Quantum Embeddings (QE) is an important component of Quantum Machine Learning (QML) algorithms to load classical data present in Euclidean space onto quantum Hilbert space, which are then later forwarded to the Parametric Quantum Circuit (PQC) for training and finally measured to compute the cost classically. The performance of the QML algorithm can vary according to the type of QE used, and also on mapping of features within the embedding (i.e., onto the qubits). This provides motivation to search for the optimal quantum embedding (i.e., feature to qubit mapping). Typically this problem is presented as an optimization problem, where the quantum embedding has trainable parameters and the optimal embedding is found out by training the embedding. In this work, we present identification of the optimal embedding as a search problem rather than an optimization problem. We show that for fixed number of qubits and model initialization of a Quantum Neural Network (QNN), different mapping of features onto qubits via QE changes the final performance of the QML algorithm. We propose Genetic Algorithm (GA) based search to find the optimal mapping of the features to the qubits. We perform experiments to find the optimal QE for binary classes of MNIST and Tiny Imagenet datasets and compare the results with randomly selected feature to qubit mapping (under identical number of runs). Our results show that GA-based approach performs better than random selection for MNIST (Tiny Imagenet) by 0.33-3.33 (0.5-3.36) higher average fitness score with up to 8.1%-15% (for MNIST) and 5.3%-8.8% (for Tiny Imagenet) less runtime. For both the datasets increasing the qubit counts marginally affects the GA fitness implying that the GA is scalable both in terms of dataset and in terms of QNN size. Compared to existing methodologies such as Quantum Embedding Kernel (QEK), Quantum Approximate Optimization Algorithm (QAOA)-based embedding and Quantum Random Access Code (QRAC), GA performs better by 1.003X, 1.03X and 1.06X respectively.
Quantum Embeddings (QE) is an important component of Quantum Machine Learning (QML) algorithms to load classical data present in Euclidean space onto quantum Hilbert space, which are then later forwarded to the Parametric Quantum Circuit (PQC) for training and finally measured to compute the cost classically. The performance of the QML algorithm can vary according to the type of QE used, and also on mapping of features within the embedding (i.e., onto the qubits). This provides motivation to search for the optimal quantum embedding (i.e., feature to qubit mapping). Typically this problem is presented as an optimization problem, where the quantum embedding has trainable parameters and the optimal embedding is found out by training the embedding. In this work, we present identification of the optimal embedding as a search problem rather than an optimization problem. We show that for fixed number of qubits and model initialization of a Quantum Neural Network (QNN), different mapping of features onto qubits via QE changes the final performance of the QML algorithm. We propose Genetic Algorithm (GA) based search to find the optimal mapping of the features to the qubits. We perform experiments to find the optimal QE for binary classes of MNIST and Tiny Imagenet datasets and compare the results with randomly selected feature to qubit mapping (under identical number of runs). Our results show that GA-based approach performs better than random selection for MNIST (Tiny Imagenet) by 0.33-3.33 (0.5-3.36) higher average fitness score with up to 8.1%-15% (for MNIST) and 5.3%-8.8% (for Tiny Imagenet) less runtime. For both the datasets increasing the qubit counts marginally affects the GA fitness implying that the GA is scalable both in terms of dataset and in terms of QNN size. Compared to existing methodologies such as Quantum Embedding Kernel (QEK), Quantum Approximate Optimization Algorithm (QAOA)-based embedding and Quantum Random Access Code (QRAC), GA performs better by 1.003X, 1.03X and 1.06X respectively.
In recent years, machine learning and deep learning have driven advances in domains such as image classification, speech recognition, and anomaly detection by leveraging multilayer neural networks to model complex data. Simultaneously, quantum computing (QC) promises to address classically intractable problems via quantum parallelism, motivating research in quantum machine learning (QML). Among QML techniques, quantum autoencoders show promise for compressing highdimensional quantum and classical data. However, designing effective quantum circuit architectures for quantum autoencoders remains challenging due to the complexity of selecting gates, arranging circuit layers, and tuning parameters. This paper proposes a neural architecture search (NAS) framework that automates the design of quantum autoencoders using a genetic algorithm (GA). By systematically evolving variational quantum circuit (VQC) configurations, our method seeks to identify high-performing hybrid quantum-classical autoencoders for data reconstruction without becoming trapped in local minima. We demonstrate effectiveness on image datasets, highlighting the potential of quantum autoencoders for efficient feature extraction within a noise-prone, near-term quantum era. Our approach lays a foundation for broader application of genetic algorithms to quantum architecture search, aiming for a robust, automated method that can adapt to varied data and hardware constraints.
In recent years, machine learning and deep learning have driven advances in domains such as image classification, speech recognition, and anomaly detection by leveraging multi-layer neural networks to model complex data. Simultaneously, quantum computing (QC) promises to address classically intractable problems via quantum parallelism, motivating research in quantum machine learning (QML). Among QML techniques, quantum autoencoders show promise for compressing high-dimensional quantum and classical data. However, designing effective quantum circuit architectures for quantum autoencoders remains challenging due to the complexity of selecting gates, arranging circuit layers, and tuning parameters.
This paper proposes a neural architecture search (NAS) framework that automates the design of quantum autoencoders using a genetic algorithm (GA). By systematically evolving variational quantum circuit (VQC) configurations, our method seeks to identify high-performing hybrid quantum-classical autoencoders for data reconstruction without becoming trapped in local minima. We demonstrate effectiveness on image datasets, highlighting the potential of quantum autoencoders for efficient feature extraction within a noise-prone, near-term quantum era. Our approach lays a foundation for broader application of genetic algorithms to quantum architecture search, aiming for a robust, automated method that can adapt to varied data and hardware constraints.
Post-Variational Quantum Neural Networks (PVQNNs) eliminate the need for quantum parameter optimization by employing fixed, non-parametric circuits and shifting all learning to the classical domain, thereby avoiding barren plateaus entirely. However, the performance of PV-QNNs critically depends on the choice of ansatz architecture. In this work, we propose an automatic ansatz optimization framework based on Genetic Algorithms (GAs) that searches for optimal circuit ensembles under discrete constraints of topology, depth, and gate types. Quantum features are extracted efficiently via classical shadows and processed by a shallow classical classifier, preserving the post-variational property. Experimental results on the Fashion-MNIST (0 vs 4) classification task demonstrate that GA-selected ensembles outperform all baselines, achieving 89.0 % accuracy with 8 qubits, exceeding random and manually designed templates by3−5%. Moreover, GA ensembles achieve up to1.9×higher accuracy per circuit and2×higher accuracy per twoqubit gate, while maintaining shallower circuits (6.0 depth vs. 8.6). These results indicate that evolutionary search effectively identifies compact, information-rich quantum circuits, enabling scalable and resource-efficient post-variational learning.
Quantum classifiers provide sophisticated embeddings of input data in Hilbert space promising quantum advantage. The advantage stems from quantum feature maps encoding the inputs into quantum states with variational quantum circuits. A recent work shows how to map discrete features with fewer quantum bits using Quantum Random Access Coding (QRAC) to encode binary strings into quantum states. We propose a new method to embed discrete features with trainable quantum circuits by combining QRAC and a recently proposed strategy for training quantum feature map called quantum metric learning. The proposed trainable embedding requires not only as few qubits as QRAC but also overcomes the limitations of QRAC to classify inputs whose classes are based on hard Boolean functions. We numerically demonstrate its use in variational quantum classifiers to achieve better performances to classify real-world datasets, and thus its possibility to use near-term quantum computers for machine learning.
Quantum Genetic Algorithms (QGA) integrate genetic programming and quantum computing to address search and optimization problems. The standard strategy of the hybrid QGA approach is to add quantum resources to classical genetic algorithms (GA), thus improving their efficacy (i.e., quantum optimization of a classical algorithm). However, the extent of such improvements is still unclear. Conversely, Reduced Quantum Genetic Algorithm (RQGA) is a fully quantum algorithm that reduces the GA search for the best fitness in a population of potential solutions to running Grover's algorithm. Unfortunately, RQGA finds the best fitness value and its corresponding chromosome (i.e., the solution or one of the solutions of the problem) in exponential runtime, [[EQUATION]], where [[EQUATION]] is the number of qubits in the individuals' quantum register. This paper introduces a novel QGA optimization strategy, namely a classical optimization of a fully quantum algorithm, to address the Reduced Quantum Genetic Algorithm (RQGA) complexity problem. Accordingly, we control the complexity of theReduced Quantum Genetic Algorithm (RQGA) algorithm by selecting a limited number of qubits in the individuals' register and fixing the remaining ones as classical values of '0' and '1' with a genetic algorithm. We also improve the performance of RQGA by discarding unfit solutions and bounding the search only in the area of valid individuals. As a result, our Hybrid Quantum Algorithm with Genetic Optimization (HQAGO) solves search problems in [[EQUATION]] oracle queries, where [[EQUATION]] is the number of fixed classical bits in the individuals' register.
Quantum Support Vector Machines (QSVM) is one of the most promising frameworks in quantum machine learning, yet their performance depends on the design of the feature map. Conventional approaches rely on fixed quantum circuits, which often fail to generalize across datasets. To address this limitation, we propose GA-QSVM, a hybrid framework that employs Genetic Algorithms (GA) to automatically optimize feature maps. The proposed method introduces a configurable framework that flexibly defines the evolutionary parameters, enabling the construction of adaptive circuits. Experimental evaluation of datasets, including Digits, Fashion, Wine, and Breast Cancer, demonstrates that GA-QSVMs achieve a comparable accuracy compared to classical SVMs and standard QSVMs. Furthermore, transfer learning results indicate that GA-QSVM's circuits generalize effectively across datasets. These findings highlight the potential of evolutionary strategies to automate and enhance kernel design for future quantum machine learning applications.