Topologically protected measurement-based quantum computation on the thermal state of a nearest-neighbor two-body Hamiltonian with spin-3/2 particles

TL;DR

This paper demonstrates that the thermal state of a nearest-neighbor two-body Hamiltonian with only spin-3/2 particles can support topologically protected measurement-based quantum computation, with a threshold temperature comparable to previous systems.

Contribution

It shows that a cluster state suitable for topological quantum computation can be generated from a spin-3/2 thermal state, expanding the class of feasible physical systems.

Findings

Threshold temperature for spin-3/2 system is comparable to previous models.

High-connectivity cluster states can be efficiently generated.

Topologically protected quantum computation is possible with spin-3/2 thermal states.

Abstract

Recently, Li {\it et al.} [Phys. Rev. Lett. {\bf 107}, 060501 (2011)] have demonstrated that topologically protected measurement-based quantum computation can be implemented on the thermal state of a nearest-neighbor two-body Hamiltonian with spin-2 and spin-3/2 particles provided that the temperature is smaller than a critical value, namely, threshold temperature. Here we show that the thermal state of a nearest-neighbor two-body Hamiltonian, which consists of only spin-3/2 particles, allows us to perform topologically protected measurement-based quantum computation. The threshold temperature is calculated and turns out to be comparable to that with the spin-2 and spin-3/2 system. Furthermore, we generally show that a cluster state of high connectivity can be efficiently generated from the thermal state of the spin-3/2 system without severe thermal noise accumulation.