Quantum Convolutional Neural Networks are Effectively Classically Simulable

Quantum convolutional neural networks (QCNNs) are widely regarded as a promising model for quantum machine learning (QML). In this work, we analyze the most widely used variants of these models (i.e., tracing out- and measurement-based QCNNs), and we relate their heuristic success to two facts. First, that when randomly initialized, they can only operate on the information encoded in low-bodyness measurements of their input states. And second, that they are commonly benchmarked on “locally easy” datasets whose states are precisely classifiable by the information encoded in these low-bodyness observables subspace. From these insights, we argue that the QCNN’s action on this subspace should be efficiently…

• DI
  Donostia International Physics Center
• LD
  Laboratory Directed Research and Development

  Awards: 20230527ECR, 20230049DR
• LA
  Los Alamos National Laboratory

  Awards: 20230049DR, 20230527ECR