Variational Quantum Approximate Spectral Clustering for Binary Clustering Problems

In quantum machine learning, algorithms with parameterized quantum circuits (PQC) based on a hardware-efficient ansatz (HEA) offer the potential for speed-ups over traditional classical algorithms. While much attention has been devoted to supervised learning tasks, unsupervised learning using PQC remains relatively unexplored. One promising approach within quantum machine learning involves optimizing fewer parameters in PQC than in its classical counterparts, under the assumption that a sub-optimal solution exists within the Hilbert space. In this paper, we introduce the Variational Quantum Approximate Spectral Clustering (VQASC) algorithm - a NISQ-compatible method that requires optimization of fewer parameters than the system size, N, traditionally required in classical problems. We present numerical results from both synthetic and real-world datasets. Furthermore, we propose a descriptor, complemented by numerical analysis, to identify an appropriate ansatz circuit tailored for VQASC.Comment: 21 pages, 6 figure

Optimizing Quantum Convolutional Neural Network Architectures for Arbitrary Data Dimension

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.Comment: 17 pages, 7 figure

Extraordinary Off-Stoichiometric Bismuth Telluride for Enhanced n‑Type Thermoelectric Power Factor

Thermoelectrics directly converts waste heat into electricity and is considered a promising means of sustainable energy generation. While most of the recent advances in the enhancement of the thermoelectric figure of merit (<i>ZT</i>) resulted from a decrease in lattice thermal conductivity by nanostructuring, there have been very few attempts to enhance electrical transport properties, i.e., the power factor. Here we use nanochemistry to stabilize bulk bismuth telluride (Bi₂Te₃) that violates phase equilibrium, namely, phase-pure n-type K_0.06Bi₂Te_3.18. Incorporated potassium and tellurium in Bi₂Te₃ far exceed their solubility limit, inducing simultaneous increase in the electrical conductivity and the Seebeck coefficient along with decrease in the thermal conductivity. Consequently, a high power factor of ∼43 μW cm^–1 K^–2 and a high <i>ZT</i> > 1.1 at 323 K are achieved. Our current synthetic method can be used to produce a new family of materials with novel physical and chemical characteristics for various applications