Fault-Tolerant Quantum Computing: The Threshold
Fault-tolerant quantum computing and the threshold theorem: how codes, syndrome measurement and careful circuits keep errors from spreading.
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Quantum Error Correction
Qubits are fragile. Surface codes, stabilizers, fault tolerance and error mitigation — the engineering that turns noisy hardware into reliable computation.
68 articles
Subsystem Surface Codes and Simpler Measurement
Subsystem surface codes replace some stabilizer measurements with simpler gauge measurements on a lattice. Benefits and implementation challenges.
Rotated Surface Codes: Fewer Qubits, Same Distance
The rotated surface code achieves the same distance as the standard surface code with about half the qubits. Layout, features and experiments.
Homological Product Codes: Topology as Error Control
Homological product codes use algebraic topology to build quantum codes. Their principles, encoding and decoding, and role in error correction.
Hypergraph Product Codes: The Route to Good qLDPC
Hypergraph product codes combine two classical codes into a quantum LDPC code. How the product works and why it matters for error correction.
Quantum RS-MDS Codes: Hitting the Singleton Bound
Quantum MDS codes meet the quantum Singleton bound. How Reed-Solomon constructions yield them, their properties and their encoding.
Finite Geometry Quantum Codes and Their Structure
Quantum codes built from finite geometries such as projective spaces. Incidence structures, encoding, error correction and applications.
Quantum Polar Codes: Channel Polarisation for Qubits
Quantum polar codes use channel polarization to achieve the capacity of some quantum channels. How they are built and what limits them.
Quantum Turbo Product Codes: Two Dimensions of Parity
Quantum turbo product codes combine product constructions with iterative decoding. Their structure, advantages, applications and open questions.
Quantum Reed-Solomon Codes and Their Distance
Quantum Reed-Solomon codes adapt classical Reed-Solomon codes to qudits. Their structure, correction capability and implementation challenges.
Non-Abelian Anyon Codes: Braiding as Computation
Non-abelian anyons change a state when braided, which could give fault-tolerant gates. Codes built on them and experimental progress.
Quantum Double Codes and Their Anyon Models
Quantum double codes generalize the toric code to any finite group and host richer anyon models. Their construction and error correction.
