Description
A concatenated code whose outer code is a bosonic code. In other words, a bosonic code that can be thought of as a concatenation of a possibly non-bosonic inner code and another bosonic outer code.
Decoding
Decoder exploiting analog information from the outer code for bosonic codes concatenated with qubit QLDPC codes [1].
Parents
- Bosonic code
- Concatenated quantum code — A concatenated bosonic code is a bosonic code that can be thought of as a concatenation of a possibly non-bosonic outer code and another bosonic inner code.
Cousins
- Coherent-state constellation code — Coherent-state constellation codes consisting of points from a Gaussian quadrature rule can be concatenated with quantum polar codes to achieve the Gaussian coherent information of the thermal noise channel [2,3].
- Dual-rail quantum code — The KLM protocol, one of the first protocols for fault-tolerant quantum computation, utilizes concatenations of the dual-rail code with a stabilizer code [4]. Concatenating the dual-rail code with an \([[n,k,d]]\) stabilizer code yields an \([[2n,k,d]]\) constant-excitation code [5] that protects against \(d-1\) AD errors [6]. Concatenating the outer dual-rail code with an inner single-mode bosonic code yields several gates that are independent of the inner code [7].
- Two-mode binomial code — Two-mode binomial codes can be concatenated with repetition codes to yield bosonic analogues of QPCs [8].
- Hybrid cat code — Hybrid cat codes can be concatenated with RBH codes [9].
References
- [1]
- L. Berent et al., “Analog Information Decoding of Bosonic Quantum Low-Density Parity-Check Codes”, PRX Quantum 5, (2024) arXiv:2311.01328 DOI
- [2]
- F. Lacerda, J. M. Renes, and V. B. Scholz, “Coherent-state constellations and polar codes for thermal Gaussian channels”, Physical Review A 95, (2017) arXiv:1603.05970 DOI
- [3]
- F. Lacerda, J. M. Renes, and V. B. Scholz, “Coherent state constellations for Bosonic Gaussian channels”, 2016 IEEE International Symposium on Information Theory (ISIT) (2016) DOI
- [4]
- E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics”, Nature 409, 46 (2001) DOI
- [5]
- Y. Ouyang, “Avoiding coherent errors with rotated concatenated stabilizer codes”, npj Quantum Information 7, (2021) arXiv:2010.00538 DOI
- [6]
- R. Duan et al., “Multi-error-correcting amplitude damping codes”, 2010 IEEE International Symposium on Information Theory (2010) arXiv:1001.2356 DOI
- [7]
- H.-K. Lau and M. B. Plenio, “Universal Quantum Computing with Arbitrary Continuous-Variable Encoding”, Physical Review Letters 117, (2016) arXiv:1605.09278 DOI
- [8]
- M. Bergmann and P. van Loock, “Quantum error correction against photon loss using NOON states”, Physical Review A 94, (2016) arXiv:1512.07605 DOI
- [9]
- J. Lee et al., “Fault-tolerant quantum computation by hybrid qubits with bosonic cat-code and single photons”, (2023) arXiv:2401.00450
Page edit log
- Victor V. Albert (2023-11-05) — most recent
Cite as:
“Concatenated bosonic code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/oscillators_concatenated