  Quantum computers have the potential to revolutionize diverse fields,
including quantum chemistry, materials science, and machine learning. However,
contemporary quantum computers experience errors that often cause quantum
programs run on them to fail. Until quantum computers can reliably execute
large quantum programs, stakeholders will need fast and reliable methods for
assessing a quantum computer's capability-i.e., the programs it can run and how
well it can run them. Previously, off-the-shelf neural network architectures
have been used to model quantum computers' capabilities, but with limited
success, because these networks fail to learn the complex quantum physics that
determines real quantum computers' errors. We address this shortcoming with a
new quantum-physics-aware neural network architecture for learning capability
models. Our architecture combines aspects of graph neural networks with
efficient approximations to the physics of errors in quantum programs. This
approach achieves up to $\sim50\%$ reductions in mean absolute error on both
experimental and simulated data, over state-of-the-art models based on
convolutional neural networks.
