Qudit-into-oscillator code

Description

Encodes \(K\)-dimensional Hilbert space into Hilbert space of \(\ell^2\)-normalizable functions on \(\mathbb{R}^n\).

Decoding

Given an encoding of a finite-dimensional code, a decoder that yields the optimal entanglement fidelity can be obtained by solving a semi-definite program [1][2] (see also Ref. [3]). This approximate QEC technique can be adapted to bosonic codes as long as they are restricted to a finite-dimensional subspace of the oscillator Hilbert space [4].

Parent

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

Children

Cousins

Zoo code information

Internal code ID: qudits_into_oscillators

Your contribution is welcome!

on github.com (edit & pull request)

edit on this site

Zoo Code ID: qudits_into_oscillators

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

References

[1]
K. Audenaert and B. De Moor, “Optimizing completely positive maps using semidefinite programming”, Physical Review A 65, (2002). DOI; quant-ph/0109155
[2]
M. Reimpell and R. F. Werner, “Iterative Optimization of Quantum Error Correcting Codes”, Physical Review Letters 94, (2005). DOI; quant-ph/0307138
[3]
Andrew S. Fletcher, “Channel-Adapted Quantum Error Correction”. 0706.3400
[4]
V. V. Albert et al., “Performance and structure of single-mode bosonic codes”, Physical Review A 97, (2018). DOI; 1708.05010

Cite as:

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

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