Union-find decoder for surface code achieves finite threshold under circuit-level stochastic errors with quasi-polylog parallel runtime bound.
Quantum Error Correction for Quantum Memories
3 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
abstract
Active quantum error correction using qubit stabilizer codes has emerged as a promising, but experimentally challenging, engineering program for building a universal quantum computer. In this review we consider the formalism of qubit stabilizer and subsystem stabilizer codes and their possible use in protecting quantum information in a quantum memory. We review the theory of fault-tolerance and quantum error-correction, discuss examples of various codes and code constructions, the general quantum error correction conditions, the noise threshold, the special role played by Clifford gates and the route towards fault-tolerant universal quantum computation. The second part of the review is focused on providing an overview of quantum error correction using two-dimensional (topological) codes, in particular the surface code architecture. We discuss the complexity of decoding and the notion of passive or self-correcting quantum memories. The review does not focus on a particular technology but discusses topics that will be relevant for various quantum technologies.
fields
quant-ph 3years
2026 3representative citing papers
Knill error correction reduces circuit-level decoding for quantum LDPC codes to the simpler code-capacity decoder while remaining fault-tolerant under locally decaying noise.
A homological framework identifies necessary and sufficient obstruction conditions for transversal logical diagonal gates in quantum CSS codes.
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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Simplified circuit-level decoding using Knill error correction
Knill error correction reduces circuit-level decoding for quantum LDPC codes to the simpler code-capacity decoder while remaining fault-tolerant under locally decaying noise.
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Homological origin of transversal implementability of logical diagonal gates in quantum CSS codes
A homological framework identifies necessary and sufficient obstruction conditions for transversal logical diagonal gates in quantum CSS codes.