Efficient Preparation of Solvable Anyons with Adaptive Quantum Circuits

TL;DR

This paper presents a method using adaptive quantum circuits to prepare and classify all solvable anyon theories with gapped boundaries, including non-Abelian anyons, advancing topological quantum state engineering.

Contribution

It introduces a sequential gauging and ungauging procedure with adaptive circuits to produce and manipulate topological states in solvable anyon theories, extending previous classifications.

Findings

Successfully prepares string-net ground states for various solvable anyon theories.

Extends classification to non-Abelian anyons with irrational quantum dimensions.

Demonstrates procedures on complex theories like doubled Ising and $SU(2)_4$ anyons.

Abstract

The classification of topological phases of matter is a fundamental challenge in quantum many-body physics, with applications to quantum technology. Recently, this classification has been extended to the setting of Adaptive Finite-Depth Local Unitary (AFDLU) circuits which allow global classical communication. In this setting, the trivial phase is the collection of all topological states that can be prepared via AFDLU. Here, we propose a complete classification of the trivial phase by showing how to prepare all solvable anyon theories that admit a gapped boundary via AFDLU, extending recent results on solvable groups. Our construction includes non-Abelian anyons with irrational quantum dimensions, such as Ising anyons, and more general acyclic anyons. Specifically, we introduce a sequential gauging procedure, with an AFDLU implementation, to produce a string-net ground state in any topological phase described by a solvable anyon theory with gapped boundary. In addition, we introduce a sequential ungauging and regauging procedure, with an AFDLU implementation, to apply string operators of arbitrary length for anyons and symmetry twist defects in solvable anyon theories. We apply our procedure to the quantum double of the group $S_3$ and to several examples that are beyond solvable groups, including the doubled Ising theory, the $\mathbb{Z}_3$ Tambara-Yamagami string-net, and doubled $SU(2)_4$ anyons.