This paper presents the SINAI team's approach to Task 1 (Feature Selection) at QuantumCLEF 2025, focusing on the use of quantum annealing with D-Wave hardware to tackle feature selection for learning-to-rank models. We formulate the feature selection problem as a Quadratic Unconstrained Binary Optimization problem based on mutual information to balance feature relevance and redundancy. Candidate feature subsets are generated by the quantum annealer and then post-processed through normalization and energy projection strategies to obtain robust feature rankings. Evaluation on the MQ2007 LETOR dataset demonstrates the potential of quantum computing to support efective feature selection in information retrieval tasks, despite current hardware limitations. Our results highlight promising directions for integrating quantum optimization in practical machine learning workflows.
The remainder of this paper is organized as follows: Section 2, Methodology, describes our QUBO formulation and post-processing strategies. Section 3, Results, presents our experimental evaluation. Section 4, Conclusions, summarizes our contributions and outlines directions for future work.
The main objective of this task is to select the most relevant features from the MQ2007 dataset, which
belongs to the LETOR 4.0 collection [
The MQ2007 dataset originates from the LETOR (LEarning TO Rank) benchmark, developed by
Microsoft Research Asia, and is specifically designed for learning-to-rank tasks. MQ2007 uses documents
from the Gov2 web collection, which comprises approximately 25 million pages, and queries derived
from the Million Query track (TREC 2007) [
Each data instance corresponds to a query-document pair, characterized by 46 features that include classical IR and NLP measures such as TF-IDF, BM25, language models (LMIR), PageRank, document length, and URL structure. The dataset is preprocessed and normalized at the query level (QueryLevelNorm version), which allows for its direct use in machine learning models.
Quadratic Unconstrained Binary Optimization (QUBO) is a mathematical framework used to express a
wide range of combinatorial optimization problems [
min • ∈ {0, 1} is a binary vector of size , • ∈ R× is a symmetric matrix of coeficients that encodes the interactions between variables.
This formulation enables the modeling of problems involving selection, assignment, or combination. It is especially suitable for solution via metaheuristic algorithms or specialized hardware such as quantum computing systems. To incorporate constraints (e.g., a maximum number of selected elements), penalty terms are added to the objective function.
In this work, we implemented a formulation based on Mutual Information, called MIQUBO, as
provided in the baseline for the feature selection problem. This formulation reflects both the relevance
and redundancy between pairs of features [
The diagonal terms encode the individual relevance of each feature with respect to the target variable :
= − (; ) = − (() − ( | )) Here, (· ) denotes the entropy of a variable, and (· | · ) is the conditional entropy.
The of-diagonal terms represent the redundancy between pairs of features, penalizing the joint selection of two variables that provide similar information. These are defined using conditional mutual information:
= − (; | ) = − (( | ) − ( | , ))
The negative sign is a necessary adaptation for the matrix to be used in quantum hardware, aiming to minimize energy.
To impose a constraint on the total number of selected features (e.g., selecting exactly ), a quadratic penalty term is incorporated: ︃( ∑︁ − )︃2 Thus, the complete MIQUBO objective function is defined as: min ∑︁ + ∑︁ + < ︃( ∑︁ − )︃2 (4) (5) (6)
Here, is a regularization hyperparameter that controls the strength of the penalty for selecting more or fewer than features, which typically takes high values.
Once the problem was defined and the QUBO matrix was built based on mutual information and conditional mutual information, our approach focused on the postprocessing of the solutions provided by the quantum hardware.
The quantum hardware used, via the D-Wave library, returns a set of candidate solutions, each accompanied by its corresponding energy value, which is determined by the objective function the system aims to minimize. The number of solutions returned is controlled by a parameter called the number of reads. For example, if this is set to 100, the quantum system will return 100 solutions, each with its associated energy.
Our approach is to leverage this diversity of solutions to build a more robust and stable ranking of features, taking into account both the frequency with which each feature appears in the selected solutions and the energy associated with those solutions.
To analyze the behavior of the quantum system for diferent subset sizes of selected features, the program was executed for a selected range of values, rather than uniformly across all possible values. These values were chosen strategically to explore the solution space broadly in an initial phase, with the objective of identifying regions that showed promising performance. Based on this preliminary analysis, subsequent executions focused on narrower intervals to refine the search around the most favorable configurations. Each solution set obtained corresponds to a partial feature selection for a specific value of , and these were later used to build a global ranking that reflects the overall importance of each feature across the explored configurations.
To guide the selection of the optimal value of , the minimum energy obtained in each of the runs was recorded and analyzed. These values form a discrete energy profile across the range of . By interpolating or fitting a smooth curve to these minimum energy values, it becomes possible to identify trends and locate the global minimum more precisely. The value of corresponding to this global minimum is then selected as the most suitable number of features to retain.
To achieve this aggregation, two postprocessing strategies were designed and implemented, aiming to transform energy values into normalized or projected importance scores that enable consistent feature ranking.
Below are the two implemented strategies:
In this strategy, the energy values returned by the quantum system were linearly normalized to the
interval [
− min max − min where is the energy of an individual solution.
Then, for each feature, the normalized energy values of the solutions in which it appears were
summed and divided by the number of times the feature occurred, resulting in its average normalized
energy score. Once all feature scores were obtained, a final normalization to the [
In this approach, a diferentiated projection was applied based on the sign of the energy: • Negative energy values were projected linearly to the interval [− 1, 0].
• Positive energy values were projected to the interval [
Let be the energy value of a solution, and let min and max be the minimum negative energy and maximum positive energy observed, respectively. The projected energy ′ was computed as: (7) (8) = ⎪ ⎩ max
, ⎧ − min , if < 0 ⎪ ⎨ min if ≥ 0
For each feature, the projected energy values of all the solutions in which it appears were summed
and divided by the number of occurrences of that feature, resulting in its average projected energy
score. This score was then linearly normalized to the range [
The quality of the selected features will be evaluated by training a LambdaMART model and testing its performance on a held-out test set. The evaluation metric will be the normalized Discounted Cumulative Gain at rank 10 (nDCG@10), defined as:
The generation of solutions was carried out using quantum computing techniques based on the quantum annealing paradigm. However, the process was constrained by technical limitations due to restricted access to the quantum hardware. These restrictions prevented us from exploring all the predefined possibilities; nonetheless, we present the analysis of our execution strategy.
Several executions were performed, each consisting of 100 reads, yielding 100 candidate solutions per run. The parameter of interest in this experiment was the number of selected features, denoted as , which was varied in increments of 5 units, from = 5 to = 45. For each , the energies of the 100 obtained solutions were collected.
After gathering all results, the relationship between the number of selected features and the minimum observed quantum energy was analyzed. This relationship was modeled by fitting a quadratic function. Figure 1 shows the fitted curve, illustrating how the energy evolves as a function of . The minimum of this fitted curve indicates the value of associated with the most energetically favorable configurations. This minimum was calculated analytically using the vertex formula for a parabola: * = − 2 (9) where and are the coeficients of the fitted quadratic function. The optimal number of features was found to be * = 21.026.
Following this, two post-processing strategies described in Section 2.3 were applied to select the final
feature sets. The first strategy normalized the quantum solutions to a [
Subsequently, the second post-processing strategy was applied, which used an alternative
normalization method also described in the methodology. This technique enabled the generation of an alternative
ifnal ranking based on more robust statistical criteria. The computed scores revealed that there are 23
features with negative energy values after normalization. These scores were then linearly scaled to the
range [
Although both generated rankings could not be directly evaluated due to technical and time limitations related to the execution environment, they were used as a reference to select the best solutions obtained via the quantum hardware. For this purpose, additional runs were performed in steps of 2 from = 21 to = 29 with 100 reads, as previously done. The same experiments were also run using quantum simulation with 3000 reads to compare the eficiency of each configuration.
The results shown in Table 1 reveal that the best performance, according to the ndcg@10 metric, was achieved with a quantum execution using = 21 features and 100 reads, obtaining a score of 0.4580. This value aligns closely with the optimal feature count estimated from the quadratic fitting analysis.
In general, quantum executions with fewer reads tend to slightly outperform their simulated counterparts with a larger number of reads, suggesting that the actual quantum annealing process may capture more favorable solutions under certain configurations. Nonetheless, the diferences across configurations are relatively small, indicating that the selected subset sizes ( ∈ [21, 29]) all yield competitive results.
This work presented the SINAI team’s approach to the Feature Selection task at QuantumCLEF 2025, leveraging D-Wave’s quantum annealing hardware to optimize feature selection for learning-to-rank models. By formulating the problem as a QUBO model based on mutual information, we efectively captured the trade-of between feature relevance and redundancy. Our post-processing strategies—direct normalization and signed energy projection—enabled us to derive stable and interpretable feature rankings from the quantum solutions.
The results, evaluated on the MQ2007 dataset using LambdaMART and nDCG@10 as the performance metric, demonstrated that quantum executions can yield competitive results, even under limited access constraints. The optimal subset of 21 features, as identified through a quadratic energy fitting process, achieved the highest score among tested configurations, suggesting that the energy landscape provided by quantum annealing correlates meaningfully with model performance.
Although hardware and execution limitations prevented exhaustive experimentation, our findings indicate that quantum annealing holds promise as a tool for feature selection in information retrieval contexts. Future work will focus on expanding the evaluation, incorporating other datasets, and exploring hybrid quantum-classical methods to further exploit the advantages of quantum optimization.
This work has been partially supported by projects CONSENSO (PID2021-122263OB-C21), MODERATES (TED2021-130145B-I00), SocialTOX (PDC2022-133146-C21) funded by Plan Nacional I+D+i from the Spanish Government, and by the scholarship (FPI-PRE2022-105603) from the Ministry of Science, Innovation and Universities of the Spanish Government. Also, this work has been funded by the Ministerio para la Transformación Digital y de la Función Pública and Plan de Recuperación, Transformación y Resiliencia - Funded by EU – NextGenerationEU within the framework of the project Desarrollo Modelos ALIA. During the preparation of this work, the authors used generative AI in order to: Grammar and spelling check. After using this tool, the authors reviewed and edited the content as needed and take full responsibility for the publication’s content.