Almost-linear time decoding algorithm for topological codes
In order to build a large scale quantum computer, one must be able to correct errors extremely fast. We design a fast decoding algorithm for topological codes to correct for Pauli errors and erasure and combination of both errors and erasure. Our algorithm has a worst case complexity of $O(n \alpha(...
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Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
2021
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oai:doaj.org-article:99b602641df348c0b03502e6d25c52102021-12-02T16:06:54ZAlmost-linear time decoding algorithm for topological codes2521-327X10.22331/q-2021-12-02-595https://doaj.org/article/99b602641df348c0b03502e6d25c52102021-12-01T00:00:00Zhttps://quantum-journal.org/papers/q-2021-12-02-595/pdf/https://doaj.org/toc/2521-327XIn order to build a large scale quantum computer, one must be able to correct errors extremely fast. We design a fast decoding algorithm for topological codes to correct for Pauli errors and erasure and combination of both errors and erasure. Our algorithm has a worst case complexity of $O(n \alpha(n))$, where $n$ is the number of physical qubits and $\alpha$ is the inverse of Ackermann's function, which is very slowly growing. For all practical purposes, $\alpha(n) \leq 3$. We prove that our algorithm performs optimally for errors of weight up to $(d-1)/2$ and for loss of up to $d-1$ qubits, where $d$ is the minimum distance of the code. Numerically, we obtain a threshold of $9.9\%$ for the 2d-toric code with perfect syndrome measurements and $2.6\%$ with faulty measurements.Nicolas DelfosseNaomi H. NickersonVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenarticlePhysicsQC1-999ENQuantum, Vol 5, p 595 (2021) |
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DOAJ |
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DOAJ |
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EN |
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Physics QC1-999 |
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Physics QC1-999 Nicolas Delfosse Naomi H. Nickerson Almost-linear time decoding algorithm for topological codes |
| description |
In order to build a large scale quantum computer, one must be able to correct errors extremely fast. We design a fast decoding algorithm for topological codes to correct for Pauli errors and erasure and combination of both errors and erasure. Our algorithm has a worst case complexity of $O(n \alpha(n))$, where $n$ is the number of physical qubits and $\alpha$ is the inverse of Ackermann's function, which is very slowly growing. For all practical purposes, $\alpha(n) \leq 3$. We prove that our algorithm performs optimally for errors of weight up to $(d-1)/2$ and for loss of up to $d-1$ qubits, where $d$ is the minimum distance of the code. Numerically, we obtain a threshold of $9.9\%$ for the 2d-toric code with perfect syndrome measurements and $2.6\%$ with faulty measurements. |
| format |
article |
| author |
Nicolas Delfosse Naomi H. Nickerson |
| author_facet |
Nicolas Delfosse Naomi H. Nickerson |
| author_sort |
Nicolas Delfosse |
| title |
Almost-linear time decoding algorithm for topological codes |
| title_short |
Almost-linear time decoding algorithm for topological codes |
| title_full |
Almost-linear time decoding algorithm for topological codes |
| title_fullStr |
Almost-linear time decoding algorithm for topological codes |
| title_full_unstemmed |
Almost-linear time decoding algorithm for topological codes |
| title_sort |
almost-linear time decoding algorithm for topological codes |
| publisher |
Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften |
| publishDate |
2021 |
| url |
https://doaj.org/article/99b602641df348c0b03502e6d25c5210 |
| work_keys_str_mv |
AT nicolasdelfosse almostlineartimedecodingalgorithmfortopologicalcodes AT naomihnickerson almostlineartimedecodingalgorithmfortopologicalcodes |
| _version_ |
1718384857199935488 |