Enrique Solano

Antonio Ferrer-Sánchez, Carlos Flores-Garrigos, Carlos Hernani-Morales et al.

We introduce a novel methodology that leverages the strength of Physics-Informed Neural Networks (PINNs) to address the counterdiabatic (CD) protocol in the optimization of quantum circuits comprised of systems with $N_{Q}$ qubits. The primary objective is to utilize physics-inspired deep learning techniques to accurately solve the time evolution of the different physical observables within the quantum system. To accomplish this objective, we embed the necessary physical information into an underlying neural network to effectively tackle the problem. In particular, we impose the hermiticity condition on all physical observables and make use of the principle of least action, guaranteeing the acquisition of the most appropriate counterdiabatic terms based on the underlying physics. The proposed approach offers a dependable alternative to address the CD driving problem, free from the constraints typically encountered in previous methodologies relying on classical numerical approximations. Our method provides a general framework to obtain optimal results from the physical observables relevant to the problem, including the external parameterization in time known as scheduling function, the gauge potential or operator involving the non-adiabatic terms, as well as the temporal evolution of the energy levels of the system, among others. The main applications of this methodology have been the $\mathrm{H_{2}}$ and $\mathrm{LiH}$ molecules, represented by a 2-qubit and 4-qubit systems employing the STO-3G basis. The presented results demonstrate the successful derivation of a desirable decomposition for the non-adiabatic terms, achieved through a linear combination utilizing Pauli operators. This attribute confers significant advantages to its practical implementation within quantum computing algorithms.

Carlos Hernani-Morales, Gabriel Alvarado, Francisco Albarrán-Arriagada et al.

We propose machine learning (ML) methods to characterize the memristive properties of single and coupled quantum memristors. We show that maximizing the memristivity leads to large values in the degree of entanglement of two quantum memristors, unveiling the close relationship between quantum correlations and memory. Our results strengthen the possibility of using quantum memristors as key components of neuromorphic quantum computing.

Carlos Flores-Garrigós, Anton Simen, Qi Zhang et al.

We present a quantum feature-selection framework based on a higher-order unconstrained binary optimization (HUBO) formulation that explicitly incorporates multivariate dependencies beyond standard quadratic encodings. In contrast to QUBO-based approaches, the proposed model includes one-, two-, and three-body interaction terms derived from mutual-information measures, enabling the objective function to capture feature relevance, pairwise redundancy, and higher-order statistical structure within a unified energy model. To suppress trivial all-selected solutions, we further include structured linear penalties that promote sparsity while preserving informative variables. The resulting HUBO instances are optimized with digitized counterdiabatic quantum optimization on IonQ Forte and compared against noiseless quantum simulation as well as two classical dimensionality-reduction baselines: SelectKBest based on mutual information and principal component analysis (PCA). We evaluate the proposed workflow on two benchmark classification datasets, namely the Gallstone dataset and the Spambase dataset, and analyze both predictive performance and selected-subset structure. The results show good qualitative agreement between hardware executions and noiseless simulations, supporting the feasibility of implementing higher-order feature-selection Hamiltonians on current trapped-ion processors. In addition, the quantum approach yields competitive classification performance while producing compact and informative feature subsets, highlighting the potential of higher-order quantum optimization for machine-learning preprocessing tasks.

Qi Zhang, Anton Simen, Carlos Flores-Garrigós et al.

We demonstrate the application of a quantum feature extraction method to enhance multi-class image classification for space applications. By harnessing the dynamics of many-body spin Hamiltonians, the method generates expressive quantum features that, when combined with classical processing, lead to quantum-enhanced classification accuracy. Using a strong and well-established ResNet50 baseline, we achieved a maximum classical accuracy of 83%, which can be improved to 84% with a transfer learning approach. In contrast, applying our quantum-classical method the performance is increased to 87% accuracy, demonstrating a clear and reproducible improvement over robust classical approaches. Implemented on several of IBM's quantum processors, our hybrid quantum-classical approach delivers consistent gains of 2-3% in absolute accuracy. These results highlight the practical potential of current and near-term quantum processors in high-stakes, data-driven domains such as satellite imaging and remote sensing, while suggesting broader applicability in real-world machine learning tasks.

Rui Wang, Carlos Hernani-Morales, José D. Martín-Guerrero et al.

This paper proposes a machine learning method to characterize photonic states via a simple optical circuit and data processing of photon number distributions, such as photonic patterns. The input states consist of two coherent states used as references and a two-mode unknown state to be studied. We successfully trained supervised learning algorithms that can predict the degree of entanglement in the two-mode state as well as perform the full tomography of one photonic mode, obtaining satisfactory values in the considered regression metrics.

Tasio Gonzalez-Raya, Xiao-Hang Cheng, Iñigo L. Egusquiza et al.

The Hodgkin-Huxley model describes the behavior of the cell membrane in neurons, treating each part of it as an electric circuit element, namely capacitors, memristors, and voltage sources. We focus on the activation channel of potassium ions, due to its simplicity, while keeping most of the features displayed by the original model. This reduced version is essentially a classical memristor, a resistor whose resistance depends on the history of electric signals that have crossed it, coupled to a voltage source and a capacitor. Here, we will consider a quantized Hodgkin-Huxley model based on a quantum memristor formalism. We compare the behavior of the membrane voltage and the potassium channel conductance, when the circuit is subjected to AC sources, in both classical and quantum realms. Numerical simulations show an expected adaptation of the considered channel conductance depending on the signal history in all regimes. Remarkably, the computation of higher moments of the voltage manifest purely quantum features related to the circuit zero-point energy. Finally, we study the implementation of the Hodgkin-Huxley quantum memristor as an asymmetric rf SQUID in superconducting circuits. This study may allow the construction of quantum neuron networks inspired in the brain function, as well as the design of neuromorphic quantum architectures for quantum machine learning.

Yongcheng Ding, Lucas Lamata, Mikel Sanz et al.

Quantum autoencoders allow for reducing the amount of resources in a quantum computation by mapping the original Hilbert space onto a reduced space with the relevant information. Recently, it was proposed to employ approximate quantum adders to implement quantum autoencoders in quantum technologies. Here, we carry out the experimental implementation of this proposal in the Rigetti cloud quantum computer employing up to three qubits. The experimental fidelities are in good agreement with the theoretical prediction, thus proving the feasibility to realize quantum autoencoders via quantum adders in state-of-the-art superconducting quantum technologies.

Francisco Silva, Mikel Sanz, João Seixas et al.

Memristors, resistors with memory whose outputs depend on the history of their inputs, have been used with success in neuromorphic architectures, particularly as synapses and non-volatile memories. However, to the best of our knowledge, no model for a network in which both the synapses and the neurons are implemented using memristors has been proposed so far. In the present work we introduce models for single and multilayer perceptrons based exclusively on memristors. We adapt the delta rule to the memristor-based single-layer perceptron and the backpropagation algorithm to the memristor-based multilayer perceptron. Our results show that both perform as expected for perceptrons, including satisfying Minsky-Papert's theorem. As a consequence of the Universal Approximation Theorem, they also show that memristors are universal function approximators. By using memristors for both the neurons and the synapses, our models pave the way for novel memristor-based neural network architectures and algorithms. A neural network based on memristors could show advantages in terms of energy conservation and open up possibilities for other learning systems to be adapted to a memristor-based paradigm, both in the classical and quantum learning realms.

Feng Hu, Lucas Lamata, Mikel Sanz et al.

As the building block in symmetric cryptography, designing Boolean functions satisfying multiple properties is an important problem in sequence ciphers, block ciphers, and hash functions. However, the search of $n$-variable Boolean functions fulfilling global cryptographic constraints is computationally hard due to the super-exponential size $\mathcal{O}(2^{2^n})$ of the space. Here, we introduce a codification of the cryptographically relevant constraints in the ground state of an Ising Hamiltonian, allowing us to naturally encode it in a quantum annealer, which seems to provide a quantum speedup. Additionally, we benchmark small $n$ cases in a D-Wave machine, showing its capacity of devising bent functions, the most relevant set of cryptographic Boolean functions. We have complemented it with local search and chain repair to improve the D-Wave quantum annealer performance related to the low connectivity. This work shows how to codify super-exponential cryptographic problems into quantum annealers and paves the way for reaching quantum supremacy with an adequately designed chip.

Unai Alvarez-Rodriguez, Lucas Lamata, Pablo Escandell-Montero et al.

We propose a quantum machine learning algorithm for efficiently solving a class of problems encoded in quantum controlled unitary operations. The central physical mechanism of the protocol is the iteration of a quantum time-delayed equation that introduces feedback in the dynamics and eliminates the necessity of intermediate measurements. The performance of the quantum algorithm is analyzed by comparing the results obtained in numerical simulations with the outcome of classical machine learning methods for the same problem. The use of time-delayed equations enhances the toolbox of the field of quantum machine learning, which may enable unprecedented applications in quantum technologies.