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International Conference on Machine Learning Technologies (ICMLT)

QLDT+: Efficient Construction of a Quantum Logic Decision Tree

Ingo Schmitt

Published Mar 10, 2023• 5 citations
Publisher

Abstract

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.

DOI
10.1145/3589883.3589895

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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.
We propose a post-hoc explanation layer for binary Quantum Logic Decision Tree classifiers constructed with QLDT+. The layer does not modify the fitted tree, the decision threshold, or the predicted label. It translates the class-labelled QLDT+ paths into IF–THEN rules and attaches an explanation-based confidence score to each prediction. This score is the equal-weight average of three quantities: rule support, the activation mass of the contributing rules of the predicted class; path reliability, a class-specific reliability derived from the training evidence ratio; and the normalized distance of the QLDT+ score from the decision threshold. In a stratified 5-fold cross-validation on the Banknote and Diabetes datasets, which was repeated with ten random seeds, correct predictions received a higher mean score than incorrect ones in every run (mean difference 0.18 and 0.14), and near-threshold decisions received lower scores. In selective prediction, the error decreased as coverage decreased; on Diabetes, however, the decisions retained at 40% coverage or less were all predicted as class 0. The layer is therefore best read as a decomposable explanation of a fixed QLDT+ decision rather than as a calibrated probability or an optimized selective-prediction score.
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.
Besides a good prediction a classifier is to give an explanation how the input data is related to the classification result. There is a general agreement that logic expressions provide a better explanation than other methods like SVM, logistic regression, and neural networks. However, a classifier based on Boolean logic needs to map continuous data to Boolean values which can cause a loss of information. In contrast, we design a quantum-logic-inspired classifier where continuous data are directly processed and the laws of the Boolean algebra are maintained. As a result from our approach we obtain a CQQL condition which provides good insights into the relation of input features to the class decision. Furthermore, our experiment shows a good prediction accuracy.
In the paper, we focus on complexity of C5.0 algorithm for constructing decision tree classifier that is the models for the classification problem from machine learning. In classical case the decision tree is constructed in O(hd(NM+Nlog⁡N))O(hd(NM+N \log N))O(hd(NM+NlogN)) running time, where MMM is a number of classes, NNN is the size of a training data set, ddd is a number of attributes of each element, hhh is a tree height. Firstly, we improved the classical version, the running time of the new version is O(h⋅d⋅Nlog⁡N)O(h\cdot d\cdot N\log N)O(h⋅d⋅NlogN). Secondly, we suggest a quantum version of this algorithm, which uses quantum subroutines like the amplitude amplification and the D{ü}rr-Høyer minimum search algorithms that are based on Grover's algorithm. The running time of the quantum algorithm is O(h⋅dlog⁡d⋅Nlog⁡N)O\big(h\cdot \sqrt{d}\log d \cdot N \log N\big)O(h⋅d​logd⋅NlogN) that is better than complexity of the classical algorithm.
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.