Braiding defects in topological stabiliser codes of any dimension cannot be universal
arXiv:1811.11789
Abstract
Braiding defects in topological stabiliser codes has been widely studied as a promising approach to fault-tolerant quantum computing. We present a no-go theorem that places very strong limitations on the potential of such schemes for universal fault-tolerant quantum computing in any spatial dimension. In particular, we show that, for the natural encoding of quantum information in defects in topological stabiliser codes, the set of logical operators implementable by braiding defects is contained in the Clifford group. Indeed, we show that this remains true even when supplemented with locality-preserving logical operators.
arXiv comment6 pages; results from this preprint are now fully contained in the longer manuscript arXiv:1906.01045 (published as Phys. Rev. A 102, 022403 (2020))
References in corpus (29)
- Anyons in an exactly solved model and beyond
- Universal Quantum Computation with ideal Clifford gates and noisy ancillas
- Quantum Error Correction for Quantum Memories
- Fault-tolerant quantum computation with high threshold in two dimensions
- Topological Quantum Distillation
- Topological fault-tolerance in cluster state quantum computation
- High threshold universal quantum computation on the surface code
- Topological Order with a Twist: Ising Anyons from an Abelian Model
- Topological Computation without Braiding
- Braiding statistics of loop excitations in three dimensions
- Theory of defects in Abelian topological states
- Single-shot fault-tolerant quantum error correction
- Classification of Topological Defects in Abelian Topological States
- Fault-tolerant logical gates in quantum error-correcting codes
- Three-dimensional surface codes: Transversal gates and fault-tolerant architectures
- A fault-tolerant non-Clifford gate for the surface code in two dimensions
- Clifford Gates by Code Deformation
- Cheshire charge in (3+1)-D topological phases
- Protected gates for topological quantum field theories
- Sorting topological stabilizer models in three dimensions
- Universal Quantum Computation with Gapped Boundaries
- Fault-Tolerant Quantum Gates with Defects in Topological Stabiliser Codes
- Locality-Preserving Logical Operators in Topological Stabiliser Codes
- Changing topology by topological defects in three-dimensional topologically ordered phases
- Generalized Cluster States Based on Finite Groups
- 2D quantum computation with 3D topological codes
- Universal fault-tolerant quantum computation with Bacon-Shor codes
- An Interferometry-Free Protocol for Demonstrating Topological Order
- Transversal gates and error propagation in 3D topological codes