Hierarchy of universal entanglement in 2D measurement-based quantum computation

TL;DR

This paper introduces a new 2D resource state with symmetry-protected topological order that enables universal measurement-based quantum computation using only single-qubit Pauli measurements, expanding understanding of entanglement in quantum computing.

Contribution

The paper presents a novel 2D resource state with genuine SPTO that allows universal quantum computation with simple measurements, differing from the traditional cluster state.

Findings

New resource state exhibits genuine 2D SPTO.

Enables universal quantum computation with only Pauli X, Y, Z measurements.

Links many-body entanglement to macroscopic quantum orders.

Abstract

Measurement-based quantum computation (MQC) is a paradigm for studying quantum computation using many-body entanglement and single-qubit measurements. While MQC has inspired wide-ranging discoveries throughout quantum information, our understanding of the general principles underlying MQC seems to be biased by its historical reliance upon the archetypal 2D cluster state. Here, we utilize recent advances in the subject of symmetry-protected topological order (SPTO) to introduce a novel MQC resource state, whose physical and computational behavior differs fundamentally from the cluster state. We show that, in sharp contrast to the cluster state, our state enables universal quantum computation using only measurements of single-qubit Pauli X, Y, and Z operators. This novel computational feature is related to the "genuine" 2D SPTO possessed by our state, and which is absent in the cluster state. Our concrete connection between the latent computational complexity of many-body systems and macroscopic quantum orders may find applications in quantum many-body simulation for benchmarking classically intractable complexity.