Symmetry-protected phases for measurement-based quantum computation

TL;DR

This paper explores symmetry-protected topological phases in 1D spin systems, demonstrating that such phases can inherently support robust measurement-based quantum gates, making quantum computation more resilient to imperfections.

Contribution

It introduces a class of symmetry-protected topological orders that guarantee perfect identity gate operations in measurement-based quantum computation.

Findings

Symmetry-protected phases ensure robust identity gates.

Measurement-based gates can be phase-wide properties.

Protection by symmetry enhances quantum gate stability.

Abstract

Ground states of spin lattices can serve as a resource for measurement-based quantum computation. Ideally, the ability to perform quantum gates via measurements on such states would be insensitive to small variations in the Hamiltonian. Here, we describe a class of symmetry-protected topological orders in one-dimensional systems, any one of which ensures the perfect operation of the identity gate. As a result, measurement-based quantum gates can be a robust property of an entire phase in a quantum spin lattice, when protected by an appropriate symmetry.