Identification of symmetry-protected topological states on noisy quantum computers

TL;DR

This paper introduces two protocols for identifying symmetry-protected topological states on noisy quantum computers, linking quantum information processing with topological phase classification, and demonstrates their implementation on IBM quantum hardware.

Contribution

The paper presents novel protocols using entanglement measures and measurement-based algorithms to detect SPT states on noisy quantum devices, bridging quantum computing and topological matter.

Findings

Protocols successfully detect SPT states on IBM quantum computers

Topological states show stability under noise and perturbations

Experimental results align with noisy simulations

Abstract

Identifying topological properties is a major challenge because, by definition, topological states do not have a local order parameter. While a generic solution to this challenge is not available yet, a broad class of topological states, namely symmetry-protected topological (SPT) states, can be identified by distinctive degeneracies in their entanglement spectrum. Here, we propose and realize two complementary protocols to probe these degeneracies based on, respectively, symmetry-resolved entanglement entropies and measurement-based computational algorithms. The two protocols link quantum information processing to the classification of SPT phases of matter. They invoke the creation of a cluster state, and are implemented on an IBM quantum computer. The experimental findings are compared to noisy simulations, allowing us to study the stability of topological states to perturbations and noise.