Testing measurement-based computational phases of quantum matter on a quantum processor

TL;DR

This paper experimentally verifies theoretical predictions about measurement-based quantum computation in symmetry-protected phases of quantum matter using an IBM quantum processor, focusing on how imperfections affect logical decoherence and computational efficiency.

Contribution

It provides the first experimental validation of theoretical predictions regarding the stability and efficiency of measurement-based quantum computation in symmetry-protected phases.

Findings

Symmetric imperfections cause logical decoherence, which can be mitigated.

Uniformity of computational power scales with system size.

Densest packing of measurement algorithms remains most efficient despite correlations.

Abstract

Many symmetry protected or symmetry enriched phases of quantum matter have the property that every ground state in a given such phase endows measurement based quantum computation with the same computational power. Such phases are called computational phases of quantum matter. Here, we experimentally verify four theoretical predictions for them on an IBM superconducting quantum device. We comprehensively investigate how symmetric imperfections of the resource states translate into logical decoherence, and how this decoherence is mitigated. In particular, the central experiment probes the scaling law from which the uniformity of computational power follows. We also analyze the correlated regime, where local measurements give rise to logical operations collectively. We test the prediction that densest packing of a measurement-based algorithms remains the most efficient, in spite of the correlations. Our experiments corroborate the operational stability of measurement based quantum computation in quantum phases of matter with symmetry.