Berlin 2024 – wissenschaftliches Programm
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QI: Fachverband Quanteninformation
QI 33: Quantum Materials and Many-Body Systems
QI 33.4: Vortrag
Freitag, 22. März 2024, 10:15–10:30, HFT-TA 441
Renormalisation Through The Lens Of Quantum Convolutional Neural Networks — •Nathan A. McMahon1, Petr Zapel2, and Michael J. Hartmann1 — 1Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU) — 2University of Basel, Switzerland.
A quantum convolutional neural network (QCNN) can be used to perform quantum phase recognition for the cluster-Ising model. This circuit outputs +1 if the input state is in the symmetry protected topological (SPT) phase, called the target phase, and 0 if it is in either of the other phases. This observation has been shown numerically and experimentally, but much less is known analytically. In this talk we first introduce a set of conditions on a QCNN that describes success at the phase recognition task restricted to a subset of possible input quantum states and proceed to show the cluster-Ising QCNN satisfies these conditions via random circuit analysis. When averaged over random circuits, if the QCNN outputs can distinguish between phases, some input states must be non-typical. In contrast, the rate of change of the QCNN outputs with respect to perturbations of the input state also has an operator representation, where all input states we consider are typical and converge to zero with QCNN depth. Since all input states can be generated from a reference state under these perturbations, this explains how the QCNN performs phase recognition and extends to incoherent perturbations.This suggests QCNNs may provide insight in how to extend the corresponding SPT phase to mixed states.
Keywords: Quantum Machine Learning; Renormalisation; Symmetry Protected Topological Phases; Random Circuits