Opportunities and limitations of explaining quantum machine learning

TL;DR

Quantum machine learning (QML) faces a gap in explainability, motivating the proposed XQML framework. The authors introduce two PQC-specific explainability methods—Taylor-$\infty$ and quantum layerwise relevance propagation (QLRP)—and compare them with existing XAI approaches on synthetic tasks. They provide a structured analysis of PQC explainability, discuss fundamental quantum constraints (e.g., no cloning, exponential Hilbert space), and present initial numerical demonstrations to illustrate pipelines and trade-offs. The work outlines scalability- and encoding-related challenges and sketches future directions toward inherently interpretable PQC architectures and efficient, hardware-aware explanation techniques.

Abstract

A common trait of many machine learning models is that it is often difficult to understand and explain what caused the model to produce the given output. While the explainability of neural networks has been an active field of research in the last years, comparably little is known for quantum machine learning models. Despite a few recent works analyzing some specific aspects of explainability, as of now there is no clear big picture perspective as to what can be expected from quantum learning models in terms of explainability. In this work, we address this issue by identifying promising research avenues in this direction and lining out the expected future results. We additionally propose two explanation methods designed specifically for quantum machine learning models, as first of their kind to the best of our knowledge. Next to our pre-view of the field, we compare both existing and novel methods to explain the predictions of quantum learning models. By studying explainability in quantum machine learning, we can contribute to the sustainable development of the field, preventing trust issues in the future.

Figures (7)

• Figure 1: Framework of eXplainability in quantum machine learning (XQML) as presented in this work.
• Figure 1: Sketch illustrating the relation between the quantum functions used in QML and the conceptually closest fully-classical probabilistic functions one could use for ML. (a) Classical probability distributions can be represented as diagonal matrices. Then, information on the data or trainable parameters can be encoded as a bi-stochastic transformation, resulting in a parametrized final distribution. A real-valued function can be recovered from evaluating the expectation value of any function of bitstrings with respect to the classical final distribution. (b) The same idea applies, just that now the classical information is stored in quantum states, represented as positive semi-definite, unit trace, Hermitian matrices. The core mechanisms are left unchanged, just now we have access to complex-valued entries outside the main diagonal. Again, a real-valued function can be recovered as the expectation value of a fixed quantum observable with respect to the final parametrized quantum state.
• Figure 2: Average predicted explanation for data in the first class, for two synthetic learning tasks. For this class, the relevant components should be the first three. For the right task, with $m=\pi$, we observe that most explanation methods have average relevance close to $0$ for all components.
• Figure 2: Visualization of the data-set across different subsets of $\mathbb{R}^6$.
• Figure 3: Quality of explanation for methods covered in this work, full report can be found in Appendix \ref{['a:experiments']} and Fig. \ref{['fig:full-eval']}. The difference in opacity differentiates between the existing local attribution methods introduced in Section \ref{['ss:posthoc']} and the ones we introduce for quantum learning models in Section \ref{['s:methods']}.

Theorems & Definitions (10)

• Proposition 1: Taylor explanation
• proof
• Lemma 2: The map $\mathsf{M}$ is an isomorphism
• proof
• Lemma 3: Trace of $\mathsf{M}(H)$
• proof
• Lemma 4: Entries of $A$
• proof
• Lemma 5: Expectation values
• proof