  Neural network-based algorithms have garnered considerable attention in
condensed matter physics for their ability to learn complex patterns from very
high dimensional data sets towards classifying complex long-range patterns of
entanglement and correlations in many-body quantum systems. Small-scale quantum
computers are already showing potential gains in learning tasks on large
quantum and very large classical data sets. A particularly interesting class of
algorithms, the quantum convolutional neural networks (QCNN) could learn
features of a quantum data set by performing a binary classification task on a
nontrivial phase of quantum matter. Inspired by this promise, we present a
generalization of QCNN, the branching quantum convolutional neural network, or
bQCNN, with substantially higher expressibility. A key feature of bQCNN is that
it leverages mid-circuit (intermediate) measurement results, realizable on
current trapped-ion systems, obtained in pooling layers to determine which sets
of parameters will be used in the subsequent convolutional layers of the
circuit. This results in a branching structure, which allows for a greater
number of trainable variational parameters in a given circuit depth. This is of
particular use on current-day NISQ devices, where circuit depth is limited by
gate noise. We present an overview of the ansatz structure and scaling, and
provide evidence of its enhanced expressibility compared to QCNN. Using
artificially-constructed large data sets of training states as a
proof-of-concept we demonstrate the existence of training tasks in which bQCNN
far outperforms an ordinary QCNN. Finally, we present future directions where
the classical branching structure and increased density of trainable parameters
in bQCNN would be particularly valuable.
