Union-find decoder for surface code achieves finite threshold under circuit-level stochastic errors with quasi-polylog parallel runtime bound.
Optimal Resources for Topological 2D Stabilizer Codes: Comparative Study
2 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
abstract
We study the resources needed to construct topological 2D stabilizer codes as a way to estimate in part their efficiency and this leads us to perform a comparative study of surface codes and color codes. This study clarifies the similarities and differences between these two types of stabilizer codes. We compute the error correcting rate $C:=n/d^2$ for surface codes $C_s$ and color codes $C_c$ in several instances. On the torus, typical values are $C_s=2$ and $C_c=3/2$, but we find that the optimal values are $C_s=1$ and $C_c=9/8$. For planar codes, a typical value is $C_s=2$, while we find that the optimal values are $C_s=1$ and $C_c=3/4$. In general, a color code encodes twice as much logical qubits as a surface code does.
fields
quant-ph 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
Concatenates Laflamme and Iceberg codes with selective filtering for a partially fault-tolerant quantum computation scheme that simulations indicate performs reliably at realistic noise levels.
citing papers explorer
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Proof of a finite threshold for the union-find decoder
Union-find decoder for surface code achieves finite threshold under circuit-level stochastic errors with quasi-polylog parallel runtime bound.
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Fire and ice: Partially fault-tolerant quantum computing with selective state filtering
Concatenates Laflamme and Iceberg codes with selective filtering for a partially fault-tolerant quantum computation scheme that simulations indicate performs reliably at realistic noise levels.