Measurement-based quantum computation in symmetry protected topological states of one-dimensional integer spin systems

TL;DR

This paper extends the algebraic framework for measurement-based quantum computation to include integer spin chains in one-dimensional symmetry protected topological states, linking quantum information processing with condensed matter physics.

Contribution

The work generalizes existing MBQC frameworks to integer spins and identifies a key order parameter for computational efficiency in spin-1 chains.

Findings

Integer spin chains can be incorporated into MBQC frameworks.

The computational order parameter matches the string order parameter in the Haldane phase.

Framework unifies quantum computation and condensed matter topological phases.

Abstract

In this work, we generalize the algebraic framework for measurement-based quantum computation (MBQC) in one-dimensional symmetry protected topological states recently developed in [Quantum 7, 1215 (2023)], such that in addition to half-odd-integer spins, the integer spin chains can also be incorporated in the framework. The computational order parameter characterizing the efficiency of MBQC is identified, which, for spin-$1$ chains in the Haldane phase, coincides with the conventional string order parameter in condensed matter physics.