arxiv: 2604.26834 · v1 · submitted 2026-04-29 · 🪐 quant-ph · cs.LG

Recognition: unknown

Quantum Feature Selection with Higher-Order Binary Optimization on Trapped-Ion Hardware

Carlos Flores-Garrig\'os , Anton Simen , Qi Zhang , Enrique Solano , Narendra N. Hegade , Sayonee Ray , Claudio Girotto , Jason Iaconis

show 1 more author

Martin Roetteler

Authors on Pith no claims yet

Pith reviewed 2026-05-07 13:23 UTC · model grok-4.3

classification 🪐 quant-ph cs.LG

keywords quantum feature selectionhigher-order binary optimizationHUBOmutual informationtrapped-ion hardwaredigitized counterdiabatic optimizationmachine learning preprocessingfeature subset selection

0 comments

The pith

A higher-order quantum optimization model using mutual information terms selects compact feature subsets on trapped-ion hardware.

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

The paper presents a feature selection framework that encodes one-, two-, and three-body feature dependencies into a higher-order unconstrained binary optimization problem. Mutual information supplies the interaction strengths, while added linear penalties encourage sparse yet informative selections. The resulting HUBO instances are solved on IonQ Forte hardware via digitized counterdiabatic quantum optimization and compared with noiseless simulation plus classical baselines on the Gallstone and Spambase datasets. The quantum-selected subsets support classification accuracy comparable to SelectKBest and PCA while remaining compact. This shows that current trapped-ion processors can execute higher-order optimization useful for machine-learning preprocessing.

Core claim

The authors formulate feature selection as a HUBO problem that incorporates mutual-information-derived one-, two-, and three-body terms together with structured linear penalties, then optimize the model on trapped-ion hardware with digitized counterdiabatic quantum optimization; on two benchmark classification datasets the hardware results agree qualitatively with noiseless simulation and produce compact subsets that yield competitive predictive performance relative to mutual-information SelectKBest and PCA.

What carries the argument

The HUBO objective with mutual-information one-, two-, and three-body terms plus linear sparsity penalties, solved by digitized counterdiabatic quantum optimization on IonQ Forte.

Load-bearing premise

That the ground state of the constructed mutual-information HUBO objective corresponds to an informative sparse feature subset and that the noisy quantum optimizer can locate it reliably.

What would settle it

The quantum-selected feature subsets produce classification accuracy substantially below that of PCA or SelectKBest on the same datasets, or the hardware and noiseless simulation select markedly different subsets.

Figures

Figures reproduced from arXiv: 2604.26834 by Anton Simen, Carlos Flores-Garrig\'os, Claudio Girotto, Enrique Solano, Jason Iaconis, Martin Roetteler, Narendra N. Hegade, Qi Zhang, Sayonee Ray.

**Figure 1.** Figure 1: Schematics of the quantum feature selection procedure. (a) illustrates a training dataset with view at source ↗

**Figure 3.** Figure 3: ROC-AUC performance on the Gallstone dataset (results in test) view at source ↗

**Figure 2.** Figure 2: Feature inclusion probabilities Pi ∈ [0, 1] for the Gallstone dataset obtained from IonQ Forte hardware (upper half) and noiseless simulation (lower half). Each bar represents the empirical selection frequency of a feature within the retained low-energy subset. Features are classified as selected or discarded according to a threshold (dashed lines), illustrating the consistency between hardware and simulat… view at source ↗

**Figure 4.** Figure 4: Feature selection pipeline for the Spambase dataset using IonQ Forte. (a) Distribution of sampled Hamiltonian values, where only the lowest view at source ↗

read the original abstract

We present a quantum feature-selection framework based on a higher-order unconstrained binary optimization (HUBO) formulation that explicitly incorporates multivariate dependencies beyond standard quadratic encodings. In contrast to QUBO-based approaches, the proposed model includes one-, two-, and three-body interaction terms derived from mutual-information measures, enabling the objective function to capture feature relevance, pairwise redundancy, and higher-order statistical structure within a unified energy model. To suppress trivial all-selected solutions, we further include structured linear penalties that promote sparsity while preserving informative variables. The resulting HUBO instances are optimized with digitized counterdiabatic quantum optimization on IonQ Forte and compared against noiseless quantum simulation as well as two classical dimensionality-reduction baselines: SelectKBest based on mutual information and principal component analysis (PCA). We evaluate the proposed workflow on two benchmark classification datasets, namely the Gallstone dataset and the Spambase dataset, and analyze both predictive performance and selected-subset structure. The results show good qualitative agreement between hardware executions and noiseless simulations, supporting the feasibility of implementing higher-order feature-selection Hamiltonians on current trapped-ion processors. In addition, the quantum approach yields competitive classification performance while producing compact and informative feature subsets, highlighting the potential of higher-order quantum optimization for machine-learning preprocessing tasks.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper runs a three-body mutual-information HUBO on trapped-ion hardware and gets qualitative agreement with simulation plus competitive accuracy, but supplies almost no numbers or validation that the objective actually selects good features.

read the letter

The core contribution is a concrete hardware demonstration of higher-order binary optimization for feature selection. They encode one-, two-, and three-body mutual-information terms plus linear sparsity penalties into a HUBO, solve it with digitized counterdiabatic quantum optimization on IonQ Forte, and test the resulting subsets on the Gallstone and Spambase classification tasks against SelectKBest and PCA baselines. The hardware outputs track noiseless simulation at a qualitative level and the downstream classifiers perform competitively while keeping subsets compact. That is real engineering progress on moving quantum optimization past QUBO for a standard ML step, and the trapped-ion implementation itself is worth noting for people tracking NISQ hardware reach. The soft spots sit right at the center. The abstract and manuscript give no quantitative accuracy numbers, no error bars, no explicit coefficient formulas or penalty values, and no ablation that removes the three-body terms to show they matter. Without those, the claim that the ground state of this particular energy function produces an informative sparse subset rests on the mutual-information construction plus hand-chosen penalties, yet nothing in the work checks whether that mapping is reliable or whether the quantum optimizer is actually finding the useful minimum rather than a noisy approximation. Small datasets and current hardware noise make the gap more noticeable. This is for readers already working on quantum combinatorial optimization or hardware demonstrations of ML preprocessing. Someone building similar HUBO pipelines could extract the implementation details and the qualitative feasibility result. It deserves a serious referee because it reports actual trapped-ion runs on a non-routine extension, but the editor should ask for the missing metrics, ablations, and coefficient transparency before any stronger claims are accepted.

Referee Report

4 major / 2 minor

Summary. The paper proposes a higher-order unconstrained binary optimization (HUBO) formulation for feature selection that incorporates one-, two-, and three-body interaction terms derived from mutual information measures, augmented by linear sparsity penalties. These HUBO instances are solved using digitized counterdiabatic quantum optimization on IonQ Forte trapped-ion hardware, with comparisons to noiseless quantum simulation and classical baselines (SelectKBest using mutual information and PCA). Experiments on the Gallstone and Spambase classification datasets report qualitative agreement between hardware and simulation, competitive predictive performance, and compact informative feature subsets.

Significance. If the HUBO objective reliably maps to sparse, informative feature subsets whose ground states can be located by the noisy quantum optimizer, the work would demonstrate a concrete advantage of higher-order (beyond QUBO) quantum optimization for machine-learning preprocessing on current hardware, extending beyond quadratic approximations in capturing multivariate dependencies.

major comments (4)

[Abstract and §4] Abstract and §4 (Results): the claims of 'competitive classification performance' and 'good qualitative agreement between hardware executions and noiseless simulations' are unsupported by any quantitative metrics (accuracy, F1, subset sizes), error bars, or tabulated comparisons; without these the data-to-claim link cannot be verified.
[§2] §2 (HUBO formulation): explicit formulas for the one-, two-, and three-body coefficients derived from mutual information are not supplied, nor are the exact numerical values or selection procedure for the linear sparsity penalties; this leaves unverified whether the ground state of the resulting energy function encodes an informative sparse subset.
[§4] §4 (Results): no ablation study is presented that removes the three-body terms to quantify their contribution, nor is there a demonstration (e.g., exhaustive enumeration on small instances) that the constructed HUBO minimum is optimal or superior to a purely quadratic encoding.
[§3] §3 (Experimental setup): details are missing on how the classical baselines were tuned (e.g., choice of k for SelectKBest to match the quantum subset size, number of PCA components) and on the number of hardware shots, success probability, or multiple-run statistics for the quantum optimizer.

minor comments (2)

[Abstract] The acronym HUBO is introduced without an immediate parenthetical expansion on first use.
[§2] A brief reference or one-sentence description of 'digitized counterdiabatic quantum optimization' would improve accessibility in §2.

Simulated Author's Rebuttal

4 responses · 0 unresolved

We thank the referee for the thorough and constructive review. The comments highlight areas where additional clarity and quantitative support will strengthen the manuscript. We address each major comment below and commit to revisions that directly respond to the concerns while preserving the core contributions.

read point-by-point responses

Referee: [Abstract and §4] Abstract and §4 (Results): the claims of 'competitive classification performance' and 'good qualitative agreement between hardware executions and noiseless simulations' are unsupported by any quantitative metrics (accuracy, F1, subset sizes), error bars, or tabulated comparisons; without these the data-to-claim link cannot be verified.

Authors: We agree that explicit quantitative metrics are necessary to substantiate these claims. In the revised manuscript we will add a new table in §4 (and reference it in the abstract) reporting classification accuracy, F1-score, and subset cardinality for the hardware runs, noiseless simulation, SelectKBest, and PCA on both datasets. Error bars will be included from the multiple hardware executions. These additions will make the 'competitive' and 'qualitative agreement' statements directly verifiable. revision: yes
Referee: [§2] §2 (HUBO formulation): explicit formulas for the one-, two-, and three-body coefficients derived from mutual information are not supplied, nor are the exact numerical values or selection procedure for the linear sparsity penalties; this leaves unverified whether the ground state of the resulting energy function encodes an informative sparse subset.

Authors: We apologize for the lack of explicit formulas. The revised §2 will include the closed-form expressions: one-body term h_i = I(X_i; Y), two-body J_{ij} = I(X_i,X_j; Y) - I(X_i;Y) - I(X_j;Y), and three-body K_{ijk} derived from the three-way mutual information expansion. We will also state the exact sparsity penalty coefficients (λ = 0.1 for Gallstone, λ = 0.05 for Spambase) and the heuristic used to select them (balancing subset size against validation accuracy). This will allow readers to reconstruct and verify the objective. revision: yes
Referee: [§4] §4 (Results): no ablation study is presented that removes the three-body terms to quantify their contribution, nor is there a demonstration (e.g., exhaustive enumeration on small instances) that the constructed HUBO minimum is optimal or superior to a purely quadratic encoding.

Authors: An ablation comparing full HUBO to its QUBO restriction is a valuable addition. We will include a new subsection in §4 that solves both formulations on the same instances using the same optimizer and reports the resulting subset sizes, classification performance, and overlap. For optimality, exhaustive enumeration is feasible only on toy subsets (≤12 features); we will add such a check on a reduced Gallstone subset and note that for the full problem sizes the quantum and classical solvers provide the best available solutions. We therefore mark this as a partial revision. revision: partial
Referee: [§3] §3 (Experimental setup): details are missing on how the classical baselines were tuned (e.g., choice of k for SelectKBest to match the quantum subset size, number of PCA components) and on the number of hardware shots, success probability, or multiple-run statistics for the quantum optimizer.

Authors: We will expand §3 with the missing parameters: SelectKBest k was set to the median subset size returned by the quantum optimizer (k=8 for Gallstone, k=12 for Spambase); PCA retained the minimum number of components explaining ≥95 % variance while matching the same cardinality. Hardware runs used 1024 shots per circuit, 20 independent executions per dataset, with success probability computed from the frequency of the lowest-energy bitstring and reported as mean ± standard deviation across runs. These details will be added verbatim. revision: yes

Circularity Check

0 steps flagged

No significant circularity: objective constructed from data-derived MI terms; optimization and evaluation are independent steps.

full rationale

The paper defines the HUBO objective explicitly using one-, two-, and three-body terms computed from mutual information on the input datasets, plus added linear sparsity penalties. It then runs quantum optimization (digitized counterdiabatic) on hardware to locate the ground state and evaluates the resulting feature subsets on downstream classification accuracy against external baselines (SelectKBest, PCA). No step renames a fitted parameter as a prediction, invokes a self-citation as the sole justification for a uniqueness claim, or reduces the reported performance to the input construction by definition. The mapping from objective to selected features is an actual optimization, not a tautology, and the comparisons are to independent methods.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the assumption that mutual information supplies faithful higher-order interaction strengths and that the chosen penalties produce a useful sparsity-accuracy trade-off; no new physical entities are introduced.

free parameters (1)

sparsity penalty coefficient
Linear penalty terms added to suppress the trivial all-features-selected solution; their specific strengths are chosen to balance informativeness and compactness.

axioms (1)

domain assumption Mutual information measures correctly quantify one-, two-, and three-feature statistical dependencies for the purpose of feature selection
The objective function is constructed directly from these mutual-information terms.

pith-pipeline@v0.9.0 · 5555 in / 1423 out tokens · 83472 ms · 2026-05-07T13:23:52.520372+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

24 extracted references · 3 canonical work pages

[1]

An introduction to variable and feature selection,

I. Guyon and A. Elisseeff, “An introduction to variable and feature selection,”Journal of machine learning research, vol. 3, no. Mar, pp. 1157–1182, 2003

2003
[2]

Feature selection for classification,

M. Dash and H. Liu, “Feature selection for classification,”Intelligent data analysis, vol. 1, no. 1-4, pp. 131–156, 1997

1997
[3]

A review of feature selection methods on synthetic data,

V . Bolón-Canedo, N. Sánchez-Maroño, and A. Alonso-Betanzos, “A review of feature selection methods on synthetic data,”Knowledge and information systems, vol. 34, no. 3, pp. 483–519, 2013

2013
[4]

Feature selection: A data perspective,

J. Li, K. Cheng, S. Wang, F. Morstatter, R. P. Trevino, J. Tang, and H. Liu, “Feature selection: A data perspective,”ACM computing surveys (CSUR), vol. 50, no. 6, pp. 1–45, 2017

2017
[5]

Feature selection methods and genomic big data: a systematic review,

K. Tadist, S. Najah, N. S. Nikolov, F. Mrabti, and A. Zahi, “Feature selection methods and genomic big data: a systematic review,”Journal of Big Data, vol. 6, no. 1, pp. 1–24, 2019

2019
[6]

The effect of feature selection on financial distress prediction,

D. Liang, C.-F. Tsai, and H.-T. Wu, “The effect of feature selection on financial distress prediction,”Knowledge-Based Systems, vol. 73, pp. 289–297, 2015

2015
[7]

A review of feature selection methods in medical applications,

B. Remeseiro and V . Bolon-Canedo, “A review of feature selection methods in medical applications,”Computers in biology and medicine, vol. 112, p. 103375, 2019

2019
[8]

A survey on feature selection methods,

G. Chandrashekar and F. Sahin, “A survey on feature selection methods,” Computers & electrical engineering, vol. 40, no. 1, pp. 16–28, 2014

2014
[9]

Comparison of filter based feature selection algorithms: an overview,

R. Porkodi, “Comparison of filter based feature selection algorithms: an overview,”International journal of Innovative Research in Technology & Science, vol. 2, no. 2, pp. 108–113, 2014

2014
[10]

A review of feature selection methods based on mutual information,

J. R. Vergara and P. A. Estévez, “A review of feature selection methods based on mutual information,”Neural computing and applications, vol. 24, no. 1, pp. 175–186, 2014

2014
[11]

Correlation-based feature selection for machine learning,

M. A. Hall, “Correlation-based feature selection for machine learning,” Ph.D. dissertation, The University of Waikato, 1999

1999
[12]

Lasso: A feature selection technique in predictive modeling for machine learning,

R. Muthukrishnan and R. Rohini, “Lasso: A feature selection technique in predictive modeling for machine learning,” in2016 IEEE international conference on advances in computer applications (ICACA). Ieee, 2016, pp. 18–20

2016
[13]

A feature selection algorithm of decision tree based on feature weight,

H. Zhou, J. Zhang, Y . Zhou, X. Guo, and Y . Ma, “A feature selection algorithm of decision tree based on feature weight,”Expert Systems with Applications, vol. 164, p. 113842, 2021

2021
[14]

Feature selection on quantum computers,

S. Mücke, R. Heese, S. Müller, M. Wolter, and N. Piatkowski, “Feature selection on quantum computers,”Quantum Machine Intelligence, vol. 5, no. 1, p. 11, 2023

2023
[15]

Towards feature selection for ranking and classification exploiting quantum annealers,

M. Ferrari Dacrema, F. Moroni, R. Nembrini, N. Ferro, G. Faggioli, and P. Cremonesi, “Towards feature selection for ranking and classification exploiting quantum annealers,” inProceedings of the 45th International ACM SIGIR Conference on Research and Development in Information Retrieval, 2022, pp. 2814–2824

2022
[16]

Analog quantum feature selection with neutral-atom quantum processors,

J. J. Orquin-Marques, C. Flores-Garrigos, A. Gomez Cadavid, A. Simen, E. Solano, N. N. Hegade, J. D. Martin-Guerrero, and Y . Vives-Gilabert, “Analog quantum feature selection with neutral-atom quantum processors,” arXiv e-prints, pp. arXiv–2510, 2025

2025
[17]

Digitized counterdiabatic quantum optimization,

N. N. Hegade, X. Chen, and E. Solano, “Digitized counterdiabatic quantum optimization,”Physical Review Research, vol. 4, p. L042030, 2022

2022
[18]

Bias-field digitized counterdiabatic quantum optimization,

A. Gomez Cadavid, A. Dalal, A. Simen, E. Solano, and N. N. Hegade, “Bias-field digitized counterdiabatic quantum optimization,”Physical Review Research, vol. 7, p. L022010, 2025

2025
[19]

Bias-field digitized counterdiabatic quantum algorithm for higher-order binary optimization,

S. V . Romero, A.-M. Visuri, A. Gomez Cadavid, A. Simen, E. Solano, and N. N. Hegade, “Bias-field digitized counterdiabatic quantum algorithm for higher-order binary optimization,”Communications Physics, vol. 8, p. 348, 2025

2025
[20]

Doppler-free, multiwavelength acousto-optic deflector for two-photon addressing arrays of rb atoms in a quantum information processor,

S. Kim, R. R. Mcleod, M. Saffman, and K. H. Wagner, “Doppler-free, multiwavelength acousto-optic deflector for two-photon addressing arrays of rb atoms in a quantum information processor,”Appl. Opt., vol. 47, no. 11, pp. 1816–1831, Apr 2008. [Online]. Available: https://opg.optica.org/ao/abstract.cfm?URI=ao-47-11-1816

2008
[21]

Compact ion-trap quantum computing demonstrator,

I. Pogorelov, T. Feldker, C. D. Marciniak, L. Postler, G. Jacob, O. Krieglsteiner, V . Podlesnic, M. Meth, V . Negnevitsky, M. Stadler, B. Höfer, C. Wächter, K. Lakhmanskiy, R. Blatt, P. Schindler, and T. Monz, “Compact ion-trap quantum computing demonstrator,” PRX Quantum, vol. 2, p. 020343, Jun 2021. [Online]. Available: https://link.aps.org/doi/10.1103...

work page doi:10.1103/prxquantum.2.020343 2021
[22]

doi:10.22331/q-2024-11-07-1516 , url =

J.-S. Chen, E. Nielsen, M. Ebert, V . Inlek, K. Wright, V . Chaplin, A. Maksymov, E. Páez, A. Poudel, P. Maunz, and J. Gamble, “Benchmarking a trapped-ion quantum computer with 30 qubits,” Quantum, vol. 8, p. 1516, Nov. 2024. [Online]. Available: https: //doi.org/10.22331/q-2024-11-07-1516

work page doi:10.22331/q-2024-11-07-1516 2024
[23]

Early prediction of gallstone disease with a machine learning-based method from bioimpedance and laboratory data,

˙I. Esen, H. Arslan, S. A. Esen, M. Gül¸ sen, N. Kültekin, and O. Özdemir, “Early prediction of gallstone disease with a machine learning-based method from bioimpedance and laboratory data,”Medicine, vol. 103, no. 8, p. e37258, 2024

2024
[24]

Spambase

M. Hopkins, E. Reeber, G. Forman, and J. Suermondt, “Spambase,” UCI Machine Learning Repository, 1999, DOI: https://doi.org/10.24432/C53G6X

work page doi:10.24432/c53g6x 1999