Representation of binary classification trees with binary features by quantum circuits

Heese, Raoul; Bickert, Patricia; Niederle, Astrid Elisa

doi:10.22331/q-2022-03-30-676

Cited by 9 publications

(8 citation statements)

References 79 publications

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“…• A quantum decision tree classifier (QTree) trained on the tic-tac-toe endgame data set [52] with 16 qubits as described in [53].…”

Section: Transpilationmentioning

confidence: 99%

See 1 more Smart Citation

Explainable Quantum Machine Learning

Heese¹,

Gerlach²,

Sascha³

et al. 2023

Preprint

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Methods of artificial intelligence (AI) and especially machine learning (ML) have been growing ever more complex, and at the same time have more and more impact on people's lives. This leads to explainable AI (XAI) manifesting itself as an important research field that helps humans to better comprehend ML systems. In parallel, quantum machine learning (QML) is emerging with the ongoing improvement of quantum computing hardware combined with its increasing availability via cloud services. QML enables quantum-enhanced ML in which quantum mechanics is exploited to facilitate ML tasks, typically in form of quantum-classical hybrid algorithms that combine quantum and classical resources. Quantum gates constitute the building blocks of gate-based quantum hardware and form circuits that can be used for quantum computations. For QML applications, quantum circuits are typically parameterized and their parameters are optimized classically such that a suitably defined objective function is minimized. Inspired by XAI, we raise the question of explainability of such circuits by quantifying the importance of (groups of) gates for specific goals. To this end, we transfer and adapt the well-established concept of Shapley values to the quantum realm. The resulting attributions can be interpreted as explanations for why a specific circuit works well for a given task, improving the understanding of how to construct parameterized (or variational) quantum circuits, and fostering their human interpretability in general. An experimental evaluation on simulators and two superconducting quantum hardware devices demonstrates the benefits of the proposed framework for classification, generative modeling, transpilation, and optimization. Furthermore, our results shed some light on the role of specific gates in popular QML approaches.

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“…• A quantum decision tree classifier (QTree) trained on the tic-tac-toe endgame data set [52] with 16 qubits as described in [53].…”

Section: Transpilationmentioning

confidence: 99%

“…• Quantum Fourier transforms (QFTs) [54] for three to five qubits. (a) QTree [53] containing four subsequent branches, each represented by a decision layer U i qtree . The circuit operates on 16 qubits.…”

Section: Transpilationmentioning

confidence: 99%

Explainable Quantum Machine Learning

Heese¹,

Gerlach²,

Sascha³

et al. 2023

Preprint

View full text Add to dashboard Cite

show abstract

“…In the work by Khadiev et al [28], the classical decision tree induction algorithm C5.0 is extended to a quantum version using Grover search-based algorithm. The quantum algorithm has a run-time complexity that is nearly quadratic better than the classical algorithm in terms of feature number d. Heese et al [30] introduce a quantum representation of binary classification trees called Q-tree. The tree is constructed through probabilistic traversal via quantum circuit measurements, and the work explores its implementation in superconducting qubit hardware.…”

Section: Introductionmentioning

confidence: 99%

Des-q: a Quantum Algorithm to Construct and Efficiently Retrain Decision Trees for Regression and Binary Classification

Kumar,

Yalovetzky,

et al. 2023

Preprint

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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.

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“…With the development and flourishing of quantum computing architecture [18][19][20][21][22][23][24], the interplay between quantum physics and AI has attracted a wide range of interests [25][26][27][28]. Along this line, many heuristic quantum machine learning models have been proposed, including the quantum decision tree classifiers [29,30], quantum support vector machines [31], quantum Boltzmann machines [32], quantum generative models [33][34][35][36], quantum CNNs [37][38][39][40][41], and perception-based quantum neural networks [42], etc. Some of these works show potential quantum advantages over their classical counterparts, which have boosted the development of quantum AI [26].…”

Section: Introductionmentioning

confidence: 99%

Quantum capsule networks

Zidu¹,

Shen²,

Li³

et al. 2022

Quantum Sci. Technol.

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Capsule networks, which incorporate the paradigms of connectionism and symbolism, have brought fresh insights into artificial intelligence. The capsule, as the building block of capsule networks, is a group of neurons represented by a vector to encode different features of an entity. The information is extracted hierarchically through capsule layers via routing algorithms. Here, we introduce a quantum capsule network (dubbed QCapsNet) together with an efficient quantum dynamic routing algorithm. To benchmark the performance of the QCapsNet, we carry out extensive numerical simulations on the classification of handwritten digits and symmetry-protected topological phases, and show that the QCapsNet can achieve an enhanced accuracy and outperform conventional quantum classifiers evidently. We further unpack the output capsule state and find that a particular subspace may correspond to a human-understandable feature of the input data, which indicates the potential explainability of such networks. Our work reveals an intriguing prospect of quantum capsule networks in quantum machine learning, which may provide a valuable guide towards explainable quantum artificial intelligence.

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Representation of binary classification trees with binary features by quantum circuits

Cited by 9 publications

References 79 publications

Explainable Quantum Machine Learning

Explainable Quantum Machine Learning

Des-q: a Quantum Algorithm to Construct and Efficiently Retrain Decision Trees for Regression and Binary Classification

Quantum capsule networks

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