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 α ( n...
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| Published in: | Quantum (Vienna, Austria) Vol. 5; p. 595 |
|---|---|
| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
02.12.2021
|
| ISSN: | 2521-327X, 2521-327X |
| Online Access: | Get full text |
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| Summary: | 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
α
(
n
)
)
, where
n
is the number of physical qubits and
α
is the inverse of Ackermann's function, which is very slowly growing. For all practical purposes,
α
(
n
)
≤
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. |
|---|---|
| ISSN: | 2521-327X 2521-327X |
| DOI: | 10.22331/q-2021-12-02-595 |