Quantum Measurement Classification with Qudits

TL;DR

The paper tackles density estimation and supervised classification in high-dimensional quantum systems using qudits, by implementing the DMKDE and DMKDC frameworks as quantum circuits. It introduces a three-phase workflow (state preparation, training, prediction) and leverages spectral decompositions $\rho_j = U_j \Lambda_j U_j^{\dag}$ and feature maps (e.g., random Fourier features) within the QuantumSkynet simulator to realize predictions. Empirical results on synthetic and toy datasets show that the qudit circuits reproduce the performance of the original TensorFlow implementations, demonstrating viability for density estimation and classification on high-dimensional quantum hardware. The work points to scalable extensions, including larger feature maps and stochastic optimization to learn density matrices, enabling practical quantum-assisted density estimation and classification.

Abstract

This paper presents a hybrid classical-quantum program for density estimation and supervised classification. The program is implemented as a quantum circuit in a high-dimensional quantum computer simulator. We show that the proposed quantum protocols allow to estimate probability density functions and to make predictions in a supervised learning manner. This model can be generalized to find expected values of density matrices in high-dimensional quantum computers. Experiments on various data sets are presented. Results show that the proposed method is a viable strategy to implement supervised classification and density estimation in a high-dimensional quantum computer.

Figures (8)

• Figure 1: a High-dimensional gate $X^{m}$. b High-dimensional gate $X^{-1}$.
• Figure 2: High-dimensional control gate $CU$.
• Figure 3: High-dimensional generalized control gate $CU^k$.
• Figure 4: Qudit-based implementation of DMKDE and DMKDC methods. The quantum feature map and the training were performed in a classical computer, while the prediction was done in a high-dimensional quantum computer simulator.
• Figure 5: DMDKE high-dimensional quantum circuit.