skip to main content
Caltech

IQIM Postdoctoral and Graduate Student Seminar

Friday, April 24, 2015
4:00pm to 5:00pm
Add to Cal
East Bridge 114
Unfolding the color code
Alex Kubica, Graduate Student - Preskill Group,

Abstract: The topological color code and the toric code are two leading candidates for realizing fault-tolerant quantum computation. In the talk, I will start with introducing these two models. Then, I will show that the color code in d dimensions is equivalent to multiple decoupled copies of the d-dimensional toric code up to local unitary transformations and adding or removing ancilla qubits. This finding generalizes the previous results for two-dimensional systems to higher dimensions and to systems without translation invariance. I will also analyze the case of codes with boundaries and explain how one can attach d+1 copies of the d-dimensional toric code in order to obtain the d-dimensional color code. In particular, for d=2, I show that the (triangular) color code with boundaries is equivalent to the (folded) toric code with boundaries. The last result concerns implementability of a logical non-Pauli gate from the d-th level of the Clifford hierarchy in the d-dimensional color code. In particular, I present how the d-qubit control-Z logical gate can be fault-tolerantly implemented on the stack of d copies of the toric code by a local unitary transformation, saturating the bound by Bravyi and Koenig.

 

This is a joint work with Beni Yoshida and Fernando Pastawski.

http://arxiv.org/abs/1503.02065

For more information, please contact Marcia Brown by phone at 626-395-4013 or by email at [email protected].