Constraints on measurement-based quantum computation in effective cluster states

TL;DR

This paper investigates the physical limitations of measurement-based quantum computation in effective low-energy cluster states, highlighting their fragility under certain perturbations and implications for practical implementations.

Contribution

It provides a detailed analysis of the stability of effective cluster states in perturbative regimes, identifying conditions that compromise their robustness.

Findings

Effective cluster states are fragile against specific external perturbations.

Optimal working conditions depend on temperature and system parameters.

Implications for implementing low-energy models with strong multi-site interactions.

Abstract

The aim of this work is to study the physical properties of a one-way quantum computer in an effective low-energy cluster state. We calculate the optimal working conditions as a function of the temperature and of the system parameters. The central result of our work is that any effective cluster state implemented in a perturbative framework is fragile against special kinds of external perturbations. Qualitative aspects of our work are important for any implementation of effective low-energy models containing strong multi-site interactions.