Oscillator-into-oscillator code[1][2]

Description

Encodes Hilbert space of \(\ell^2\)-normalizable functions on \(\mathbb{R}^k\) into that on \(\mathbb{R}^n\). Usually denoted as \(((n,k))_{\mathbb{R}}\).

Parent

  • Bosonic code — Bosonic code with infinite-dimensional logical subspace.

Children

Zoo code information

Internal code ID: oscillators_into_oscillators

Your contribution is welcome!

on github.com (edit & pull request)

edit on this site

Zoo Code ID: oscillators_into_oscillators

Cite as:
“Oscillator-into-oscillator code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/oscillators_into_oscillators
BibTeX:
@incollection{eczoo_oscillators_into_oscillators, title={Oscillator-into-oscillator code}, booktitle={The Error Correction Zoo}, year={2022}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/oscillators_into_oscillators} }
Permanent link:
https://errorcorrectionzoo.org/c/oscillators_into_oscillators

References

[1]
S. Lloyd and J.-J. E. Slotine, “Analog Quantum Error Correction”, Physical Review Letters 80, 4088 (1998). DOI; quant-ph/9711021
[2]
S. L. Braunstein, “Error Correction for Continuous Quantum Variables”, Physical Review Letters 80, 4084 (1998). DOI; quant-ph/9711049

Cite as:

“Oscillator-into-oscillator code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/oscillators_into_oscillators

Github: https://github.com/errorcorrectionzoo/eczoo_data/tree/main/codes/quantum/oscillators/oscillators_into_oscillators.yml.