Dynamics of quantum geometry in the fractional quantum Hall effect

A. Kirmani,1 K. Bull,2 C.-Y. Hou,3 Z. Papic,2 A. Rahmani,1 P. Ghaemi4

1Department of Physics and Astronomy, Western Washington University, Bellingham, Washington 98225,

2School of Physics and Astronomy, University of Leeds, Leeds LS2 9JT, United Kingdom

3Schlumberger-Doll Research, Cambridge, MA 02139, USA

4Physics Department, City College of the City University of New York, New York, NY 10031, USA

Intermediate-scale quantum technologies provide unprecedented opportunities for scientific discoveries while posing the challenge of identifying important problems that can take advantage of them through algorithmic innovations. A major open problem in quantum many-body physics is the table-top generation and detection of emergent excitations analogous to gravitons — the elusive mediators of gravitational force in a quantum theory of gravity. In solid state materials, fractional quantum Hall phases are one of the leading platforms for realizing graviton-like excitations, however their direct observation remains an experimental challenge. Here, we generate these excitations on the IBM quantum processor. We first identify an effective one-dimensional model that captures the geometric properties and graviton dynamics of fractional quantum Hall states. We then develop an efficient, optimal-control-based variational quantum algorithm to simulate geometric quench and the subsequent graviton dynamics, which we successfully implement on the IBM quantum computer. Our results [1] open a new avenue for studying the emergence of gravitons in a new class of tractable models that lend themselves to direct implementations on the existing quantum hardware.

1. A. Kirmani et al., arXiv:2107.10267

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