diff --git a/src/thesis/chapters/abstract.tex b/src/thesis/chapters/abstract.tex index b889141..61df5cc 100644 --- a/src/thesis/chapters/abstract.tex +++ b/src/thesis/chapters/abstract.tex @@ -4,6 +4,8 @@ \Ac{qec} protects fragile quantum states against decoherence by 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 noisy quantum hardware, practical \ac{qec} must be fault-tolerant, 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. Sliding-window decoding addresses this challenge by exploiting the 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. -This allows for an earlier start to the decoding process, before all -syndrome measurements have been completed, thereby lowering the latency. +Therefore, decoding can begin as soon as the syndrome components +associated with the first window have been measured. % Our work: Identify research gap In this thesis, we perform a review of the existing literature on 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. We recognize that in contrast to the latter, existing realizations 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 % TODO: Quantify improvement. Also for conclusion -We propose warm-start sliding-window decoding, in which the -\ac{bp} messages on the edges crossing into the overlap region of the previous -window are reused to initialize the corresponding messages of the -next window. -The warm start is formulated first for plain \ac{bp} and then extended to +To take this information into account, we propose warm-start +sliding-window decoding, in which the \ac{bp} messages on the edges +crossing into the overlap region of the previous window are reused to +initialize the corresponding messages of the next window. +The warm start is formulated first for standard \ac{bp} and then extended to \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 parameter settings. We attribute this to an effective increase in \ac{bp} iterations on