Zapletal, Petr
Date: Wednesday, October 18, 2023
Time: 16:00
Place: ETH Campus Hönggerberg, HPF G 6
Host: Christoph Hellings
Error-tolerant quantum convolutional neural networks for symmetry-protected topological phases
Petr Zapletal – University of Basel, Switzerland
Abstract: The analysis of noisy quantum states prepared on current quantum computers is getting beyond the capabilities of classical computing. Quantum neural networks based on parametrized quantum circuits, measurements and feed-forward can process large amounts of quantum data to reduce measurement and computational costs of detecting non-local quantum correlations. The tolerance of errors due to decoherence and gate infidelities is a key requirement for the application of quantum neural networks on near-term quantum computers. Here we construct quantum convolutional neural networks (QCNNs) that can, in the presence of incoherent errors, recognize different symmetry-protected topological phases of generalized cluster-Ising Hamiltonians from one another as well as from topologically trivial phases. Using matrix product state simulations, we show that the QCNN output is robust against symmetry-breaking errors below a threshold error probability and against all symmetry-preserving errors provided the error channel is invertible [1]. This is in contrast to string order parameters and the output of previously designed QCNNs, which vanish in the presence of any symmetry-breaking errors. A shallow-depth QCNN recently realized on a 7-qubit superconducting quantum processor exhibited robustness against errors [2]. Despite being composed of finite-fidelity gates itself, the QCNN detected a topological phase with higher fidelity than the direct measurement of string order parameters. The QCNNs reduce sample complexity exponentially with system size in comparison to direct sampling using local Pauli measurements.
References
[1] P. Zapletal, N. A. McMahon, and M. J. Hartmann, arXiv:2307.03711 (2023).
[2] J. Herrmann, S. M. Llima, A. Remm, P. Zapletal, N. A. McMahon, C. Scarato, F. Swiadek, C. K. Andersen, C. Hellings, S. Krinner, N. Lacroix, S. Lazar, M. Kerschbaum, D. C. Zanuz, G. J. Norris, M. J. Hartmann, A. Wallraff, and C. Eichler, Nat. Commun. 13, 4144 (2022).