Topological color codes on Union Jack lattices: A stable implementation of the whole Clifford group
arXiv:0910.0573 · doi:10.1103/PhysRevA.81.012319
Abstract
We study the error threshold of topological color codes on Union Jack lattices that allow for the full implementation of the whole Clifford group of quantum gates. After mapping the error-correction process onto a statistical mechanical random 3-body Ising model on a Union Jack lattice, we compute its phase diagram in the temperature-disorder plane using Monte Carlo simulations. Surprisingly, topological color codes on Union Jack lattices have similar error stability than color codes on triangular lattices, as well as the Kitaev toric code. The enhanced computational capabilities of the topological color codes on Union Jack lattices with respect to triangular lattices and the toric code demonstrate the inherent robustness of this implementation.
8 pages, 4 figures, 1 table
References in corpus (19)
- Non-Abelian Anyons and Topological Quantum Computation
- A Rydberg Quantum Simulator
- Topological Quantum Distillation
- Experimental demonstration of topological error correction
- Topological Computation without Braiding
- Optimal Resources for Topological 2D Stabilizer Codes: Comparative Study
- Exact Topological Quantum Order in D=3 and Beyond: Branyons and Brane-Net Condensates
- Error Threshold for Color Codes and Random 3-Body Ising Models
- Topological Subsystem Codes
- Homological Error Correction: Classical and Quantum Codes
- On measurement-based quantum computation with the toric code states
- Completeness of the classical 2D Ising model and universal quantum computation
- Locations of multicritical points for spin glasses on regular lattices
- Strong-disorder paramagnetic-ferromagnetic fixed point in the square-lattice +- J Ising model
- Statistical Mechanical Models and Topological Color Codes
- Unifying all classical spin models in a Lattice Gauge Theory
- Graphical algorithms and threshold error rates for the 2d colour code
- Self-Correcting Quantum Computers
- Experimental demonstration of topological error correction
Cited by in corpus (24)
- Quantum Error Correction for Beginners
- Roads towards fault-tolerant universal quantum computation
- Surface code implementation of block code state distillation
- Coping with qubit leakage in topological codes
- Universal topological phase of 2D stabilizer codes
- Structure of 2D Topological Stabilizer Codes
- Subsystem codes with spatially local generators
- Scalable in-situ qubit calibration during repetitive error detection
- Error Thresholds for Abelian Quantum Double Models: Increasing the bit-flip Stability of Topological Quantum Memory
- A decoder for the triangular color code by matching on a Möbius strip
- Optimal Thresholds for Fracton Codes and Random Spin Models with Subsystem Symmetry
- The random Blume-Capel model on cubic lattice: first order inverse freezing in a 3D spin-glass system
- Analytic asymptotic performance of topological codes
- Simulating the Transverse Ising Model on a Quantum Computer: Error Correction with the Surface Code
- Generalized Toric Codes Coupled to Thermal Baths
- The role of entropy in topological quantum error correction
- Fundamental thresholds of realistic quantum error correction circuits from classical spin models
- Stability of topologically-protected quantum computing proposals as seen through spin glasses
- Analyticity of the energy in an Ising spin glass with correlated disorder
- Frustration in vicinity of transition point of Ising spin glasses
- Transversal Clifford and T-gate codes of short length and high distance
- Resource comparison of two surface code implementations of small angle Z rotations
- Construction of Hyperbolic Signal Sets from the Uniformization of Hyperelliptic Curves
- Ion-Trap Chip Architecture Optimized for Implementation of Quantum Error-Correcting Code