Quantum BCH Codes: Classical Codes, Quantised
Quantum BCH codes are built from classical BCH codes. Their history, how they encode quantum information and how decoding works.
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The Quantum Hamming Code and Its Bound
The quantum Hamming bound limits how efficiently codes can correct errors. The five-qubit perfect code, quantum Hamming codes and their costs.
Majorana Fermion Codes: Hardware-Level Protection
Majorana zero modes could store qubits non-locally and process them by braiding. The theory, error correction role and experimental status.
Kitaev’s Code: The Origin of Topological Protection
Kitaev’s contributions to topological error correction: the toric code, anyons and the idea of protecting qubits through topological order.
The Toric Code: Kitaev’s Topological Memory
The toric code stores qubits in the topology of a lattice on a torus. Stabilizers, anyons, logical operators and why local errors do little harm.
CSS Codes: Calderbank-Shor-Steane Construction
CSS codes build a quantum code from two classical codes, one for bit flips and one for phase flips. The construction, examples and uses.
Stabilizer Codes: The Framework Behind Most QEC
Stabilizer codes define protected qubit states as the joint +1 eigenstates of commuting Pauli operators. How they detect and correct errors.
Quantum Reed-Muller Codes and Their Gate Sets
Quantum Reed-Muller codes are built from classical polynomial codes and support useful transversal gates. Their construction, uses and limits.
Concatenated Quantum Codes: Stacking Protection
Concatenated codes nest one error-correcting code inside another so error rates fall with each level. Design, fault tolerance and trade-offs.
Topological Quantum Codes: Protection by Geometry
Topological quantum codes store information in global properties of a lattice, following Kitaev’s work. Key concepts, implementations and challenges.
Quantum LDPC Codes: Low Overhead Error Correction
Quantum LDPC codes use sparse parity checks to protect qubits with less overhead than surface codes. Their principles, decoding and prospects.
The Surface Code: The Leading Path to Fault Tolerance
The surface code stores logical qubits in a 2D lattice of physical qubits. Stabilizer measurements, error thresholds, scaling and recent experiments.