Daniel K. Park

Jaewoong Heo, Daniel K. Park

Many practically relevant applications of quantum machine learning involve classical data, for which performance depends critically on how inputs are embedded into quantum states. Yet the use of a fixed embedding circuit ansatz remains standard practice. We propose an energy-based generative learning framework that synthesizes gate sequences to optimize embedding structures and refine data-tailored parameters, using a fidelity-based surrogate objective to guide the search toward improved class distinguishability. Empirically, the method improves classification performance across diverse settings, while also revealing datasets where architecture search within the present embedding family yields only limited additional gains. We explain this saturation by deriving bounds on the achievable empirical risk in terms of the Wasserstein distance in the input space, showing that classical data geometry provides an \emph{a priori} diagnostic for regimes in which substantial gains from embedding optimization are unlikely. The results establish a practically useful and theoretically motivated framework for searching effective quantum data embeddings through generative optimization, with the attainable gains diagnosed through the geometry of the underlying classical data.

Matt Lourens, Ilya Sinayskiy, Daniel K. Park et al.

Machine learning with hierarchical quantum circuits, usually referred to as Quantum Convolutional Neural Networks (QCNNs), is a promising prospect for near-term quantum computing. The QCNN is a circuit model inspired by the architecture of Convolutional Neural Networks (CNNs). CNNs are successful because they do not need manual feature design and can learn high-level features from raw data. Neural Architecture Search (NAS) builds on this success by learning network architecture and achieves state-of-the-art performance. However, applying NAS to QCNNs presents unique challenges due to the lack of a well-defined search space. In this work, we propose a novel framework for representing QCNN architectures using techniques from NAS, which enables search space design and architecture search. Using this framework, we generate a family of popular QCNNs, those resembling reverse binary trees. We then evaluate this family of models on a music genre classification dataset, GTZAN, to justify the importance of circuit architecture. Furthermore, we employ a genetic algorithm to perform Quantum Phase Recognition (QPR) as an example of architecture search with our representation. This work provides a way to improve model performance without increasing complexity and to jump around the cost landscape to avoid barren plateaus. Finally, we implement the framework as an open-source Python package to enable dynamic QCNN creation and facilitate QCNN search space design for NAS.

Juhyeon Kim, Joonsuk Huh, Daniel K. Park

Machine learning using quantum convolutional neural networks (QCNNs) has demonstrated success in both quantum and classical data classification. In previous studies, QCNNs attained a higher classification accuracy than their classical counterparts under the same training conditions in the few-parameter regime. However, the general performance of large-scale quantum models is difficult to examine because of the limited size of quantum circuits, which can be reliably implemented in the near future. We propose transfer learning as an effective strategy for utilizing small QCNNs in the noisy intermediate-scale quantum era to the full extent. In the classical-to-quantum transfer learning framework, a QCNN can solve complex classification problems without requiring a large-scale quantum circuit by utilizing a pre-trained classical convolutional neural network (CNN). We perform numerical simulations of QCNN models with various sets of quantum convolution and pooling operations for MNIST data classification under transfer learning, in which a classical CNN is trained with Fashion-MNIST data. The results show that transfer learning from classical to quantum CNN performs considerably better than purely classical transfer learning models under similar training conditions.

Siheon Park, Daniel K. Park, June-Koo Kevin Rhee

A kernel-based quantum classifier is the most practical and influential quantum machine learning technique for the hyper-linear classification of complex data. We propose a Variational Quantum Approximate Support Vector Machine (VQASVM) algorithm that demonstrates empirical sub-quadratic run-time complexity with quantum operations feasible even in NISQ computers. We experimented our algorithm with toy example dataset on cloud-based NISQ machines as a proof of concept. We also numerically investigated its performance on the standard Iris flower and MNIST datasets to confirm the practicality and scalability.

Chanyoung Kim, Myeonghwan Seong, Yujin Kim et al.

Partial differential equations (PDEs) are central to modeling physical and engineering systems, but repeatedly solving parametric PDEs remains computationally expensive. Operator learning enables fast surrogate inference, yet typically requires large input-output paired datasets generated by costly high-fidelity PDE solvers. Unsupervised operator learning frameworks alleviate data dependency but remain hindered by computational bottlenecks. To address this, we propose Neural Variational Quantum Linear Solver (NVQLS), the first hybrid quantum-classical operator learning framework leveraging the Legendre--Galerkin weak formulation. We critically resolve the sign ambiguity in VQLS energy minimization, preventing erroneous solution representations. Additionally, we introduce a neural embedding, a novel encoding scheme to map varying forcings and PDE coefficients into parameterized quantum circuit representations. These structural innovations provide theoretical computational complexity advantages under efficient state preparation schemes, while achieving superior accuracy compared to a representative classical baseline. Validations on 1D and 2D parametric PDEs under diverse boundary conditions demonstrate NVQLS's capability to simultaneously process varying inputs, offering a scalable unsupervised approach to quantum-enhanced operator learning.

Changjae Im, Hyeondo Oh, Daniel K. Park

One-class classification (OCC) is a fundamental problem in machine learning with numerous applications, such as anomaly detection and quality control. With the increasing complexity and dimensionality of modern datasets, there is a growing demand for advanced OCC techniques with better expressivity and efficiency. We introduce Neural Quantum Support Vector Data Description (NQSVDD), a classical-quantum hybrid framework for OCC that performs end-to-end optimized hierarchical representation learning. NQSVDD integrates a classical neural network with trainable quantum data encoding and a variational quantum circuit, enabling the model to learn nonlinear feature transformations tailored to the OCC objective. The hybrid architecture maps input data into an intermediate high-dimensional feature space and subsequently projects it into a compact latent space defined through quantum measurements. Importantly, both the feature embedding and the latent representation are jointly optimized such that normal data form a compact cluster, for which a minimum-volume enclosing hypersphere provides an effective decision boundary. Experimental evaluations on benchmark datasets demonstrate that NQSVDD achieves competitive or superior AUC performance compared to classical Deep SVDD and quantum baselines, while maintaining parameter efficiency and robustness under realistic noise conditions.

Tak Hur, Daniel K. Park

Understanding and improving generalization capabilities is crucial for both classical and quantum machine learning (QML). Recent studies have revealed shortcomings in current generalization theories, particularly those relying on uniform bounds, across both classical and quantum settings. In this work, we present a margin-based generalization bound for QML models, providing a more reliable framework for evaluating generalization. Our experimental studies on the quantum phase recognition (QPR) dataset demonstrate that margin-based metrics are strong predictors of generalization performance, outperforming traditional metrics like parameter count. By connecting this margin-based metric to quantum information theory, we demonstrate how to enhance the generalization performance of QML through a classical-quantum hybrid approach when applied to classical data.

Yujin Kim, Daniel K. Park

Deterministic quantum computation with one qubit (DQC1) is of significant theoretical and practical interest due to its computational advantages in certain problems, despite its subuniversality with limited quantum resources. In this work, we introduce parameterized DQC1 as a quantum machine learning model. We demonstrate that the gradient of the measurement outcome of a DQC1 circuit with respect to its gate parameters can be computed directly using the DQC1 protocol. This allows for gradient-based optimization of DQC1 circuits, positioning DQC1 as the sole quantum protocol for both training and inference. We then analyze the expressivity of the parameterized DQC1 circuits, characterizing the set of learnable functions, and show that DQC1-based machine learning (ML) is as powerful as quantum neural networks based on universal computation. Our findings highlight the potential of DQC1 as a practical and versatile platform for ML, capable of rivaling more complex quantum computing models while utilizing simpler quantum resources.

Junggu Choi, Tak Hur, Daniel K. Park et al.

Following the recent development of quantum machine learning techniques, the literature has reported several quantum machine learning algorithms for disease detection. This study explores the application of a hybrid quantum-classical algorithm for classifying region-of-interest time-series data obtained from resting-state functional magnetic resonance imaging in patients with early-stage cognitive impairment based on the importance of cognitive decline for dementia or aging. Classical one-dimensional convolutional layers are used together with quantum convolutional neural networks in our hybrid algorithm. In the classical simulation, the proposed hybrid algorithms showed higher balanced accuracies than classical convolutional neural networks under the similar training conditions. Moreover, a total of nine brain regions (left precentral gyrus, right superior temporal gyrus, left rolandic operculum, right rolandic operculum, left parahippocampus, right hippocampus, left medial frontal gyrus, right cerebellum crus, and cerebellar vermis) among 116 brain regions were found to be relatively effective brain regions for the classification based on the model performances. The associations of the selected nine regions with cognitive decline, as found in previous studies, were additionally validated through seed-based functional connectivity analysis. We confirmed both the improvement of model performance with the quantum convolutional neural network and neuroscientific validities of brain regions from our hybrid quantum-classical model.

Changwon Lee, Israel F. Araujo, Dongha Kim et al.

Quantum convolutional neural networks (QCNNs) represent a promising approach in quantum machine learning, paving new directions for both quantum and classical data analysis. This approach is particularly attractive due to the absence of the barren plateau problem, a fundamental challenge in training quantum neural networks (QNNs), and its feasibility. However, a limitation arises when applying QCNNs to classical data. The network architecture is most natural when the number of input qubits is a power of two, as this number is reduced by a factor of two in each pooling layer. The number of input qubits determines the dimensions (i.e. the number of features) of the input data that can be processed, restricting the applicability of QCNN algorithms to real-world data. To address this issue, we propose a QCNN architecture capable of handling arbitrary input data dimensions while optimizing the allocation of quantum resources such as ancillary qubits and quantum gates. This optimization is not only important for minimizing computational resources, but also essential in noisy intermediate-scale quantum (NISQ) computing, as the size of the quantum circuits that can be executed reliably is limited. Through numerical simulations, we benchmarked the classification performance of various QCNN architectures when handling arbitrary input data dimensions on the MNIST and Breast Cancer datasets. The results validate that the proposed QCNN architecture achieves excellent classification performance while utilizing a minimal resource overhead, providing an optimal solution when reliable quantum computation is constrained by noise and imperfections.

Gilhan Kim, Daniel K. Park

Variational autoencoders (VAEs) learn compact latent representations of complex data, but their generative capacity is fundamentally constrained by the choice of prior distribution over the latent space. Energy-based priors offer a principled way to move beyond factorized assumptions and capture structured interactions among latent variables, yet training such priors at scale requires accurate and efficient sampling from intractable distributions. Here we present Boltzmann-machine--prior VAEs (BM-VAEs) trained using quantum annealing--based sampling in three distinct operational modes within a single generative system. During training, diabatic quantum annealing (DQA) provides unbiased Boltzmann samples for gradient estimation of the energy-based prior; for unconditional generation, slower quantum annealing (QA) concentrates samples near low-energy minima; for conditional generation, bias fields are added to direct sampling toward attribute-specific regions of the energy landscape (c-QA). Using up to 2000 qubits on a D-Wave Advantage2 processor, we demonstrate stable and efficient training across multiple datasets, with faster convergence and lower reconstruction loss than a Gaussian-prior VAE. The learned Boltzmann prior enables unconditional generation by sampling directly from the energy-based latent distribution, a capability that plain autoencoders lack, and conditional generation through latent biasing that leverages the learned pairwise interactions.

Nayeli A. Rodríguez-Briones, Daniel K. Park

This work introduces an approach rooted in quantum thermodynamics to enhance sampling efficiency in quantum machine learning (QML). We propose conceptualizing quantum supervised learning as a thermodynamic cooling process. Building on this concept, we develop a quantum refrigerator protocol that enhances sample efficiency during training and prediction without the need for Grover iterations or quantum phase estimation. Inspired by heat-bath algorithmic cooling protocols, our method alternates entropy compression and thermalization steps to decrease the entropy of qubits, increasing polarization towards the dominant bias. This technique minimizes the computational overhead associated with estimating classification scores and gradients, presenting a practical and efficient solution for QML algorithms compatible with noisy intermediate-scale quantum devices.

Changwon Lee, Tak Hur, Daniel K. Park

Real-time, scalable, and accurate decoding is a critical component for realizing a fault-tolerant quantum computer. While Transformer-based neural decoders such as \textit{AlphaQubit} have demonstrated high accuracy, the computational complexity of their core attention mechanism, which scales as $\mathcal{O}(d^4)$ with code distance $d$, results in decoding speeds insufficient for practical real-time applications. In this work, we introduce and evaluate a \textit{Mamba}-based decoder, a state-space model with $\mathcal{O}(d^2)$ complexity. In memory experiments using Sycamore hardware data, our Mamba decoder matches the performance of its Transformer-based counterpart, providing that its superior efficiency does not come at the cost of performance. Crucially, in simulated real-time scenarios that account for decoder-induced noise, the Mamba decoder significantly outperforms the Transformer, exhibiting a higher error threshold of $0.0104$ compared to $0.0097$. These results demonstrate that Mamba decoders offer a compelling balance between speed and accuracy, making them a promising architecture for scalable, real-time quantum error correction.

Yujin Kim, Changjae Im, Taehyun Kim et al.

Classification using variational quantum circuits is a promising frontier in quantum machine learning. Quantum supervised learning (QSL) applied to classical data using variational quantum circuits involves embedding the data into a quantum Hilbert space and optimizing the circuit parameters to train the measurement process. In this context, the efficacy of QSL is inherently influenced by the selection of quantum embedding. In this study, we introduce a classical-quantum hybrid approach for optimizing quantum embedding beyond the limitations of the standard circuit model of quantum computation (i.e., completely positive and trace-preserving maps) for general multi-channel data. We benchmark the performance of various models in our framework using the CIFAR-10 and Tiny ImageNet datasets and provide theoretical analyses that guide model design and optimization.

Hyunho Cha, Daniel K. Park, Jungwoo Lee

Quantum data re-uploading has proved powerful for classical inputs, where repeatedly encoding features into a small circuit yields universal function approximation. Extending this idea to quantum inputs remains underexplored, as the information contained in a quantum state is not directly accessible in classical form. We propose and analyze a quantum data re-uploading architecture in which a qubit interacts sequentially with fresh copies of an arbitrary input state. The circuit can approximate any bounded continuous function using only one ancilla qubit and single-qubit measurements. By alternating entangling unitaries with mid-circuit resets of the input register, the architecture realizes a discrete cascade of completely positive and trace-preserving maps, analogous to collision models in open quantum system dynamics. Our framework provides a qubit-efficient and expressive approach to designing quantum machine learning models that operate directly on quantum data.

Israel F. Araujo, Daniel K. Park, Francesco Petruccione et al.

Advantages in several fields of research and industry are expected with the rise of quantum computers. However, the computational cost to load classical data in quantum computers can impose restrictions on possible quantum speedups. Known algorithms to create arbitrary quantum states require quantum circuits with depth O(N) to load an N-dimensional vector. Here, we show that it is possible to load an N-dimensional vector with a quantum circuit with polylogarithmic depth and entangled information in ancillary qubits. Results show that we can efficiently load data in quantum devices using a divide-and-conquer strategy to exchange computational time for space. We demonstrate a proof of concept on a real quantum device and present two applications for quantum machine learning. We expect that this new loading strategy allows the quantum speedup of tasks that require to load a significant volume of information to quantum devices.