Measuring the Hall Viscosity of the Laughlin State on Noisy Quantum Computers

TL;DR

This paper demonstrates a quantum-circuit protocol to measure the Hall viscosity of a fractional quantum Hall state on noisy quantum computers, showing promising agreement with theoretical predictions despite hardware limitations.

Contribution

It introduces a novel quantum-circuit approach to probe Hall viscosity in FQH states using NISQ devices, bridging theory and experiment.

Findings

Hardware data aligns with analytical predictions

Protocol successfully captures geometric response dynamics

Truncation limits access to fully quantized Hall viscosity

Abstract

Hall viscosity is a quantized nondissipative stress response of a fractional quantum Hall (FQH) fluid to adiabatic geometric deformations. Despite strong theoretical interest, its experimental observation in the FQH state has remained elusive, making it a promising target for realization on current NISQ devices. In this work, we employ a quasi-one-dimensional model of an FQH state coupled to a background metric to probe the geometric response under a metric quench. We design and implement a quantum-circuit protocol that realizes a Hilbert-space-truncated version of the model and extracts the Hall viscosity from the geometric response encoded in the wavefunction dynamics of the device. While the truncation prevents us from accessing the fully quantized value of Hall viscosity, the hardware data nevertheless show excellent agreement with analytical and numerical predictions within this restricted regime.