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valbert4 committed Oct 7, 2024
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#######################################################
## This is a code entry in the error correction zoo. ##
## https://github.com/errorcorrectionzoo ##
#######################################################

code_id: ampdamp_post_selected
physical: qubits
logical: qubits

name: 'Post-selected PI code'
introduced: '\cite{arxiv:2410.00155}'

description: |
PI qubit code whose recovery succeeds at protecting against \hyperref[topic:ad]{AD} errors with a success probability less than one.
The simplest code admits a codeword basis of
\begin{align}
\begin{split}
|\overline{0}\rangle&=\frac{1}{\sqrt{3}}\left(|100\rangle+|010\rangle+|001\rangle\right)\\|\overline{1}\rangle&=|111\rangle~.
\end{split}
\end{align}
The code violates the diagonal part of the \term{Knill-Laflamme conditions}.
Nevertheless, the code admits a probabilistic recovery that protects against single losses and yields an infidelity of \hyperref[topic:asymptotics]{order} \(O(\gamma^2)\) in the noise rate \(\gamma\).
The failure probability of the recovery is of the same \hyperref[topic:asymptotics]{order} as the probability of the single loss errors, i.e., \(O(\gamma)\).
relations:
parents:
- code_id: qubit_permutation_invariant
- code_id: ampdamp


# Begin Entry Meta Information
_meta:
# Change log - most recent first
changelog:
- user_id: VictorVAlbert
date: '2024-10-05'
- user_id: SouravDutta
date: '2024-10-05'
- user_id: AdityaJain
date: '2024-10-05'
- user_id: PrabhaMandayam
date: '2024-10-05'
12 changes: 12 additions & 0 deletions users/users_db.yml
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#
- user_id: PrabhaMandayam
name: 'Prabha Mandayam'
gscholaruser: kHDUY0QAAAAJ

- user_id: AdityaJain
name: 'Aditya Jain'
gscholaruser: 29yVv_cAAAAJ

- user_id: SouravDutta
name: 'Sourav Dutta'
gscholaruser: STv-HycAAAAJ

- user_id: ShiJieSamuelTan
name: 'Shi Jie Samuel Tan'
gscholaruser: 57rSajgAAAAJ
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