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Information Systems

BBQ-Tree: A unified classifier and regressor combining Boolean and quantum logic decisions

Alexander Stahl, Ingo Schmitt

Published Sep 30, 2025• 1 citation
Publisher

Abstract

This article provides a detailed explanation of the BBQ-Tree, a unified logic-based model that integrates both classical Decision Trees and Quantum-Logic Decision Trees into a generalized framework for classification and regression. As it combines these paradigms, the BBQ-Tree effectively addresses problems with both linear and curved decision boundaries while prioritizing interpretability. We provide a detailed description of the underlying concepts, a possible training algorithm, experimental evaluations and the incorporation of regression functionality, broadening its applicability beyond classification tasks. Strategies for efficient training and model optimization are also presented. Experimental results demonstrate that the BBQ-Tree produces compact, interpretable models capable of revealing data trends, while achieving accuracy comparable to Decision Trees. Furthermore, its new regression capabilities highlight its versatility and performance across a wider range of tasks.

DOI
10.1016/j.is.2025.102632

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This article provides a detailed explanation of the BBQ-Tree, a unified logic-based model that integrates both classical Decision Trees and Quantum-Logic Decision Trees into a generalized framework for classification and regression. As it combines these paradigms, the BBQ-Tree effectively addresses problems with both linear and curved decision boundaries while prioritizing interpretability. We provide a detailed description of the underlying concepts, a possible training algorithm, experimental evaluations and the incorporation of regression functionality, broadening its applicability beyond classification tasks. Strategies for efficient training and model optimization are also presented. Experimental results demonstrate that the BBQ-Tree produces compact, interpretable models capable of revealing data trends, while achieving accuracy comparable to Decision Trees. Furthermore, its new regression capabilities highlight its versatility and performance across a wider range of tasks.
Abstract Decision trees are widely used in machine learning for their simplicity in construction and interpretability. However, as data sizes grow, traditional methods for constructing and retraining decision trees become increasingly slow, scaling polynomially with the number of training examples. We introduce a novel quantum algorithm, Des-q, for constructing and retraining decision trees in regression and binary classification. Assuming the data stream produces small increments of new training examples, Des-q significantly reduces the tree retraining time, achieving poly-logarithmic time complexity in the number of examples, even accounting for the time needed to load the new examples into quantum-accessible memory. Our approach involves building a decision tree algorithm to perform k-piecewise linear tree splits at each internal node. These splits simultaneously generate multiple hyperplanes, dividing the feature space into k distinct regions. To determine the k suitable anchor points for these splits, we develop an efficient quantum-supervised clustering method, building upon the q-means algorithm by Kerenidis et al. Des-q first efficiently estimates each feature weight using a novel quantum technique to estimate the Pearson correlation. Subsequently, we employ weighted distance estimation to cluster the training examples in k disjoint regions based on nearest-neighbor matching and then proceed to expand the tree using the same procedure. We benchmark the performance of the simulated version of our algorithm against the state-of-the-art classical decision tree on multiple data sets with numerical features. Further, we showcase that the proposed algorithm exhibits similar performance to the state-of-the-art decision tree while significantly speeding up the periodic tree retraining.
Decision trees are widely adopted machine learning models due to their simplicity and explainability. However, as training data size grows, standard methods become increasingly slow, scaling polynomially with the number of training examples. In this work, we introduce Des-q, a novel quantum algorithm to construct and retrain decision trees for regression and binary classification tasks. Assuming the data stream produces small, periodic increments of new training examples, Des-q significantly reduces the tree retraining time. Des-q achieves a logarithmic complexity in the combined total number of old and new examples, even accounting for the time needed to load the new samples into quantum-accessible memory. Our approach to grow the tree from any given node involves performing piecewise linear splits to generate multiple hyperplanes, thus partitioning the input feature space into distinct regions. To determine the suitable anchor points for these splits, we develop an efficient quantum-supervised clustering method, building upon the q-means algorithm introduced by Kerenidis et al. We benchmark the simulated version of Des-q against the state-of-the-art classical methods on multiple data sets and observe that our algorithm exhibits similar performance to the state-of-the-art decision trees while significantly speeding up the periodic tree retraining.
The performance of quantum neural network models depends strongly on architectural decisions, including circuit depth, placement of parametrized operations, and data-encoding strategies. Selecting an effective architecture is challenging and closely related to the classical difficulty of choosing suitable neural-network topologies, which is computationally hard. This work investigates automated quantum-circuit construction for regression tasks and introduces a genetic-algorithm framework that discovers Reduced Regressor QNN architectures. The approach explores depth, parametrized gate configurations, and flexible data re-uploading patterns, formulating the construction of quantum regressors as an optimization process. The discovered circuits are evaluated against seventeen classical regression models on twenty-two nonlinear benchmark functions and four analytical functions. Although classical methods often achieve comparable results, they typically require far more parameters, whereas the evolved quantum models remain compact while providing competitive performance. We further analyze dataset complexity using twelve structural descriptors and show, across five increasingly challenging meta-learning scenarios, that these measures can reliably predict which quantum architecture will perform best. The results demonstrate perfect or near-perfect predictive accuracy in several scenarios, indicating that complexity metrics offer powerful and compact representations of dataset structure and can effectively guide automated model selection. Overall, this study provides a principled basis for meta-learning-driven quantum architecture design and advances the understanding of how quantum models behave in regression settings--a topic that has received limited exploration in prior work. These findings pave the way for more systematic and theoretically grounded approaches to quantum regression.
The quantum-logic inspired decision tree (QLDT) is based on quantum logic concepts and input values from the unit interval whereas the traditional decision tree is based on Boolean values. The logic behind the QLDT obeys the rules of a Boolean algebra. The QLDT is appropriate for classification problems where for a class decision several input values interact gradually with each other. The QLDT construction for a classification problem with n input attributes requires the computation of 2n minterms. The QLDT+ method, however, uses a heuristic for obtaining a QLDT with much smaller computational complexity. As result, the QLDT+ method can be applied to classification problems with a higher number of input attributes.
In this paper, we propose a post-hoc confidence- aware explanation layer for Quantum Logic Decision Trees (QLDTs) in binary classification. The goal is to improve the decision-level interpretability of QLDT+ predictions without modifying the underlying decision mechanism. The proposed layer translates class-labelled QLDT+ paths into linguistic IF– THEN rules and attaches an object-level explanation score to each prediction. This score is computed as a transparent aggregation of three interpretable components: rule-path acti- vation, empirical path reliability, and the normalized distance from the QLDT+ decision threshold. The resulting value is not intended to estimate a posterior class probability; rather, it serves as an explanation-based confidence indicator for decision support. Since the layer is applied only after the QLDT+ prediction has been made, the predicted labels remain fully determined by the original CQQL evaluation score and the global threshold. Experiments on the Banknote Authentication and Diabetes datasets show that correctly classified instances receive higher average explanation confidence than incorrectly classified ones, while near-threshold cases receive lower confi- dence values. Selective-prediction, component-wise ablation, and weight-sensitivity analyses further indicate that the proposed score provides useful information about decision stability and reliability while preserving the original QLDT+ classifier.