59 lines
2.8 KiB
TeX
59 lines
2.8 KiB
TeX
\chapter*{Abstract}
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% Current state of the art
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\Ac{qec} protects fragile quantum states against decoherence by
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encoding logical information into a larger number of physical qubits.
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To obtain parity information on an encoded state without disturbing it, a
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syndrome extraction is performed.
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Because the syndrome extraction circuitry is itself implemented on
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noisy quantum hardware, practical \ac{qec} must be fault-tolerant,
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accounting for errors introduced by the correction procedure itself.
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Fault tolerance considerations and the syndrome extraction circuit
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are captured by \acp{dem}, which provide a unified framework for passing
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this information to the decoder.
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Accounting for fault tolerance substantially inflates the
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decoding problem.
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At the same time, \ac{qec} imposes strict latency constraints due to
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the backlog problem, where syndrome data accumulates faster than it
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can be decoded.
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Together, these factors pose a serious challenge for practical decoders.
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Sliding-window decoding addresses this challenge by exploiting the
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repeated structure of the syndrome extraction circuitry, partitioning
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the check matrix of the \ac{dem} into overlapping windows that can be
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decoded sequentially.
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Therefore, decoding can begin as soon as the syndrome components
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associated with the first window have been measured.
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% Our work: Identify research gap
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In this thesis, we perform a review of the existing literature on
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sliding-window decoding and draw an analogy to windowed
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decoding of classical spatially-coupled low-density parity-check
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(\acs{sc}-\acs{ldpc}) codes.
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We recognize that in contrast to the latter, existing realizations
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of sliding-window decoding for \ac{qec} discard the soft information
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produced inside one window before moving to the subsequent window.
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% Our work: Warm-start
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% TODO: Quantify improvement. Also for conclusion
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To take this information into account, we propose warm-start
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sliding-window decoding, in which the \ac{bp} messages on the edges
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crossing into the overlap region of the previous window are reused to
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initialize the corresponding messages of the next window.
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The warm start is formulated first for standard \ac{bp} and then extended to
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\ac{bp} with guided decimation (\acs{bpgd}).
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For both standard \ac{bp} and \ac{bpgd} decoding, the warm-start
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initialization provides a consistent improvement across all examined
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parameter settings.
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We attribute this to an effective increase in \ac{bp} iterations on
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variable nodes in the overlap regions: each such VN is processed by
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multiple consecutive windows, and warm-starting lets these
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invocations accumulate iterations rather than restart from scratch.
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Crucially, the warm-start modification incurs no additional
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computational cost relative to cold-start decoding, as it differs
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only in the initialization of the \ac{bp} messages.
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