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Topological Quantum Distillation
H. Bombin, M. A. Martin-Delgado
TL;DR
Quantum entanglement distillation relies on Clifford-group operations, motivating topological implementations that protect quantum information without explicit syndrome correction. The paper constructs triangular topological codes implementing the Clifford group without selective addressing, extending the approach to teleportation, superdense coding, and magic-state computation.
Problem
Quantum entanglement distillation requires Clifford-group operations, while topological quantum information protocols seek protection from local errors without explicit syndrome measurement and correction.
Method
The paper introduces color codes and triangular codes based on lattice geometry, colored borders, homology, and string operators, with suitably chosen lattices implementing Clifford operations topologically.
Results
Triangular codes implement the whole Clifford group fault tolerantly and topologically without selective addressing or quasiparticle braiding, supporting entanglement distillation, teleportation, and superdense coding.
Takeaways & Limitations
The codes provide topological implementations of several Clifford-based protocols using ground-state operators rather than quasiparticle excitations.
Takeaways & Limitations
Implementing the phase-shift gate K generally requires a suitable lattice because the bitwise operation may not preserve ground states.
Abstract
from arXiv · showhide
We construct a class of topological quantum codes to perform quantum entanglement distillation. These codes implement the whole Clifford group of unitary operations in a fully topological manner and without selective addressing of qubits. This allows us to extend their application also to quantum teleportation, dense coding and computation with magic states.