Probing Geometric Excitations of Fractional Quantum Hall States on Quantum Computers

TL;DR

This paper demonstrates the simulation of geometric excitations, akin to gravitons, in fractional quantum Hall states using IBM quantum computers, introducing models and algorithms for studying emergent quantum geometrical phenomena.

Contribution

It introduces a quasi-one-dimensional model capturing FQH geometric properties and develops quantum algorithms for simulating graviton dynamics on current hardware.

Findings

Successful simulation of graviton dynamics on IBM quantum hardware

Development of an efficient variational quantum algorithm for larger systems

Identification of a model capturing FQH geometric excitations

Abstract

Intermediate-scale quantum technologies provide new opportunities for scientific discovery, yet they also pose the challenge of identifying suitable problems that can take advantage of such devices in spite of their present-day limitations. In solid-state materials, fractional quantum Hall (FQH) phases continue to attract attention as hosts of emergent geometrical excitations analogous to gravitons, resulting from the non-perturbative interactions between the electrons. However, the direct observation of such excitations remains a challenge. Here, we identify a quasi-one-dimensional model that captures the geometric properties and graviton dynamics of FQH states. We then simulate geometric quench and the subsequent graviton dynamics on the IBM quantum computer using an optimally-compiled Trotter circuit with bespoke error mitigation. Moreover, we develop an efficient, optimal-control-based variational quantum algorithm that can efficiently simulate graviton dynamics in larger systems. Our results open a new avenue for studying the emergence of gravitons in a new class of tractable models on the existing quantum hardware.