Measurement-Based Quantum Computation on Symmetry Breaking Thermal States

TL;DR

This paper demonstrates that symmetry breaking thermal states in an interacting cluster Hamiltonian significantly improve the robustness of measurement-based quantum computation against thermal noise, enabling operation at higher temperatures.

Contribution

It introduces an interacting cluster Hamiltonian model that enhances MBQC robustness and proves topological protection below a critical temperature.

Findings

Long-range order enhances MBQC robustness.

MBQC is topologically protected below critical temperature.

Operation temperature can be increased by an order of magnitude.

Abstract

We consider measurement-based quantum computation (MBQC) on thermal states of the interacting cluster Hamiltonian containing interactions between the cluster stabilizers that undergoes thermal phase transitions. We show that the long-range order of the symmetry breaking thermal states below a critical temperature drastically enhance the robustness of MBQC against thermal excitations. Specifically, we show the enhancement in two-dimensional cases and prove that MBQC is topologically protected below the critical temperature in three-dimensional cases. The interacting cluster Hamiltonian allows us to perform MBQC even at a temperature an order of magnitude higher than that of the free cluster Hamiltonian.