” Science 345, 420–424 (2014)

2014
[53]

Demonstration of a scaling advantage for a quantum annealer over simu- lated annealing,

Tameem Albash and Daniel A. Lidar, “Demonstration of a scaling advantage for a quantum annealer over simu- lated annealing,” Physical Review X 8, 031016– (2018)

2018
[54]

A decep- tive step towards quantum speedup detection,

Salvatore Mandr` a and Helmut G Katzgraber, “A decep- tive step towards quantum speedup detection,” Quantum Sci. Technol. 3, 04LT01 (2018)

2018
[55]

Entanglement in a quantum anneal- ing processor,

Trevor Lanting, Anthony J Przybysz, A Yu Smirnov, Federico M Spedalieri, Mohammad H Amin, Andrew J Berkley, Richard Harris, Fabio Altomare, Sergio Boixo, Paul Bunyk, et al., “Entanglement in a quantum anneal- ing processor,” Physical Review X 4, 021041 (2014)

2014
[56]

Computational multi- qubit tunnelling in programmable quantum annealers,

Sergio Boixo, Vadim N. Smelyanskiy, Alireza Shabani, Sergei V. Isakov, Mark Dykman, Vasil S. Denchev, Mohammad H. Amin, Anatoly Yu Smirnov, Masoud Mohseni, and Hartmut Neven, “Computational multi- qubit tunnelling in programmable quantum annealers,” Nat Commun 7 (2016)

2016
[57]

What is the computational value of ﬁnite-range tunneling?

Vasil S. Denchev, Sergio Boixo, Sergei V. Isakov, Nan Ding, Ryan Babbush, Vadim Smelyanskiy, John Marti- nis, and Hartmut Neven, “What is the computational value of ﬁnite-range tunneling?” Phys. Rev. X 6, 031015 (2016)

2016
[58]

Searching for quantum speedup in quasistatic quantum annealers,

Mohammad H. Amin, “Searching for quantum speedup in quasistatic quantum annealers,” Physical Review A 92, 052323– (2015)

2015
[59]

Observation of topological phenomena in a pro- grammable lattice of 1,800 qubits,

Andrew D. King, Juan Carrasquilla, Jack Raymond, Isil Ozﬁdan, Evgeny Andriyash, Andrew Berkley, Mauricio Reis, Trevor Lanting, Richard Harris, Fabio Altomare, Kelly Boothby, Paul I. Bunyk, Colin Enderud, Alexandre Fr´ echette, Emile Hoskinson, Nicolas Ladizinsky, Travis Oh, Ga...

2018
[60]

Phase transitions in a programmable quantum spin glass simu- lator,

R. Harris, Y. Sato, A. J. Berkley, M. Reis, F. Al- tomare, M. H. Amin, K. Boothby, P. Bunyk, C. Deng, C. Enderud, S. Huang, E. Hoskinson, M. W. Johnson, E. Ladizinsky, N. Ladizinsky, T. Lanting, R. Li, T. Med- ina, R. Molavi, R. Neufeld, T. Oh, I. Pavlov, I. Perminov, G. Pouli...

2018
[61]

Source code for the QAML-Z algorithm is provided at https://github.com/quantummind/qaml-z/
[62]

Kinematics variables of higgs and background data,

Alex Mott, Joshua Job, Jean-Roch Vlimant, Daniel Li- dar, and Maria Spiropulu, “Kinematics variables of higgs and background data,” (2020)

2020
[63]

Analog errors in quantum annealing: doom and hope,

Adam Pearson, Anurag Mishra, Itay Hen, and Daniel A. Lidar, “Analog errors in quantum annealing: doom and hope,” npj Quantum Information 5, 107 (2019)

2019
[64]

Quantum optimization of fully connected spin glasses,

Davide Venturelli, Salvatore Mandr` a, Sergey Knysh, Bryan O’Gorman, Rupak Biswas, and Vadim Smelyan- skiy, “Quantum optimization of fully connected spin glasses,” Phys. Rev. X 5, 031040 (2015)

2015
[65]

Xgboost: A scal- able tree boosting system,

Tianqi Chen and Carlos Guestrin, “Xgboost: A scal- able tree boosting system,” in Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge 9 Discovery and Data Mining , KDD ’16 (Association for Computing Machinery, New York, NY, USA, 2016) pp. 785–794

2016
[66]

Opti- mization by simulated annealing,

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Opti- mization by simulated annealing,” Science 220, 671–680 (1983)

1983

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

[1] [1]

Computa- tional methods in drug discovery,

Sumudu P Leelananda and Steﬀen Lindert, “Computa- tional methods in drug discovery,” Beilstein journal of organic chemistry 12, 2694–2718 (2016). 7

work page 2016

[2] [2]

Machine learning and its applications to biology,

Adi L Tarca, Vincent J Carey, Xue-wen Chen, Roberto Romero, and Sorin Dr˘ aghici, “Machine learning and its applications to biology,” PLoS computational biology 3, e116 (2007)

work page 2007

[3] [3]

William W Hsieh, Machine learning methods in the envi- ronmental sciences: Neural networks and kernels (Cam- bridge university press, 2009)

work page 2009

[4] [4]

Machine learning phases of matter,

Juan Carrasquilla and Roger G Melko, “Machine learning phases of matter,” Nature Physics 13, 431 (2017)

work page 2017

[5] [5]

Searching for exotic particles in high-energy physics with deep learning,

Pierre Baldi, Peter Sadowski, and Daniel Whiteson, “Searching for exotic particles in high-energy physics with deep learning,” Nature communications 5, 4308 (2014)

work page 2014

[6] [6]

Machine learning at the energy and intensity fron- tiers of particle physics,

Alexander Radovic, Mike Williams, David Rousseau, Michael Kagan, Daniele Bonacorsi, Alexander Himmel, Adam Aurisano, Kazuhiro Terao, and Taritree Wongji- rad, “Machine learning at the energy and intensity fron- tiers of particle physics,” Nature 560, 41 (2018)

work page 2018

[7] [7]

Quantum machine learning,

Jacob Biamonte, Peter Wittek, Nicola Pancotti, Patrick Rebentrost, Nathan Wiebe, and Seth Lloyd, “Quantum machine learning,” Nature 549, 195 (2017)

work page 2017

[8] [8]

Quantum support vector machine for big data classiﬁ- cation,

Patrick Rebentrost, Masoud Mohseni, and Seth Lloyd, “Quantum support vector machine for big data classiﬁ- cation,” Physical review letters 113, 130503 (2014)

work page 2014