Low-depth random Clifford-circuit qubit code[1] 

Description

An \([[n,k]]\) qubit stabilizer code whose encoder is an \(n\)-qubit unitary transformation that takes a \(k\)-qubit state as input (with \(k\leq n\), and the remaining \(n-k\) qubits initialized to \(|0\rangle^{\otimes n-k}\) ) to give a corresponding state in the codespace as the output. An \(n\)-qubit quantum circuit with random two-qubit Clifford gates can act as an encoder into a code with distance \(d\) with high probability, with a size (i.e. number of gates in the circuit) at most \(O(n^2 log n)\)). Noting that two gates acting on disjoint qubits could in fact be executed simultaneously, this is equivalent to the depth (number of time steps in the circuit) being at most \(O(log^3 n)\).

Protection

Creates a random \([[n,k,d]]\) stabilizer code that detects errors on \(d-1\) qubits, and corrects errors on \(\left\lfloor (d-1)/2 \right\rfloor\) qubits.

Parents

References

[1]
W. Brown and O. Fawzi, “Short random circuits define good quantum error correcting codes”, 2013 IEEE International Symposium on Information Theory (2013) arXiv:1312.7646 DOI
Page edit log

Your contribution is welcome!

on github.com (edit & pull request)

edit on this site

Zoo Code ID: nonlocal_lowdepth

Cite as:
“Low-depth random Clifford-circuit qubit code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/nonlocal_lowdepth
BibTeX:
@incollection{eczoo_nonlocal_lowdepth, title={Low-depth random Clifford-circuit qubit code}, booktitle={The Error Correction Zoo}, year={2022}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/nonlocal_lowdepth} }
Share via:
Twitter | Mastodon |  | E-mail
Permanent link:
https://errorcorrectionzoo.org/c/nonlocal_lowdepth

Cite as:

“Low-depth random Clifford-circuit qubit code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/nonlocal_lowdepth

Github: https://github.com/errorcorrectionzoo/eczoo_data/tree/main/codes/quantum/qubits/dynamic_gen/random/nonlocal_lowdepth.yml.