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Incorporate Jonathan's corrections to Abstract

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Andreas Tsouchlos
2026-05-04 15:36:15 +02:00
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@@ -4,6 +4,8 @@
\Ac{qec} protects fragile quantum states against decoherence by \Ac{qec} protects fragile quantum states against decoherence by
encoding logical information into a larger number of physical qubits. encoding logical information into a larger number of physical qubits.
To obtain parity information on an encoded state without disturbing it, a
syndrome extraction is performed.
Because the syndrome extraction circuitry is itself implemented on Because the syndrome extraction circuitry is itself implemented on
noisy quantum hardware, practical \ac{qec} must be fault-tolerant, noisy quantum hardware, practical \ac{qec} must be fault-tolerant,
accounting for errors introduced by the correction procedure itself. accounting for errors introduced by the correction procedure itself.
@@ -19,31 +21,31 @@ can be decoded.
Together, these factors pose a serious challenge for practical decoders. Together, these factors pose a serious challenge for practical decoders.
Sliding-window decoding addresses this challenge by exploiting the Sliding-window decoding addresses this challenge by exploiting the
repeated structure of the syndrome extraction circuitry, partitioning repeated structure of the syndrome extraction circuitry, partitioning
the \ac{dem}'s check matrix into overlapping windows that can be the check matrix of the \ac{dem} into overlapping windows that can be
decoded sequentially. decoded sequentially.
This allows for an earlier start to the decoding process, before all Therefore, decoding can begin as soon as the syndrome components
syndrome measurements have been completed, thereby lowering the latency. associated with the first window have been measured.
% Our work: Identify research gap % Our work: Identify research gap
In this thesis, we perform a review of the existing literature on In this thesis, we perform a review of the existing literature on
sliding-window decoding and draw an analogy to windowed sliding-window decoding and draw an analogy to windowed
decoding for classical spatially-coupled low-density parity-check decoding of classical spatially-coupled low-density parity-check
(\acs{sc}-\acs{ldpc}) codes. (\acs{sc}-\acs{ldpc}) codes.
We recognize that in contrast to the latter, existing realizations We recognize that in contrast to the latter, existing realizations
of sliding-window decoding for \ac{qec} discard the soft information of sliding-window decoding for \ac{qec} discard the soft information
produced inside one window before moving to the next. produced inside one window before moving to the subsequent window.
% Our work: Warm-start % Our work: Warm-start
% TODO: Quantify improvement. Also for conclusion % TODO: Quantify improvement. Also for conclusion
We propose warm-start sliding-window decoding, in which the To take this information into account, we propose warm-start
\ac{bp} messages on the edges crossing into the overlap region of the previous sliding-window decoding, in which the \ac{bp} messages on the edges
window are reused to initialize the corresponding messages of the crossing into the overlap region of the previous window are reused to
next window. initialize the corresponding messages of the next window.
The warm start is formulated first for plain \ac{bp} and then extended to The warm start is formulated first for standard \ac{bp} and then extended to
\ac{bp} with guided decimation (\acs{bpgd}). \ac{bp} with guided decimation (\acs{bpgd}).
For both plain min-sum \ac{bp} and \ac{bpgd} decoding, the warm-start For both standard \ac{bp} and \ac{bpgd} decoding, the warm-start
initialization provides a consistent improvement across all examined initialization provides a consistent improvement across all examined
parameter settings. parameter settings.
We attribute this to an effective increase in \ac{bp} iterations on We attribute this to an effective increase in \ac{bp} iterations on