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Abstract Recently, several quantum benchmarking algorithms have been developed to characterize noisy quantum gates on today’s quantum devices. A fundamental issue in benchmarking is that not everything about quantum noise is learnable due to the existence of gauge freedom, leaving open the question what information is learnable and what is not, which is unclear even for a single CNOT gate. Here we give a precise characterization of the learnability of Pauli noise channels attached to Clifford gates using graph theoretical tools. Our results reveal the optimality of cycle benchmarking in the sense that it can extract all learnable information about Pauli noise. We experimentally demonstrate noise characterization of IBM’s CNOT gate up to 2 unlearnable degrees of freedom, for which we obtain bounds using physical constraints. In addition, we show that an attempt to extract unlearnable information by ignoring state preparation noise yields unphysical estimates, which is used to lower bound the state preparation noise. 

In computer-aided drug discovery, quantitative structure activity relation models are trained to predict biological activity from chemical structure. Despite the recent success of applying graph neural network to this task, important chemical information such as molecular chirality is ignored. To fill this crucial gap, we propose Molecular-Kernel Graph NeuralNetwork (MolKGNN) for molecular representation learning, which features SE(3)-/conformation invariance, chirality-awareness, and interpretability. For our MolKGNN, we first design a molecular graph convolution to capture the chemical pattern by comparing the atom's similarity with the learnable molecular kernels. Furthermore, we propagate the similarity score to capture the higher-order chemical pattern. To assess the method, we conduct a comprehensive evaluation with nine well-curated datasets spanning numerous important drug targets that feature realistic high class imbalance and it demonstrates the superiority of MolKGNN over other graph neural networks in computer-aided drug discovery. Meanwhile, the learned kernels identify patterns that agree with domain knowledge, confirming the pragmatic interpretability of this approach. Our code and supplementary material are publicly available at https://github.com/meilerlab/MolKGNN.