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IEEE International Conference on Quantum Computing and Engineering (QCE)

Variational Decision Trees with Structured Ansatzes

Alessandro Poggiali, Giacomo Antonioli, Alessandro Berti, Gianna M. Del Corso, Riccardo Guidotti

Published Aug 30, 2025• 0 citations
Publisher

Abstract

Decision trees are among the most interpretable models in machine learning, widely valued for their transparency, simplicity, and alignment with human reasoning. However, traditional decision tree algorithms rely on greedy heuristics, splitting nodes one at a time based on local criteria, which often leads to suboptimal trees and limits their effectiveness in complex scenarios. In this work, we propose a quantum-enhanced approach for learning decision trees, with the aim of identifying a optimal tree according to a specified global criterion. This approach employs a Variational Quantum Algorithm (VQA) to encode and optimize the decision tree represented as matrix, leveraging tailored ansatzes that constrain the search to a specific subspace of the Hilbert space.

DOI
10.1109/qce65121.2025.10379

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Decision trees are among the most interpretable models in machine learning, widely valued for their transparency, simplicity, and alignment with human reasoning. However, traditional decision tree algorithms rely on greedy heuristics, splitting nodes one at a time based on local criteria, which often leads to suboptimal trees and limits their effectiveness in complex scenarios. In this work, we propose a quantum-enhanced approach for learning decision trees, with the aim of identifying a optimal tree according to a specified global criterion. This approach employs a Variational Quantum Algorithm (VQA) to encode and optimize the decision tree represented as matrix, leveraging tailored ansatzes that constrain the search to a specific subspace of the Hilbert space.
Quantum Machine Learning (QML) has emerged as a promising field, offering the potential to revolutionize various computational tasks, including machine learning. This paper investigates the application of QML to decision tree algorithms, specifically focusing on the development of a novel non-linear decision tree model designed for optimized decision-solving. We explore how quantum computation can enhance the optimization process inherent in decision tree construction, leading to improved efficiency and accuracy. The core claim is that leveraging quantum mechanics allows for automatic parameter adjustment within the decision tree, significantly increasing its effectiveness. This work introduces a framework where quantum algorithms are employed to refine the decision tree structure, addressing limitations of traditional methods. The research also investigates the potential benefits of this approach in complex decision scenarios, highlighting the advantages over conventional techniques. The paper concludes with a discussion of future research directions and the expected impact of QML on the field of decision tree learning.
This paper investigates the application of quantum machine learning to dynamic decision tree models, aiming to enhance optimization processes and achieve efficient planning. Traditional decision trees often rely on fixed parameters, limiting their adaptability to complex scenarios. We propose a novel approach utilizing quantum computing to dynamically adjust decision tree parameters, fostering improved accuracy and efficiency. The core mechanism centers around leveraging quantum properties to guide the tree's growth and refinement, offering a significant advancement over conventional methods. This work explores the potential of quantum-enhanced decision tree optimization for various applications, including complex logistics and resource allocation.
Abstract The search for quantum algorithms to tackle classical combinatorial optimization problems has long been one of the most attractive yet challenging research topics in quantum computing. In this context, variational quantum algorithms (VQAs) are a promising family of hybrid quantum–classical methods tailored to cope with the limited capability of near-term quantum hardware. However, their effectiveness is hampered by the complexity of the classical parameter optimization which is prone to getting stuck either in local minima or in flat regions of the cost-function landscape. The clever design of efficient optimization methods is therefore of fundamental importance for fully leveraging the potential of VQAs. In this work, we approach parameter optimization as a sequential decision-making problem and tackle it with an adaptation of Monte Carlo Tree Search, a powerful artificial intelligence technique designed for efficiently exploring complex decision graphs. We show that leveraging regular parameter patterns deeply affects the decision-tree structure and allows for a flexible and noise-resilient optimization strategy suitable for near-term quantum devices. Our results shed further light on the interplay between artificial intelligence and quantum information and provide a valuable addition to the toolkit of variational quantum circuits.
A significant hurdle in the noisy intermediate-scale quantum (NISQ) era is identifying functional quantum circuits. These circuits must also adhere to the constraints imposed by current quantum hardware limitations. Variational quantum algorithms (VQAs), a class of quantum-classical optimization algorithms, were developed to address these challenges in the currently available quantum devices. However, the overall performance of VQAs depends on the initialization strategy of the variational circuit, the structure of the circuit (also known as ansatz), and the configuration of the cost function. Focusing on the structure of the circuit, in this thesis, we improve the performance of VQAs by automating the search for an optimal structure for the variational circuits using reinforcement learning (RL). Within the thesis, the optimality of a circuit is determined by evaluating its depth, the overall count of gates and parameters, and its accuracy in solving the given problem. The task of automating the search for optimal quantum circuits is known as quantum architecture search (QAS). The majority of research in QAS is primarily focused on a noiseless scenario. Yet, the impact of noise on the QAS remains inadequately explored. In this thesis, we tackle the issue by introducing a tensor-based quantum circuit encoding, restrictions on environment dynamics to explore the search space of possible circuits efficiently, an episode halting scheme to steer the agent to find shorter circuits, a double deep Q-network (DDQN) with an εεε-greedy policy for better stability. The numerical experiments on noiseless and noisy quantum hardware show that in dealing with various VQAs, our RL-based QAS outperforms existing QAS. Meanwhile, the methods we propose in the thesis can be readily adapted to address a wide range of other VQAs.
We describe a quantum-assisted machine learning method in which multivariate data are encoded into quantum states in a Hilbert space whose dimension is exponentially large in the length of the data vector. Learning in this space occurs through applying a low-depth quantum circuit with a tree-tensor-network (TTN) topology acting as an unsupervised feature extractor to identify the most relevant quantum states in a data-driven fashion and then applying a supervised linear classifier encoding the class decision in a small-dimensional quantum register. We present tools for making TTN classifiers amenable to implementation on gate-based quantum computing devices, including an embedding map with accuracy similar to the recently defined exponential machines (A. Novikov et al., arXiv:1605.03795) but which produces valid quantum state embeddings of classical data vectors, and the use of manifold-based gradient optimization schemes to produce isometric operations mapping quantum states to a register of qubits defining a class decision. We detail methods for efficiently obtaining one-point and two-point correlation functions of the vectors defining the decision boundary of the quantum model, which can be used for model interpretability, as well as methods for obtaining classification decisions from partial data vectors. Further, we show that the use of isometric tensors can significantly aid in the human interpretability of the correlation functions extracted from the decision weights and may produce models that are less susceptible to adversarial perturbations. Finally, we discuss in detail the problem of compiling classically optimized isometric TTN models into unitary operations to be run on quantum computers and how isometric models requiring postselection on quantum hardware can be used to precondition variational Ans\"atze for models without postselection. We demonstrate our methodologies in applications utilizing the MNIST database of handwritten digits and a multivariate time-series data set of human activity recognition.
The advent of Noisy Intermediate-Scale Quantum (NISQ) devices provides crucial promise for the development of quantum algorithms. Variational quantum algorithms have emerged as one of the best hopes to utilize NISQ devices. Among these is the famous Variational Quantum Eigensolver (VQE), where one trains a parameterized and fixed quantum circuit (or an ansatz) to accomplish the task. However, VQE also suffers from some serious challenges, which are training difficulty and accuracy reduction due to deep quantum circuit and hardware noise. To be motivated by these issues, we propose a runtime and resource efficient scheme, monto-carlo tree (MCT) search based quantum circuit architecture optimization, where the ansatz is built in the variable form. Our approach first models the search space with a MCT and regards it as a supernet, where we make use of layers dependence to reduce the size of the search space . Second, a two-stage scheme is proposed for the search space training where weight sharing and warm-up strategies are employed to avoid huge computation cost. Training results are stored in nodes of the MCT for future decisions and a hierarchical node selection is presented to obtain an optimal ansatz. As a proof of principle, we carry out a series of numerical experiments for condensed matter and quantum chemistry in the quantum simulator with and without noise. Consequently, our scheme can be efficient to mitigate trainability and accuracy issues by minimizing the ansatz depth and the number of entanglement gates.