Quantum neural networks for the simulation of condensed matter systems on quantum computers

Abstract:
One of the major challenges in developing scalable quantum computers is analyzing quantum data, i.e., quantum states produced by quantum hardware. With increasing system size, standard characterization techniques using direct measurements and classical post-processing become prohibitively demanding due to large measurement counts and computational efforts. Directly processing quantum data on quantum processors can substantially reduce measurement costs. Quantum neural networks, based on parameterized quantum circuits, can process large amounts of quantum data, to efficiently detect non-local quantum correlations [1]. Characterizing non-local correlations is crucial for classifying quantum phases of matter and studying strongly correlated materials, such as topological quantum matter, on quantum computers.
In this talk, I will introduce quantum neural networks, and I will show how they can be used to study quantum phases of matter on near-term quantum computers [2, 3]. Furthermore, I will discuss the realization of these networks on a superconducting quantum processor [4].

[1] I. Cong, S. Choi, and M. D. Lukin, Nat. Phys. 15 (2019) 1273.
[2] P. Zapletal, N. A. McMahon, and M. J. Hartmann, Phys. Rev. Research 6, 033111 (2024).
[3] L. C. Sander, N. A. McMahon, P. Zapletal, and M. J. Hartmann, arXiv:2407.04114 (2024).
[4] J. Herrmann et al., Nat. Commun. 13 (2022) 4144.