Leveraging Pre-Trained Neural Networks to Enhance Machine Learning with Variational Quantum Circuits

TL;DR

This work introduces an innovative approach that utilizes pre-trained neural networks to enhance Variational Quantum Circuits (VQC) and effectively separates approximation error from qubit count and removes the need for restrictive conditions, making QML more viable for real-world applications.

Abstract

Quantum Machine Learning (QML) offers tremendous potential but is currently limited by the availability of qubits. We introduce an innovative approach that utilizes pre-trained neural networks to enhance Variational Quantum Circuits (VQC). This technique effectively separates approximation error from qubit count and removes the need for restrictive conditions, making QML more viable for real-world applications. Our method significantly improves parameter optimization for VQC while delivering notable gains in representation and generalization capabilities, as evidenced by rigorous theoretical analysis and extensive empirical testing on quantum dot classification tasks. Moreover, our results extend to applications such as human genome analysis, demonstrating the broad applicability of our approach. By addressing the constraints of current quantum hardware, our work paves the way for a new era of advanced QML applications, unlocking the full potential of quantum computing in fields such as machine learning, materials science, medicine, mimetics, and various interdisciplinary areas.

Figures (8)

• Figure 1: The architecture of using pre-trained neural networks for VQC. (a) A classical model $\mathcal{X}$ is pre-trained with another classical one $\mathcal{Y}$ on a generic dataset $D_{A}$ for a generic task $T_{A}$. (b) the pre-trained classical model Pre-$\mathcal{X}$ is transferred to a hybrid quantum-classical architecture, where the classical model Pre-$\mathcal{X}$ is frozen without a further parameter adjustment, and the VQC's parameters need to be trained based on a target dataset $D_{B}$ for a target task $T_{B}$.
• Figure 2: Illustration of hybrid quantum-classical architecture with a pre-trained classical neural network and a VQC. Given an input vector $\textbf{x}\in \mathbb{R}^{D}$, a pre-trained classical neural network transforms the input into a context-enriched feature representation $\hat{f}_{\mathcal{X}}(\textbf{x})$, which is transformed into classical outputs $\langle \sigma_{z}^{(i)} \rangle$ through the VQC block. A softmax operation is utilized for pattern classification, where a cross-entropy loss is used to calculate the gradients to update the VQC's parameters.
• Figure 3: Illustration of single and double quantum dot charge stability diagrams. (a) labeled clean charge stability diagrams containing the transition lines without noise; (b) labeled noisy charge stability diagrams mixed with realistic noise effects on the transition lines. Label:$0$ and Label:$1$ denote charge stability diagrams of single and double quantum dots. By detecting the transition lines using the QML approach, we aim to judge whether the charge stability diagram corresponds to the single or double quantum dots. In particular, we use the noiseless data to evaluate the models' representation power while using the noisy data to assess the models' generalization power.
• Figure 4: Experimental results on noiseless charge stability diagrams for evaluating the models' representation powers with $8$ qubits. (a) The experimental results are based on accuracy; (b) The measurement of the models' performance is conducted through the loss values. Both Pre-ResNet18+VQC and Pre-ResNet50+VQC can achieve better empirical results than VQC in terms of accuracy and loss values, and Pre-ResNet18+VQC even outperforms Pre-ResNet50+VQC on the clean dataset.
• Figure 5: Experimental results on noisy charge stability diagrams for assessing VQC models' generalization powers with $8$ qubits. (a) The experimental results are based on accuracy; (b) The measurement of the models' performance is conducted through the loss values. Both Pre-ResNet18+VQC and Pre-ResNet50+VQC obtain better empirical performance than VQC in terms of accuracy and loss values, and they eventually achieve a very close result on the noisy dataset.

Theorems & Definitions (3)

• Theorem 1
• Theorem 2
• Theorem 3