Concatenated quantum code
A combination of two codes, an inner code \(C\) and an outer code \(C^\prime\), where the physical subspace used for the outer code consists of the logical subspace of the inner code. In other words, first one encodes in the outer code \(C^\prime\), and then one encodes each of the physical registers of \(C^\prime\) in an inner code \(C\).
The first method to achieve a fault-tolerant computational threshold uses concatenated stabilizer codes .
- Concatenated code
- Quantum divisible code — A fault-tolerant \(T\) gate on the five-qubit or Steane code can be obtained by concatenating with particular quantum divisible codes.
- Quantum parity code (QPC) — A QPC is a concatenation of a phase-flip repetition code with a bit-flip repetition code.
- Shor \([[9,1,3]]\) code — Shor's code is a concatenation of a three-qubit bit-flip with a three-qubit phase-flip repetition code.
Zoo code information
- E. Knill, R. Laflamme, and W. H. Zurek, “Resilient quantum computation: error models and thresholds”, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences 454, 365 (1998). DOI; quant-ph/9702058
- Dorit Aharonov and Michael Ben-Or, “Fault-Tolerant Quantum Computation With Constant Error Rate”. quant-ph/9906129
- J. Preskill, “Reliable quantum computers”, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences 454, 385 (1998). DOI; quant-ph/9705031
- Panos Aliferis, Daniel Gottesman, and John Preskill, “Quantum accuracy threshold for concatenated distance-3 codes”. quant-ph/0504218
“Concatenated quantum code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/quantum_concatenated