# Universal Quantum Computation with Gapped Boundaries.

@article{Cong2017UniversalQC, title={Universal Quantum Computation with Gapped Boundaries.}, author={Iris Cong and Meng Cheng and Zhenghan Wang}, journal={Physical review letters}, year={2017}, volume={119 17}, pages={ 170504 } }

This Letter discusses topological quantum computation with gapped boundaries of two-dimensional topological phases. Systematic methods are presented to encode quantum information topologically using gapped boundaries, and to perform topologically protected operations on this encoding. In particular, we introduce a new and general computational primitive of topological charge measurement and present a symmetry-protected implementation of this primitive. Throughout the Letter, a concrete physical…

## 29 Citations

### Mathematics of Topological Quantum Computing

- Physics
- 2017

In topological quantum computing, information is encoded in "knotted" quantum states of topological phases of matter, thus being locked into topology to prevent decay. Topological precision has been…

### The boundaries and twist defects of the color code and their applications to topological quantum computation

- Computer ScienceQuantum
- 2018

This work builds upon the abstract theory of boundaries and domain walls of topological phases of matter to comprehensively catalog the objects realizable in color codes and provides lattice representations of these objects which include three new types of boundaries as well as a generating set for all 72 color code twist defects.

### Electric-magnetic duality of $\mathbb{Z}_2$ symmetry enriched cyclic Abelian lattice gauge theory

- Physics
- 2022

Kitaev’s quantum double model is a lattice gauge theoretic realization of Dijkgraaf-Witten topological quantum field theory (TQFT), its topologically protected ground state space has broad…

### Numerical investigation of gapped edge states in fractional quantum Hall-superconductor heterostructures

- Physics
- 2017

Fractional quantum Hall-superconductor heterostructures may provide a platform towards non-abelian topological modes beyond Majoranas. However their quantitative theoretical study remains extremely…

### Fault-tolerant quantum gates with defects in topological stabilizer codes

- Computer Science
- 2020

This work presents an approach to implement the full Clifford group via braiding in any code possessing twist defects on which a fermion can condense, and shows how the no-go theorems can be circumvented to provide a universal scheme in three-dimensional surface codes without magic state distillation.

### Tunneling Topological Vacua via Extended Operators: (Spin-)TQFT Spectra and Boundary Deconfinement in Various Dimensions

- Physics
- 2018

Distinct quantum vacua of topologically ordered states can be tunneled into each other via extended operators. The possible applications include condensed matter and quantum cosmology. We present a…

### Fractional quantum Hall states with gapped boundaries in an extreme lattice limit

- PhysicsPhysical Review B
- 2019

We present a detailed microscopic investigation of fractional quantum Hall states with gapped boundaries in a coupled bilayer lattice model featuring holes whose counterpropagating chiral edge states…

### Measuring the Unique Identifiers of Topological Order Based on Boundary-Bulk Duality and Anyon Condensation

- Physics
- 2020

A topological order is a new quantum phase that is beyond Landau's symmetry-breaking paradigm. Its defining features include robust degenerate ground states, long-range entanglement and anyons. It…

### Prediction of Toric Code Topological Order from Rydberg Blockade

- PhysicsPhysical Review X
- 2021

The physical realization of $\mathbb Z_2$ topological order as encountered in the paradigmatic toric code has proven to be an elusive goal. We show that this phase of matter can be created in a…

### Beyond anyons

- PhysicsModern Physics Letters A
- 2018

The theory of anyon systems, as modular functors topologically and unitary modular tensor categories algebraically, is mature. To go beyond anyons, our first step is the interplay of anyons with…

## References

SHOWING 1-10 OF 25 REFERENCES

### Topological Quantum Computation with Gapped Boundaries

- Physics
- 2016

This paper studies fault-tolerant quantum computation with gapped boundaries. We first introduce gapped boundaries of Kitaev's quantum double models for Dijkgraaf-Witten theories using their…

### Quantum computation

- Physics
- 1996

The theory of quantum computation can be constructed from the abstract study of anyonic systems. In mathematical terms, these are unitary topological modular functors. They underlie the Jones…

### Surface codes: Towards practical large-scale quantum computation

- Physics, Computer Science
- 2012

The concept of the stabilizer, using two qubits, is introduced, and the single-qubit Hadamard, S and T operators are described, completing the set of required gates for a universal quantum computer.

### Universal quantum computation with weakly integral anyons

- PhysicsQuantum Inf. Process.
- 2015

This work analyzes the computational power of the first non-abelian anyon system with only integral quantum dimensions and sets up three qutrit computational models, finding a universal gate set for each model.

### String-net condensation: A physical mechanism for topological phases

- Physics
- 2005

We show that quantum systems of extended objects naturally give rise to a large class of exotic phases---namely topological phases. These phases occur when extended objects, called ``string-nets,''…

### Charge 2e/3 Superconductivity and Topological Degeneracies without Localized Zero Modes in Bilayer Fractional Quantum Hall States.

- PhysicsPhysical review letters
- 2016

It is demonstrated that an analog of non-Abelian braiding is possible, despite the absence of a localized zero mode, and the superconductor induces charge 2e/3 quasiparticle-pair condensation at each boundary of the FQH state.

### The Quantum Double Model with Boundary: Condensations and Symmetries

- Mathematics
- 2011

Associated to every finite group, Kitaev has defined the quantum double model for every orientable surface without boundary. In this paper, we define boundaries for this model and characterize…

### Symmetry fractionalization, defects, and gauging of topological phases

- MathematicsPhysical Review B
- 2019

We examine the interplay of symmetry and topological order in $2+1$ dimensional topological phases of matter. We present a definition of the topological symmetry group, which characterizes the…

### Classification and analysis of two-dimensional Abelian fractional topological insulators

- Physics
- 2012

We present a general framework for analyzing fractionalized, time reversal invariant electronic insulators in two dimensions. The framework applies to all insulators whose quasiparticles have abelian…

### Gapped domain walls, gapped boundaries, and topological degeneracy.

- Mathematics, PhysicsPhysical review letters
- 2015

By studying many examples, this work finds evidence that the tunneling matrices are powerful quantities to classify different types of gapped domain walls, including closed 2-manifolds and open 2- manifolds with gapped boundaries.