In recent years, the utility of parameterized quantum circuits as function approximators has been widely studied. In the context of reinforcement learning, this approach has led to variational quantum algorithms such as quantum Q-learning. While these methods show promising empirical results, and can provide provable advantages for artificial problems, it remains unclear whether they can provide a provable quantum advantage over classical approaches for problems of practical relevance. A natural way to investigate this question is through the lens of dequantization: The construction of efficient classical algorithms capable of matching the performance of quantum variational methods. Building on recent kernel-based dequantization results for supervised learning, we take steps towards extending this surrogate-based dequantization program to reinforcement learning. Specifically, we study the simplified setting of reinforcement learning with a uniform generative model in which uniformly random state-action samples are available, which models the regime of sampling from a large experience replay buffer after sufficient exploration. Within this setting, we provide finite sample guarantees for classical kernelized Fitted Q-Iteration, with classical kernels designed to match the inductive bias of particular parameterized quantum circuits. Using these results, we then provide a set of sufficient conditions, on the data-encoding strategy of a parameterized quantum circuit, the corresponding classical kernel, and the problem structure, under which kernelized Fitted Q-Iteration provides a meaningful dequantization of quantum Q-learning, in this simplified setting. Apart from providing rigorous dequantization guarantees when these conditions are met, these results also motivate the use of kernelized fitted Q-iteration as a dequantization heuristic when these sufficient conditions cannot be verified.
Pablo Rodriguez-Grasa, Sofiène Jerbi, Mikel Sanz et al.· 0 citations
We introduce Coherent Quantum Learning (CQL), a training framework for quantum learning models in which the model parameters are quantum degrees of freedom evolved under a Hamiltonian that encodes the loss function. Current quantum machine learning retains classical optimization: parameters are updated by a classical outer loop using gradient estimates from measurements, and quantum coherence has no role in the training dynamics, just as in any classical treatment of the same problem. In the quantum case, a parameter register initialized in superposition evolves unitarily, and probability amplitude concentrates near low-loss configurations through interference, without gradient computation or classical feedback. We give an explicit construction using block encodings and Hamiltonian simulation, applicable to arbitrary parameterized circuits. Numerical experiments on binary classification and interferometric phase estimation confirm that the evolved distribution peaks at the optimal parameters, matching gradient-based performance. The construction is compatible in principle with fault-tolerant implementations and extends to batched training via sequential Hamiltonian evolution.
Ignacio B. Acedo, Javier Gonzalez-Conde, Pablo Rodriguez-Grasa et al.· 0 citations
Neural quantum kernels (NQKs) construct quantum kernels by pretraining a quantum neural network (QNN) and subsequently reusing the trained circuit as a task-adapted embedding. Extending this framework to qudits, with local unitaries in $\mathrm{SU}(d)$, provides a natural route to richer data embeddings through the increased local degrees of freedom and a direct interface for multiclass classification via intrinsically multi-level quantum systems. In this work, focusing on qutrits ($d=3$), we extend NQKs to the qudit setting and perform a systematic study of key design choices, including the number of encoded features, the number of qutrits, the kernel construction (1-to-$n$ and $n$-to-$n$), and the parameterization of $\mathrm{SU}(3)$ unitaries. Across binary and three-class tasks on four benchmark datasets, qutrit NQKs improve over the corresponding QNN baselines in nearly all settings considered and can benefit from scaling both the feature budget and the system size, although the magnitude of these gains may saturate, is dataset-dependent, and depends on the chosen parameterization. In particular, an ablation over $\mathrm{SU}(3)$ parameterizations shows that the unitary representation can substantially impact both optimization behaviour and classifier performance. These findings highlight the potential of qudit-based quantum models not only as a straightforward generalization of qubit-based architectures, but also as a promising means to better exploit complex data structures in quantum machine learning.
Camila Cristiano-Romero, Pablo Rodriguez-Grasa, Mikel Sanz· 0 citations
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