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Lorenz, Jeanette Miriam

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  • Publication
    Quantum Robustness Verification: A Hybrid Quantum-Classical Neural Network Certification Algorithm
    ( 2022)
    Franco, Nicola
    ;
    Wollschläger, Tom
    ;
    Gao, Nicholas
    ;
    Lorenz, Jeanette Miriam orcid-logo
    ;
    Günnemann, Stephan
    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 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 provides bounds on the minimum number of qubits necessary to approximate the problem. Finally, we evaluate our method within simulations and on quantum hardware.
  • Publication
    On Quantum Computing for Neural Network Robustness Verification
    ( 2022)
    Franco, Nicola
    ;
    Wollschläger, Tom
    ;
    Gao, Nicholas
    ;
    Lorenz, Jeanette Miriam orcid-logo
    ;
    Günnemann, Stephan
    In recent years, a multitude of approaches to certify the prediction of neural networks have been proposed. Classically, complete verification techniques struggle with large networks as the combinatorial space grows exponentially, implying that realistic networks are difficult to be verified. For this reason, we propose to leverage the computational power of quantum computing for the robustness verification of neural networks. Further, we introduce a new Hybrid Quantum-Classical Robustness Algorithm for Neural network verification (HQ-CRAN). By applying Benders decomposition we split the verification problem into a quadratic unconstrained binary optimization and a linear program which we solve with quantum and classical computers, respectively. Further, we 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 obtain a reasonable approximation. Finally, we evaluate our method on quantum hardware.