Concatenation Schemes for Topological Fault-tolerant Quantum Error
Correction
- URL: http://arxiv.org/abs/2209.09390v2
- Date: Sun, 6 Aug 2023 02:13:30 GMT
- Title: Concatenation Schemes for Topological Fault-tolerant Quantum Error
Correction
- Authors: Zhaoyi Li, Isaac Kim, Patrick Hayden
- Abstract summary: We propose fault-tolerant quantum error correction schemes based on the concatenation of small error detection codes with the three-dimensional cluster state.
We find a set of codes for which such a conversion is possible, and study their performance against the standard circuit-level depolarizing model.
Our best performing scheme, which is based on a concatenation with a classical code, improves the threshold by $16.5%$ and decreases the spacetime overhead by $32%$.
- Score: 1.6114012813668934
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: We investigate a family of fault-tolerant quantum error correction schemes
based on the concatenation of small error detection or error correction codes
with the three-dimensional cluster state. We propose fault-tolerant state
preparation and decoding schemes that effectively convert every circuit-level
error into an erasure error, leveraging the cluster state's high threshold
against such errors. We find a set of codes for which such a conversion is
possible, and study their performance against the standard circuit-level
depolarizing model. Our best performing scheme, which is based on a
concatenation with a classical code, improves the threshold by $16.5\%$ and
decreases the spacetime overhead by $32\%$ compared to the scheme without
concatenation, with each scheme subject to a physical error rate of $10^{-3}$
and achieving a logical error rate of $10^{-6}$.
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