Topological phases of matter, Quantum Error Correction and Topological twist

TL;DR

This paper explores topological phases, particle condensations, and error correction in topological quantum models, introducing a new efficient algorithm and examining effects of lattice twisting on quantum states.

Contribution

It introduces a novel error correction algorithm for the Doubled Semion model and investigates the impact of lattice twisting on topological quantum states and logical subspaces.

Findings

More efficient error detection and correction for Doubled Semion model.

Lattice twisting affects UMTCs and logical subspaces, revealing 'wormholes' phenomena.

Insights into topological phase transitions via particle condensation.

Abstract

Unitary Modular Tensor Categories(UMTC) have a one-to-one correspondence with Topological Quantum Field Theories (TQFT). Different identifications have been made so far associating different physical particle types (anyons) to different UMTCs. However, the area of anyon model transformations has not been discovered much, which correspond to topological phase transitions. Physical condensation of particles (quasi-particles) can correspond to functors between different UMTCs. This paper discusses a special case of doubled semion condensation. We also give an error detection and correction algorithm for the Doubled Semion model which is more efficient than the previously suggested ones. At last, we present some results about twisting the underlying lattice structure and see its effects on UMTCs and logical subspaces e.g., for Ising, Doubled Semion models, and a combination of these. This suggests some interesting "wormholes" phenomenon.