Numerically optimized code[1][2]

Description

Bosonic Fock-state code obtained from a numerical minimization procedure, e.g., from enforcing error-correction criteria against some number of losses while minimizing average occupation number.

The smallest numerically optimized code is the \(\sqrt(17)\) code, \begin{align} \begin{split} |\overline{0}\rangle&=\frac{1}{\sqrt{6}}\left(\sqrt{7-\sqrt{17}}|0\rangle+\sqrt{\sqrt{17}-1}|3\rangle\right)\\ |\overline{1}\rangle&=\frac{1}{\sqrt{6}}\left(\sqrt{9-\sqrt{17}}|1\rangle-\sqrt{\sqrt{17}-3}|4\rangle\right)~, \end{split} \end{align} correcting a single loss error. The average occupation number of the codewords is \(\approx 1.6\), which is \(0.4\) photons lower than that of the smallest binomial code with the same level of protection.

Protection

Number phase codes protect from a finite number of loss events. However, unlike Fock-state codes, their protection does not stem from a Fock-state spacing.

Parent

Zoo code information

Internal code ID: numopt

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Zoo Code ID: numopt

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

References

[1]
M. H. Michael et al., “New Class of Quantum Error-Correcting Codes for a Bosonic Mode”, Physical Review X 6, (2016). DOI; 1602.00008
[2]
V. V. Albert et al., “Performance and structure of single-mode bosonic codes”, Physical Review A 97, (2018). DOI; 1708.05010

Cite as:

“Numerically optimized code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/numopt

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