Constructions and Noise Threshold of Topological Subsystem Codes
arXiv:1012.0425 · doi:10.1088/1751-8113/44/15/155301
Abstract
Topological subsystem codes proposed recently by Bombin are quantum error correcting codes defined on a two-dimensional grid of qubits that permit reliable quantum information storage with a constant error threshold. These codes require only the measurement of two-qubit nearest-neighbor operators for error correction. In this paper we demonstrate that topological subsystem codes (TSCs) can be viewed as generalizations of Kitaev's honeycomb model to trivalent hypergraphs. This new connection provides a systematic way of constructing TSCs and analyzing their properties. We also derive a necessary and sufficient condition under which a syndrome measurement in a subsystem code can be reduced to measurements of the gauge group generators. Furthermore, we propose and implement some candidate decoding algorithms for one particular TSC assuming perfect error correction. Our Monte Carlo simulations indicate that this code, which we call the five-squares code, has a threshold against depolarizing noise of at least 2%.
30 pages, 16 figures, submitted to Jour. Phys. A
References in corpus (7)
- Fault-tolerant quantum computation with high threshold in two dimensions
- Topological Quantum Distillation
- Topological fault-tolerance in cluster state quantum computation
- An exact chiral spin liquid with non-Abelian anyons
- Quantum computing with nearest neighbor interactions and error rates over 1%
- A no-go theorem for a two-dimensional self-correcting quantum memory based on stabilizer codes
- Subsystem fault tolerance with the Bacon-Shor code
Cited by in corpus (34)
- Quantum Error Correction for Quantum Memories
- Quantum memories at finite temperature
- Sparse Blossom: correcting a million errors per core second with minimum-weight matching
- A Fault-Tolerant Honeycomb Memory
- Structure of 2D Topological Stabilizer Codes
- Floquet codes without parent subsystem codes
- Pauli stabilizer models of twisted quantum doubles
- Pauli topological subsystem codes from Abelian anyon theories
- Benchmarking the Planar Honeycomb Code
- Subsystem codes with high thresholds by gauge fixing and reduced qubit overhead
- Characterization of solvable spin models via graph invariants
- Multi-qubit parity measurement in circuit quantum electrodynamics
- Quantum memories and error correction
- Handling Leakage with Subsystem Codes
- Constructions and performance of hyperbolic and semi-hyperbolic Floquet codes
- Quantum computation from dynamic automorphism codes
- Optimal error correction in topological subsystem codes
- The XYZ hexagonal stabilizer code
- Generalized Toric Codes Coupled to Thermal Baths
- Topological quantum error correction in the Kitaev honeycomb model
- Topological Subsystem Codes From Graphs and Hypergraphs
- Fermionic approach to variational quantum simulation of Kitaev spin models
- Sparse Quantum Codes from Quantum Circuits
- Homological Quantum Rotor Codes: Logical Qubits from Torsion
- Optimal quantum subsystem codes in 2-dimensions
- Weight Reduced Stabilizer Codes with Lower Overhead
- Free-Fermion Subsystem Codes
- Hexagonal matching codes with 2-body measurements
- Quantum subspace expansion approach for simulating dynamical response functions of Kitaev spin liquids
- Relation Between Surface Codes and Hypermap-Homology Quantum Codes
- Quantum simulation and ground state preparation for the honeycomb Kitaev model
- Contextuality of Quantum Error-Correcting Codes
- Planar Floquet Codes
- Decoding Algorithms for Hypergraph Subsystem Codes and Generalized Subsystem Surface Codes