Vulnerability of quantum classification to adversarial perturbations

Abstract

High-dimensional quantum systems are vital for quantum technologies and are essential in demonstrating practical quantum advantage in quantum computing, simulation and sensing. Since dimensionality grows exponentially with the number of qubits, the potential power of noisy intermediate-scale quantum (NISQ) devices over classical resources also stems from entangled states in high dimensions. An important family of quantum protocols that can take advantage of high-dimensional Hilbert space are classification tasks. These include quantum machine learning algorithms, witnesses in quantum information processing and certain decision problems. However, due to counter-intuitive geometrical properties emergent in high dimensions, classification problems are vulnerable to adversarial attacks. We demonstrate that the amount of perturbation needed for an adversary to induce a misclassification scales inversely with dimensionality. This is shown to be a fundamental feature independent of the details of the classification protocol. Furthermore, this leads to a trade-off between the security of the classification algorithm against adversarial attacks and quantum advantages we expect for high-dimensional problems. In fact, protection against these adversarial attacks require extra resources that scale at least polynomially with the Hilbert space dimension of the system, which can erase any significant quantum advantage that we might expect from a quantum protocol. This has wide-ranging implications in the use of both near-term and future quantum technologies for classification.

arXiv comment9 pages, 1 figure

References in corpus (18)

• Quantum Computing in the NISQ era and beyond
• Quantum Machine Learning
• Advances in Quantum Metrology
• Machine learning phases of matter
• Direct Fidelity Estimation from Few Pauli Measurements
• Aspects of generic entanglement
• Randomizing quantum states: Constructions and applications
• A quantum Fredkin gate
• Quantum machine learning for quantum anomaly detection
• Optimal verification of entangled states with local measurements
• Quantum learning and universal quantum matching machine
• Random bosonic states for robust quantum metrology
• Verification of Many-Qubit States
• Quantum learning robust to noise
• Machine learning non-local correlations
• Quantum change point
• Inductive supervised quantum learning
• Concentration of measure for quantum states with a fixed expectation value

Cited by in corpus (28)

• Quantum noise protects quantum classifiers against adversaries
• Quantum Adversarial Machine Learning
• Experimental quantum adversarial learning with programmable superconducting qubits
• Recent advances for quantum classifiers
• The Quantum Wasserstein Distance of Order 1
• Towards quantum enhanced adversarial robustness in machine learning
• Benchmarking Adversarially Robust Quantum Machine Learning at Scale
• Markovian Quantum Neuroevolution for Machine Learning
• Robust in Practice: Adversarial Attacks on Quantum Machine Learning
• Optimal Provable Robustness of Quantum Classification via Quantum Hypothesis Testing
• Robustness Verification of Quantum Classifiers
• Universal Adversarial Examples and Perturbations for Quantum Classifiers
• Tree tensor network classifiers for machine learning: from quantum-inspired to quantum-assisted
• Quantum Capsule Networks
• Drastic Circuit Depth Reductions with Preserved Adversarial Robustness by Approximate Encoding for Quantum Machine Learning
• Training robust and generalizable quantum models
• Predominant Aspects on Security for Quantum Machine Learning: Literature Review
• Ensemble-learning error mitigation for variational quantum shallow-circuit classifiers
• Correlations enable lossless ergotropy transport
• Quantum Continual Learning Overcoming Catastrophic Forgetting
• Adversarial Machine Learning Phases of Matter
• Adversarial Robustness Guarantees for Quantum Classifiers
• QuanTest: Entanglement-Guided Testing of Quantum Neural Network Systems
• Generating Universal Adversarial Perturbations for Quantum Classifiers
• Quantum-Inspired Weight-Constrained Neural Network: Reducing Variable Numbers by 100x Compared to Standard Neural Networks
• Classical Autoencoder Distillation of Quantum Adversarial Manipulations
• Superior resilience to poisoning and amenability to unlearning in quantum machine learning
• Verifying Adversarial Robustness in Quantum Machine Learning: from theory to physical validation via a software tool