Harnessing Quantum Support Vector Machines for Cross-Domain Classification of Quantum States

TL;DR

The paper addresses the challenge of entanglement versus separability classification in quantum states under cross-domain conditions. It introduces a quantum support vector machine (QSVM) with a fidelity-based kernel and SWAP-test computation to perform cross-domain classification on two-qubit mixed states, comparing its performance to classical SVMs and neural networks. Results show that QSVM achieves high accuracy, including 100% for Horodecki states, and remains robust under random local unitary transformations, signaling a quantum advantage in state discrimination and non-classical correlation detection. The work suggests scalability to multi-qubit systems and provides data generated via QuTiP for reproducibility and broader application.

Abstract

In the present study, we use cross-domain classification using quantum machine learning for quantum advantages to readdress the entanglement versus separability paradigm. The inherent structure of quantum states and its relation to a particular class of quantum states are used to intuitively classify testing states from domains different from training states, called \textit{cross-domain classification}. Using our quantum machine learning algorithm, we demonstrate efficient classifications of two-qubit mixed states into entangled and separable classes. For analyzing the quantumness of correlations, our model adequately classifies Bell diagonal states as zero and non-zero discord states. In addition, we also extend our analysis to evaluate the robustness of our model using random local unitary transformations. Our results demonstrate the potential of the quantum support vector machine for classifying quantum states across the multi-dimensional Hilbert space in comparison to classical support vector machines and neural networks.

Figures (8)

• Figure 1: A geometrical representation of training and testing domains for two-qubit mixed states- the four corners represent Bell states such that (-1,-1,-1), (-1,1,1), (1,-1,1), and (1,1,-1) represent $\ket{\psi_{-}}$, $\ket{\phi_{-}}$, $\ket{\phi_{+}}$, and $\ket{\psi_{+}}$, respectively. A) The line joining from the center to the vertex represents one of the Werner states, and the part of the line confined in the octahedron depicts the separable class. The part of the line confined outside the octahedron depicts the entangled class. B) For classifying the quantumness of correlations, the inside edges (red and green lines) show zero-discord states; all other states represent non-zero discord states.
• Figure 2: The quantum circuit used in QSVM.
• Figure 3: A flow chart representing the in-domain classification where we train models (quantum and classical support vector machine) on 75% of the generated dataset and test models on the rest 25% of the generated dataset.
• Figure 4: A comparison of quantum and classical support vector machines on four evaluation metrics (accuracy, precision, recall, and F1-score) for a combined dataset containing Werner-type, Horodecki, and MEMS states.
• Figure 5: A pictorial representation of cross-domain classification where we train our model on $\rho_{\ket{\psi_{-}}}$ and test our model on $\rho_{\ket{\psi_{+}}}$, $\rho_{\ket{\phi_{-}}}$, $\rho_{\ket{\phi_{+}}}$, Horodecki and MEMS states.