Topological Quantum Error Correction with Optimal Encoding Rate
arXiv:quant-ph/0602063 · doi:10.1103/PhysRevA.73.062303
Abstract
We prove the existence of topological quantum error correcting codes with encoding rates asymptotically approaching the maximum possible value. Explicit constructions of these topological codes are presented using surfaces of arbitrary genus. We find a class of regular toric codes that are optimal. For physical implementations, we present planar topological codes.
REVTEX4 file, 5 figures
References in corpus (2)
Cited by in corpus (22)
- Topological Quantum Distillation
- Tradeoffs for reliable quantum information storage in 2D systems
- Optimal Resources for Topological 2D Stabilizer Codes: Comparative Study
- Exact Topological Quantum Order in D=3 and Beyond: Branyons and Brane-Net Condensates
- Homological Error Correction: Classical and Quantum Codes
- The boundaries and twist defects of the color code and their applications to topological quantum computation
- Logical blocks for fault-tolerant topological quantum computation
- Transversal Clifford gates on folded surface codes
- Measurement-free fault-tolerant quantum error correction in near-term devices
- Strategies for practical advantage of fault-tolerant circuit design in noisy trapped-ion quantum computers
- Topological Color Codes and Two-Body Quantum Lattice Hamiltonians
- Looped Pipelines Enabling Effective 3D Qubit Lattices in a Strictly 2D Device
- Quantum LDPC Codes for Modular Architectures
- The role of entropy in topological quantum error correction
- Codesign of quantum error-correcting codes and modular chiplets in the presence of defects
- Generalized surface codes and packing of logical qubits
- On the probabilistic quantum error correction
- Construction of optimal resources for concatenated quantum protocols
- Relation Between Surface Codes and Hypermap-Homology Quantum Codes
- Decoding Algorithms for Hypergraph Subsystem Codes and Generalized Subsystem Surface Codes
- Experimental measurement and a physical interpretation of quantum shadow enumerators
- On the Topological Origin of Entanglement in Ising Spin Glasses