QuanTest: Entanglement-Guided Testing of Quantum Neural Network Systems

TL;DR

QuanTest addresses the lack of robust testing for quantum neural networks by introducing a quantum entanglement–guided adversarial testing framework. It defines quantum entanglement adequacy (QEA) using the Meyer-Wallach entanglement measure and pairs it with two proximity metrics, AFM and ATD, to steer the generation of quantum adversarial examples. The method optimizes a joint objective that increases entanglement activation and induces incorrect QNN behaviors via gradient-based perturbations on quantum states, while ensuring unitary validity and state normalization. Experimental results across nine QNNs on MNIST and Fashion-MNIST show QuanTest generates far more adversarial samples than random or black-box baselines and yields high-fidelity test inputs that improve robustness when used for retraining. The work demonstrates the practicality and scalability of entanglement-guided testing for QNNs, with implications for secure and reliable quantum machine learning deployments.

Abstract

Quantum Neural Network (QNN) combines the Deep Learning (DL) principle with the fundamental theory of quantum mechanics to achieve machine learning tasks with quantum acceleration. Recently, QNN systems have been found to manifest robustness issues similar to classical DL systems. There is an urgent need for ways to test their correctness and security. However, QNN systems differ significantly from traditional quantum software and classical DL systems, posing critical challenges for QNN testing. These challenges include the inapplicability of traditional quantum software testing methods to QNN systems due to differences in programming paradigms and decision logic representations, the dependence of quantum test sample generation on perturbation operators, and the absence of effective information in quantum neurons. In this paper, we propose QuanTest, a quantum entanglement-guided adversarial testing framework to uncover potential erroneous behaviors in QNN systems. We design a quantum entanglement adequacy criterion to quantify the entanglement acquired by the input quantum states from the QNN system, along with two similarity metrics to measure the proximity of generated quantum adversarial examples to the original inputs. Subsequently, QuanTest formulates the problem of generating test inputs that maximize the quantum entanglement adequacy and capture incorrect behaviors of the QNN system as a joint optimization problem and solves it in a gradient-based manner to generate quantum adversarial examples. results demonstrate that QuanTest possesses the capability to capture erroneous behaviors in QNN systems. The entanglement-guided approach proves effective in adversarial testing, generating more adversarial examples.

Figures (11)

• Figure 1: Differences between classical DL testing (upper part) and QNN testing (lower part). In QNN system testing, the QNN components cannot extract effective neuron information as in classical DNN, and the generation of adversarial examples is also different from the classical approach.
• Figure 2: Differences between QNN and classical DNN during the training process.
• Figure 3: Overview of the QuanTest framework. QuanTest takes a quantum system composed of quantum states containing classical input information and a pre-trained QNN model as input. It extracts information generated by the quantum system. Based on this information, QuanTest is capable of generating quantum test samples that are adequately entangled with the QNN while inducing erroneous behaviors in the QNN system. In the diagram, black open arrows refer to the flow of classical information while the gray-blue arrows refer to the flow of quantum information.
• Figure 4: Example of QEA computation for two quantum states in the QNN. The nodes in gray denote quantum entanglement layers that are not sufficiently activated, while aqua nodes represent those that are adequately activated.
• Figure 5: Illustration of fidelity visualization between the original quantum sample $|\boldsymbol{x}\rangle$ and quantum adversarial example $|\boldsymbol{x}\rangle_{adv}$. The light orange and light green curves represent the probability distributions $p_{|\boldsymbol{x}\rangle}$ and $p_{|\boldsymbol{x}\rangle_{adv}}$ obtained through POVM measurements for the original sample and adversarial example, respectively.

Theorems & Definitions (3)

• definition 1: Quantum entanglement adequacy, QEA
• definition 2: Average fidelity measure, AFM
• definition 3: Average trace distance, ATD