Boundaries for the Honeycomb Code

Abstract

We introduce a simple construction of boundary conditions for the honeycomb code that uses only pairwise checks and allows parallelogram geometries at the cost of modifying the bulk measurement sequence. We discuss small instances of the code.

11 pages, 7 figures; v2 final version in Quantum

References in corpus (8)

• Topological Quantum Distillation
• Optimal Resources for Topological 2D Stabilizer Codes: Comparative Study
• Dynamically Generated Logical Qubits
• A magic state's fidelity can be superior to the operations that created it
• A Fault-Tolerant Honeycomb Memory
• Optimization of the surface code design for Majorana-based qubits
• A family of stabilizer codes for $D({\mathbb{Z}}_2)$ anyons and Majorana modes
• Planar Floquet Codes

Cited by in corpus (38)

• Relaxing Hardware Requirements for Surface Code Circuits using Time-dynamics
• Floquet codes without parent subsystem codes
• Anyon condensation and the color code
• Topology, criticality, and dynamically generated qubits in a stochastic measurement-only Kitaev model
• Adiabatic paths of Hamiltonians, symmetries of topological order, and automorphism codes
• Pauli topological subsystem codes from Abelian anyon theories
• Benchmarking the Planar Honeycomb Code
• Short-Depth Circuits for Dicke State Preparation
• Unifying flavors of fault tolerance with the ZX calculus
• Constructions and performance of hyperbolic and semi-hyperbolic Floquet codes
• Stability Experiments: The Overlooked Dual of Memory Experiments
• Engineering 3D Floquet codes by rewinding
• Quantum computation from dynamic automorphism codes
• Crystalline Quantum Circuits
• Tailoring quantum error correction to spin qubits
• The XYZ${}^2$ hexagonal stabilizer code
• Topological error correcting processes from fixed-point path integrals
• Fermionic approach to variational quantum simulation of Kitaev spin models
• Fault-tolerant quantum architectures based on erasure qubits
• Comparative study of quantum error correction strategies for the heavy-hexagonal lattice
• Cross-cap defects and fault-tolerant logical gates in the surface code and the honeycomb Floquet code
• Improved Pairwise Measurement-Based Surface Code
• Dynamical Logical Qubits in the Bacon-Shor Code
• XYZ ruby code: Making a case for a three-colored graphical calculus for quantum error correction in spacetime
• Accommodating Fabrication Defects on Floquet Codes with Minimal Hardware Requirements
• Error Correction in Dynamical Codes
• Tailoring Dynamical Codes for Biased Noise: The X${}^3$Z${}^3$ Floquet Code
• Distributed quantum error correction based on hyperbolic Floquet codes
• Minimising surface-code failures using a color-code decoder
• Contextuality of Quantum Error-Correcting Codes
• Multiqubit Rydberg Gates for Quantum Error Correction
• Competing automorphisms and disordered Floquet codes
• Phases of Floquet code under local decoherence
• Phase Transition of Topological Index driven by Dephasing
• Increasing the distance of topological codes with time vortex defects
• A dynamic circuit for the honeycomb Floquet code
• Subsystem many-hypercube codes: High-rate concatenated codes with low-weight syndrome measurements
• Logical operations with a dynamical qubit in Floquet-Bacon-Shor code