June-Koo Kevin Rhee

Spectral machine learning methods based on spectral graph theory are powerful but scale poorly due to costly eigen‐analysis. Although various eigenvector approximation methods have been proposed, the construction of a partial kernel matrix still remains within their frameworks. This work presents compact quantum circuit designs for spectral clustering in which the eigenproblem is approximated via a Rayleigh–Ritz formulation that bypasses kernel matrix construction and whose overall depth is dominated by the data‐embedding routine. A rigorous shot complexity analysis is provided, showing that the sampling‐based estimation remains tractable for the spectral clustering objective including a penalty term. Simulations on canonical datasets demonstrate reliable optimization behavior with an under‐parameterized hardware‐efficient ansatz. Finite‐shot simulations further confirm the predicted sampling behavior of the penalty estimator, validating the main claims as a proof of concept.

Verifying the violation of Bell's inequality is one of the most representative methods to demonstrate that entangled photon pairs prepared in a quantum optics-based system exhibit quantum properties. While experiments on Bell inequality violations have been theoretically well-established and extensively conducted to implement various quantum information technologies in laboratory settings, mathematical modeling for systematically describing the distribution of high-brightness entangled photon pairs in high-loss environments remains an issue that requires further research. As the brightness of the entangled photon pairs increases, the influence of multi-photon effects becomes more significant, leading to a decrease in the CHSH value $S$ and also a reduction in the standard deviation of the CHSH value $\Delta S$. Therefore, a new analysis of the $(S-2)/\Delta S$ value is required to more precisely confirm the degree of CHSH inequality violation including the reliability of $S$. In this paper, we propose a mathematical model to predict the $(S-2)/\Delta S$ value as a function of the brightness of the entangled photon pair source, and we also suggest the need to optimize the brightness of this source. Additionally, we provide experimental evidence supporting this model. The experiment confirms that when the mean photon number is $\mu =0.026$ in an entanglement distribution setup with a total loss of $-19.03$ dB, the CHSH value drops to 2.69, while the $(S-2)/\Delta S$ value increases to 60.95.

A high‐brightness entangled photon‐pair (HBEPP) source is essential for long‐reach entanglement‐based quantum key distribution (QKD) such as in a satellite QKD system. An ultrabright source is a good candidate to overcome significant losses and to increase the sifted key rate, but the performance is critically limited due to the multi‐photon effect that raises the error rate of the system. To accurately estimate system performance, this study first investigates an analytical model for calculating the measurement probabilities of HBEPP distribution through an asymmetric loss channel. Based on this model, this study proposes the use of a fixed‐intensity HBEPP source for satellite QKD systems, assuming a polarization‐independent channel and threshold detectors for measurement. This study confirms that fixing the mean photon number at achieves a performance of compared to the ideal one‐way communication entanglement‐based satellite QKD protocol, which is effectively optimizing the HBEPP source brightness in accordance with system losses.

Inspired by classical graph neural networks, we discuss a novel quantum graph neural network (QGNN) model to predict the chemical and physical properties of molecules and materials. QGNNs were investigated to predict the energy gap between the highest occupied and lowest unoccupied molecular orbitals of small organic molecules. The models utilize the equivariantly diagonalizable unitary quantum graph circuit (EDU-QGC) framework to allow discrete link features and minimize quantum circuit embedding. The results show QGNNs can achieve lower test loss compared to classical models if a similar number of trainable variables are used, and converge faster in training. This paper also provides a review of classical graph neural network models for materials research and various QGNNs.

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.

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.

A kernel-based quantum classifier is the most interesting and powerful quantum machine learning technique for hyperlinear classification of complex data, which can be easily realized in shallow-depth quantum circuits such as a SWAP test classifier. A variational quantum approximate support vector machine (VQASVM) can be realized inherently and explicitly on these circuits by introduction of a variational scheme to map the quadratic optimization problem of the support vector machine theory to a quantum-classical variational optimization problem. Probability weight modulation in index qubits of a classifier can designate support vectors among training vectors, which can be achieved with a parameterized quantum circuit (PQC). The classical parameters of PQC is then transferred to many copies of other decision inference circuits. Our VQASVM algorithm is experimented with toy example data sets on cloud-based quantum machines for feasibility evaluation, and numerically investigated to evaluate its performance on a standard iris flower and MNIST data set. The empirical run-time complexity of VQASVM is estimated to be sub-quadratic on the training data set size, while that of the classical solver is quadratic.