Shortening Quantum Convolutional Neural Networks to Constant Depth*

The quantum convolutional neural network (QCNN) is a quantum circuit that detects symmetry protected topological (SPT) phases, with designs drawing from renormalisation theory. In this talk I will discuss a special class of these circuits that are equivalent to constant depth circuits, local measurements, and classical post-processing. Although the quantum circuit is constant depth on N-qubits, we still observe a provable exponential (in N) time speed up compared to local Pauli measurement and post-processing of the input state. Despite the constant depth, an exponential speed up arises due to inputing non-trivial quantum states. The speed-up therefore bounded by the natural classical representation complexity of the input quantum state.

Our circuit also improves on earlier approaches for a Z2 x Z2 SPT phase detection circuit, both in time complexity and signal fidelity. This improvement arises from a quantum error correction analysis of the circuit, and works by providing protection against error channels common to NISQ devices.

This talk compliments the experimental talk by J. Herrmann (XXXX) and provides the underlying theory.