Quantum Robustness Verification: A Hybrid Quantum-Classical Neural Network Certification Algorithm

TL;DR

This paper introduces a hybrid quantum-classical algorithm for verifying the robustness of neural networks, leveraging quantum computing to solve complex verification problems more efficiently than classical methods.

Contribution

It proposes a novel hybrid quantum-classical approach using Benders decomposition for neural network verification, reducing qubit requirements and improving efficiency over existing methods.

Findings

The method provides sound certificates in simulated environments.

It establishes bounds on the minimum qubits needed for approximation.

Evaluation on quantum hardware demonstrates practical feasibility.

Abstract

In recent years, quantum computers and algorithms have made significant progress indicating the prospective importance of quantum computing (QC). Especially combinatorial optimization has gained a lot of attention as an application field for near-term quantum computers, both by using gate-based QC via the Quantum Approximate Optimization Algorithm and by quantum annealing using the Ising model. However, demonstrating an advantage over classical methods in real-world applications remains an active area of research. In this work, we investigate the robustness verification of ReLU networks, which involves solving a many-variable mixed-integer programs (MIPs), as a practical application. Classically, complete verification techniques struggle with large networks as the combinatorial space grows exponentially, implying that realistic networks are difficult to be verified by classical methods. To alleviate this issue, we propose to use QC for neural network verification and introduce a hybrid quantum procedure to compute provable certificates. By applying Benders decomposition, we split the MIP into a quadratic unconstrained binary optimization and a linear program which are solved by quantum and classical computers, respectively. We further improve existing hybrid methods based on the Benders decomposition by reducing the overall number of iterations and placing a limit on the maximum number of qubits required. We show that, in a simulated environment, our certificate is sound, and provide bounds on the minimum number of qubits necessary to approximate the problem. Finally, we evaluate our method within simulation and on quantum hardware.