# Squeezed fock-state code[1]

## Description

Approximate bosonic code that encodes a qubit into the same Fock state, but one which is squeezed in opposite directions.

Taking the Fock state \(|1\rangle\), the codewords are \begin{align} \begin{split} |\overline{0}\rangle&=S(r)|1\rangle \\ |\overline{1}\rangle&=S(-r)|1\rangle~, \end{split} \tag*{(1)}\end{align} where \(S(\pm r)\) is the squeezing operator with squeezing parameter \(\pm r\).

## Protection

The code approximately protects against loss and dephasing errors, becoming exact in the \(r\to\infty\) limit.

## Parents

- Single-mode bosonic code
- Amplitude-damping (AD) code — The squeezed Fock-state code approximately protects against loss and dephasing errors, becoming exact in the \(r\to\infty\) limit.
- Approximate quantum error-correcting code (AQECC) — The squeezed Fock-state code approximately protects against loss and dephasing errors, becoming exact in the \(r\to\infty\) limit.

## Cousin

- Squeezed cat code — Squeezed Fock-state codes and squeezed cat codes both utilize squeezing to approximately protect against loss errors.

## References

- [1]
- S. B. Korolev, E. N. Bashmakova, and T. Yu. Golubeva, “Error Correction Using Squeezed Fock States”, (2023) arXiv:2312.16000

## Page edit log

- Victor V. Albert (2023-12-30) — most recent

## Cite as:

“Squeezed fock-state code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/squeezed_fock_state