Quantum neural networks facilitating quantum state classification

TL;DR

This work tackles quantum state classification by leveraging a quantum neural network (QNN) framework that pairs a problem-inspired circuit with predefined and customised ansätze. The dataset is generated directly from a parametrised two-qubit unitary built via Kraus-dilation of noise channels, enabling controllable entanglement across two- and three-qubit states while maintaining resource efficiency. Training uses a cross-entropy objective and the COBYLA optimiser, with a focus on identifying ansätze that avoid barren plateaus; a Toffoli-enhanced, customised ansatz delivers the best three-qubit performance, outperforming standard RealAmplitudes and EfficientSU2 circuits. The results demonstrate high accuracy for two-qubit state classification and superior multi-class performance for three-qubit states, establishing a scalable approach for entanglement classification in multi-qubit quantum systems and highlighting practical pathways for QML-enabled quantum state analysis. All mathematical notation, including $|\psi_{x_i,\theta}\rangle = U_{\theta}U_{x_i}|0\rangle$ and $C(\theta)$, is presented with proper formatting to support precise interpretation.

Abstract

The classification of quantum states into distinct classes poses a significant challenge. In this study, we address this problem using quantum neural networks in combination with a problem-inspired circuit and customised as well as predefined ansätz. To facilitate the resource-efficient quantum state classification, we construct the dataset of quantum states using the proposed problem-inspired circuit. The problem-inspired circuit incorporates two-qubit parameterised unitary gates of varying entangling power, which is further integrated with the ansätz, developing an entire quantum neural network. To demonstrate the capability of the selected ansätz, we visualise the mitigated barren plateaus. The designed quantum neural network demonstrates the efficiency in binary and multi-class classification tasks. This work establishes a foundation for the classification of multi-qubit quantum states and offers the potential for generalisation to multi-qubit pure quantum states.

Figures (5)

• Figure 1: A general framework utilized for quantum neural networks for classifying the quantum state into entangled and separable classes.
• Figure 2: The problem-inspired circuits utilized for generating the desired quantum states A) correspond to the circuit for two-qubit quantum states generation, B) represent the circuit for three-qubit quantum states generation, and C) the proposed quantum circuit utilized as PQC in three-qubit quantum state classification.
• Figure 3: The barren plateau landscape for quantum state classificational models. The top row corresponds to two-qubit parameterised quantum circuits, and the bottom row corresponds to three-qubit parameterised quantum circuits.
• Figure 4: The graphs represent the loss function minimization curve over 100 iterations A) For RealAmplitudes and EfficientSU2 circuits utilized for two-qubit quantum state classification. B) Circuits utilized for three-qubit quantum state classification for the proposed circuit, RealAmplitudes, and EfficientSU2 circuits.
• Figure 5: The confusion metrics correspond to the parameterised quantum circuits utilised for three-qubit quantum state classification. The metrics demonstrate the detailed breakdown of predicted classes/labels for the test datasets vs actual labels across different classes. Specifically, A) corresponds to the proposed circuit, B) represents the EfficientSU2 circuit, and C) depicts the RealAmplitudes circuit.