Physics – Quantum Physics
Scientific paper
2006-09-10
J.Phys.A40:3481-3505,2007; J.Phys.A40:3481-3506,2007
Physics
Quantum Physics
26 pages, 5 figures
Scientific paper
10.1088/1751-8113/40/13/013
Surface codes describe quantum memory stored as a global property of interacting spins on a surface. The state space is fixed by a complete set of quasi-local stabilizer operators and the code dimension depends on the first homology group of the surface complex. These code states can be actively stabilized by measurements or, alternatively, can be prepared by cooling to the ground subspace of a quasi-local spin Hamiltonian. In the case of spin-1/2 (qubit) lattices, such ground states have been proposed as topologically protected memory for qubits. We extend these constructions to lattices or more generally cell complexes with qudits, either of prime level or of level $d^\ell$ for $d$ prime and $\ell \geq 0$, and therefore under tensor decomposition, to arbitrary finite levels. The Hamiltonian describes an exact $\mathbb{Z}_d\cong\mathbb{Z}/d\mathbb{Z}$ gauge theory whose excitations correspond to abelian anyons. We provide protocols for qudit storage and retrieval and propose an interferometric verification of topological order by measuring quasi-particle statistics.
Brennen Gavin K.
Bullock Stephen S.
No associations
LandOfFree
Qudit surface codes and gauge theory with finite cyclic groups does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Qudit surface codes and gauge theory with finite cyclic groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Qudit surface codes and gauge theory with finite cyclic groups will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-25828