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

• Published in: npj quantum information Vol. 2; no. 1; p. 16036
• Main Authors: Miller, Jacob, Miyake, Akimasa
• Format: Journal Article
• Language: English
• Published: London Nature Publishing Group UK 15.11.2016; Nature Publishing Group
• Subjects: 639/766/483/3926; 639/766/483/481; Classical and Quantum Gravitation; Physics; Physics and Astronomy; Quantum Computing; Quantum Field Theories; Quantum Information Technology; Quantum Physics; Relativity Theory; Spintronics; String Theory
• ISSN: 2056-6387; 2056-6387
• DOI: 10.1038/npjqi.2016.36

Measurement-based quantum computation (MQC) is a paradigm for studying quantum computation using many-body entanglement and single-qubit measurements. Although 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 utilise recent advances in the subject of symmetry-protected topological order (SPTO) to introduce a novel MQC resource state, whose physical and computational behaviour differs fundamentally from that of 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. Quantum physical states: The benefit of symmetries Researchers have discovered a quantum state of matter with advantageous properties for quantum computing. Jacob Miller and Akimasa Miyake from the University of New Mexico in the United States studied the physical states that form the basis for many quantum computing systems. Quantum states can require complex operations to achieve the desired computational task. In searching for a scalable implementation, Miller and Miyake focused on a class of two-dimensional states of topological matter with certain symmetries. These symmetries not only give a natural means of encoding quantum information, but also help to protect the integrity of the state against undesirable decay processes. Furthermore, the encoded information can be processed with physical measurements more easily, making the use of symmetry-protected states an attractive alternative to conventional realizations of quantum computing.