Compare commits
86 Commits
final-v1.2
...
001ca614bb
| Author | SHA1 | Date | |
|---|---|---|---|
| 001ca614bb | |||
| 9e5eaaf985 | |||
| 17191382cf | |||
| aa907ef4a3 | |||
| 12036caa91 | |||
| 4c206ae9c4 | |||
| 01a754e5da | |||
| 81292a2644 | |||
| 73958d7850 | |||
| 18e3683502 | |||
| 1eb4db289e | |||
| f56cd05890 | |||
| e9d996155d | |||
| 5e26179154 | |||
| 9ae98e07d7 | |||
| 728c8560c7 | |||
| dd30b4fc0d | |||
| 6e53ed5d1b | |||
| 0016df0004 | |||
| 9ca2698d38 | |||
| 72461fe555 | |||
| 5fabe2e146 | |||
| a90458dd8a | |||
| d2960b8f0e | |||
| 6b1821fd6b | |||
| 5687499b5b | |||
| f4718b67e7 | |||
| 0848e5dea6 | |||
| 7e18985b86 | |||
| 152e784546 | |||
| 15190ccf48 | |||
| 606d68e2c1 | |||
| 47493a6beb | |||
| 76a91c7d32 | |||
| 1632f19c47 | |||
| 3d3556689e | |||
| 4555570665 | |||
| 3b7618e1d1 | |||
| 635c0aab18 | |||
| c555151b9d | |||
| 05348579f0 | |||
| 1059b4d98f | |||
| 682eeb644e | |||
| 27f13c1db0 | |||
| 8071c9f485 | |||
| 94e4c9f8c9 | |||
| 64cf0e2269 | |||
| 76270695b9 | |||
| 62b4d4838b | |||
| 0aa425ae41 | |||
| b73a66649c | |||
| d7f05dc5b9 | |||
| 11178436b6 | |||
| dc283012ba | |||
| 87e48b5ac6 | |||
| 42a689d811 | |||
| b46df8120b | |||
| 5ced7b152e | |||
| 3953320216 | |||
| 4aa4799969 | |||
| f899942029 | |||
| a68e22d7f5 | |||
| 0955cdd14e | |||
| 7015f9d644 | |||
| b50308d014 | |||
| 93f310d843 | |||
| 163ef926e7 | |||
| 4da37dbddc | |||
| 6de9cec27e | |||
| 474b1d21da | |||
| 5483a972f9 | |||
| 5d104fbf28 | |||
| 50a10ccb4f | |||
| 569df381ee | |||
| 85771405db | |||
| 5875066581 | |||
| 494a639329 | |||
| e59120b683 | |||
| 267d431542 | |||
| 4e1bd62504 | |||
| ada6e43be3 | |||
| 6ea151ffeb | |||
| 6e2cf5b8ba | |||
| e792141afd | |||
| 1810ec8632 | |||
| 513eb7579f |
Submodule lib/cel-thesis updated: f783ba56a1...f4a0e66b88
@@ -1549,21 +1549,25 @@
|
||||
|
||||
\vspace*{-5mm}
|
||||
|
||||
\visible<3->{
|
||||
\begin{itemize}
|
||||
\visible<2->{
|
||||
\item Challenges
|
||||
}
|
||||
\begin{itemize}
|
||||
\visible<2->{
|
||||
\item Fault tolerance: Additional error locations \\
|
||||
$\implies$ \schlagwort{Increased decoding
|
||||
complexity} \citereferencemanual{GCR24}
|
||||
}
|
||||
\visible<3->{
|
||||
\item Quantum setting: Degeneracy and short
|
||||
cycles \\
|
||||
$\implies$ \schlagwort{Degraded performance}
|
||||
of belief propagation (BP)
|
||||
\citereferencemanual{BBA$^+$15}
|
||||
\item Fault tolerance: Additional error locations \\
|
||||
$\implies$ \schlagwort{Increased decoding
|
||||
complexity} \citereferencemanual{GCR24}
|
||||
\end{itemize}
|
||||
\end{itemize}
|
||||
}
|
||||
\end{itemize}
|
||||
\end{itemize}
|
||||
|
||||
\vspace*{8mm}
|
||||
|
||||
|
||||
@@ -3,21 +3,61 @@
|
||||
long=quantum error correction
|
||||
}
|
||||
|
||||
\DeclareAcronym{dem}{
|
||||
short=DEM,
|
||||
long=detector error model
|
||||
}
|
||||
|
||||
\DeclareAcronym{ler}{
|
||||
short=LER,
|
||||
long=logical error rate
|
||||
}
|
||||
|
||||
\DeclareAcronym{bp}{
|
||||
short=BP,
|
||||
long=belief propagation
|
||||
}
|
||||
|
||||
\DeclareAcronym{bpgd}{
|
||||
short=BPGD,
|
||||
long=belief propagation with guided decimation
|
||||
}
|
||||
|
||||
\DeclareAcronym{gdg}{
|
||||
short=GDG,
|
||||
long=guided decimation guessing
|
||||
}
|
||||
|
||||
\DeclareAcronym{nms}{
|
||||
short=NMS,
|
||||
long=normalized min-sum
|
||||
}
|
||||
|
||||
\DeclareAcronym{osd}{
|
||||
short=OSD,
|
||||
long=ordered statistics decoding
|
||||
}
|
||||
|
||||
\DeclareAcronym{aed}{
|
||||
short=AED,
|
||||
long=automorphism ensemble decoding
|
||||
}
|
||||
|
||||
\DeclareAcronym{bsc}{
|
||||
short=BSC,
|
||||
long=binary symetric channel
|
||||
}
|
||||
|
||||
\DeclareAcronym{spa}{
|
||||
short=SPA,
|
||||
long=sum-product algorithm
|
||||
}
|
||||
|
||||
\DeclareAcronym{css}{
|
||||
short=CSS,
|
||||
long=Calderbank-Shor-Steane
|
||||
}
|
||||
|
||||
\DeclareAcronym{llr}{
|
||||
short=LLR,
|
||||
long=log-likelihood ratio
|
||||
@@ -33,6 +73,11 @@
|
||||
long=low-density parity-check
|
||||
}
|
||||
|
||||
\DeclareAcronym{qldpc}{
|
||||
short=QLDPC,
|
||||
long=quantum low-density parity-check
|
||||
}
|
||||
|
||||
\DeclareAcronym{ml}{
|
||||
short=ML,
|
||||
long=maximum likelihood
|
||||
@@ -77,3 +122,23 @@
|
||||
short=PDF,
|
||||
long=probability density function
|
||||
}
|
||||
|
||||
\DeclareAcronym{bb}{
|
||||
short=BB,
|
||||
long=bivariate bicycle
|
||||
}
|
||||
|
||||
\DeclareAcronym{hgp}{
|
||||
short=HGP,
|
||||
long=hypergraph product
|
||||
}
|
||||
|
||||
\DeclareAcronym{lp}{
|
||||
short=LP,
|
||||
long=lifted-product
|
||||
}
|
||||
|
||||
\DeclareAcronym{bpc}{
|
||||
short=BPC,
|
||||
long=balanced product code
|
||||
}
|
||||
|
||||
File diff suppressed because it is too large
Load Diff
@@ -1 +1,197 @@
|
||||
\chapter{Introduction}
|
||||
\label{ch:Introduction}
|
||||
|
||||
\acresetall
|
||||
|
||||
% Intro to quantum computing
|
||||
|
||||
In 1982, Richard Feynman, motivated by the difficulty of simulating
|
||||
quantum-mechanical systems on classical hardware, put forward the
|
||||
idea of building computers that are themselves quantum mechanical
|
||||
\cite{feynman_simulating_1982}.
|
||||
The use of such quantum computers has since been shown to offer promising
|
||||
prospects not only with regard to simulating quantum systems but also
|
||||
for solving certain kinds of problems that are classically intractable.
|
||||
The most prominent example is Shor's algorithm for integer
|
||||
factorization \cite{shor_algorithms_1994}.
|
||||
|
||||
Similar to the way classical computers are built from bits and gates,
|
||||
quantum computers are built from \emph{qubits} and \emph{quantum gates}.
|
||||
Because of quantum entanglement, it is not enough to consider the
|
||||
qubits individually, we also have to consider correlations between them.
|
||||
For a system of $n$ qubits, this makes the state space grow with
|
||||
$2^n$ instead of linearly with $n$, as would be the case for a classical system
|
||||
\cite[Sec.~1]{gottesman_stabilizer_1997}.
|
||||
This is both the reason quantum systems are difficult to simulate and
|
||||
what provides them with their power \cite[Sec.~2.1]{roffe_decoding_2020}.
|
||||
|
||||
% The need for QEC
|
||||
|
||||
Realizing algorithms that leverage these quantum-mechanical effects
|
||||
requires hardware that can execute long quantum computations reliably.
|
||||
This poses a problem, because the qubits making up current devices
|
||||
are difficult to sufficiently isolate from their environment
|
||||
\cite[Sec.~1]{roffe_quantum_2019}.
|
||||
Their interaction with the environment acts as a continuous small-scale
|
||||
measurement, an effect we call \emph{decoherence} of the stored quantum
|
||||
state.
|
||||
Decoherence is the reason large systems don't exhibit visible quantum
|
||||
properties at human scales \cite[Sec.~1]{gottesman_stabilizer_1997}.
|
||||
|
||||
% Intro to QEC
|
||||
|
||||
\Ac{qec} has emerged as a leading candidate in solving this problem.
|
||||
It addresses the issue by encoding the information of $k$
|
||||
\emph{logical qubits} into a larger number $n>k$ of \emph{physical
|
||||
qubits}, in close analogy to classical channel coding
|
||||
\cite[Sec.~1]{roffe_quantum_2019}.
|
||||
The redundancy introduced this way can then be used to restore
|
||||
the quantum state, should it be disturbed.
|
||||
The quantum setting imposes some important constraints that do not exist in the
|
||||
classical case, however \cite[Sec.~2.4]{roffe_quantum_2019}:
|
||||
\begin{itemize}
|
||||
\item The no-cloning theorem prohibits the duplication of quantum states.
|
||||
\item In addition to the bit-flip errors we know from the
|
||||
classical setting, qubits are subject to \emph{phase-flips}.
|
||||
\item We are not allowed to directly measure the encoded qubits,
|
||||
as that would disturb their quantum states.
|
||||
\end{itemize}
|
||||
We can deal with the first constraint by not duplicating information, instead
|
||||
spreading the quantum state across the physical qubits
|
||||
\cite[Sec.~I]{calderbank_good_1996}.
|
||||
To deal with phase-flip errors, we must take special care when
|
||||
constructing \ac{qec} codes.
|
||||
Using \ac{css} codes, for example, we can use two separate classical
|
||||
binary linear codes to protect against the two kinds of errors
|
||||
\cite[Sec. 10.5.6]{nielsen_quantum_2010}.
|
||||
Finally, we can get around the last issue by using \emph{stabilizer
|
||||
measurements}.
|
||||
These are parity measurements that give us information about
|
||||
potential errors without revealing the underlying qubit states
|
||||
\cite[Sec.~II.C.]{babar_fifteen_2015}.
|
||||
This way, we perform a \emph{syndrome extraction} and base the
|
||||
subsequent decoding process on the measured syndrome.
|
||||
|
||||
Another difference between \ac{qec} and classical channel coding is
|
||||
the resource constraints.
|
||||
For \ac{qec}, low latency matters more than low overall computational
|
||||
complexity, due to the backlog problem
|
||||
\cite[Sec.~II.G.3.]{terhal_quantum_2015}: Certain gates turn
|
||||
single-qubit errors into multi-qubit ones, so errors must be
|
||||
corrected beforehand.
|
||||
A \ac{qec} system that is too slow accumulates a backlog at these points,
|
||||
causing exponential slowdown.
|
||||
|
||||
Several code constructions have been proposed for \ac{qec} codes over the years.
|
||||
Topological codes such as surface codes have been the industry
|
||||
standard for experimental applications for a long time
|
||||
\cite[Sec.~I]{koutsioumpas_colour_2025}, due to their
|
||||
reliance on only local connections between qubits
|
||||
\cite[Sec.~5]{roffe_decoding_2020}.
|
||||
Recently, \ac{qldpc} codes have been getting increasing
|
||||
attention as they have been shown to offer comparable thresholds with
|
||||
substantially improved encoding rates \cite[Sec.~1]{bravyi_high-threshold_2024}.
|
||||
\ac{qldpc} codes are generally decoded using a syndrome-based variant
|
||||
of the \ac{bp} algorithm \cite[Sec.~1]{roffe_decoding_2020}.
|
||||
We focus on \ac{qldpc} codes in our work and specifically \ac{bb} codes,
|
||||
as they are promising candidates for practical QEC due to their high
|
||||
encoding rates, large minimum distances, and short-depth syndrome
|
||||
extraction circuits \cite[Sec.~1]{bravyi_high-threshold_2024}.
|
||||
|
||||
% DEMs and fault tolerance
|
||||
|
||||
The syndrome extraction itself is implemented on quantum hardware and
|
||||
is therefore subject to the same noise as the data qubits.
|
||||
As a consequence, the \ac{qec} procedure, meant to protect the quantum
|
||||
state, itself introduces new \emph{internal errors}.
|
||||
A procedure is called \emph{fault-tolerant} if it remains effective
|
||||
even in the presence of these internal errors
|
||||
\cite[Sec.~4]{gottesman_introduction_2009}.
|
||||
To deal with internal errors that flip syndrome bits, multiple rounds
|
||||
of syndrome measurements are performed.
|
||||
|
||||
One approach of implementing fault tolerance is using \acp{dem}.
|
||||
A \ac{dem} abstracts away the underlying circuit,
|
||||
focusing only on the relationship between possible errors
|
||||
and their effects on the syndrome \cite[Sec.~1.4.3]{higgott_practical_2024}.
|
||||
A \emph{detector error matrix} is generated from the circuit, which is
|
||||
used for decoding instead of the original check matrix.
|
||||
Decoding under a \ac{dem} poses a challenge with respect to the
|
||||
latency constraint.
|
||||
This is because the detector error matrix is much larger than the
|
||||
check matrix of the underlying code, since it needs to represent many
|
||||
more error locations.
|
||||
For example, in our experiments using the $\llbracket 144,12,12
|
||||
\rrbracket$ \ac{bb} code with $12$ syndrome measurement rounds, the
|
||||
number of \acp{vn} grew from $144$ to $9504$ and the number of
|
||||
\acp{cn} grew from $72$ to $1008$.
|
||||
|
||||
To keep the latency of \ac{dem} decoding manageable, one approach is
|
||||
\emph{sliding-window decoding}.
|
||||
Instead of decoding on the entire detector error matrix at once,
|
||||
it is partitioned into several overlapping windows.
|
||||
Once decoding of one window is complete, error estimates on the initial part
|
||||
that is no longer needed are committed, and the next window is processed.
|
||||
This way, decoding can start as soon as the syndrome bits required
|
||||
for the first window have been extracted.
|
||||
The idea originates with the \emph{overlapping recovery} scheme
|
||||
proposed for the surface code in
|
||||
\cite[Sec.~IV.B]{dennis_topological_2002} and has since been studied
|
||||
for surface and toric codes \cite{kuo_fault-tolerant_2024} as well as
|
||||
for \ac{qldpc} codes under both phenomenological and circuit-level
|
||||
noise \cite{huang_increasing_2024,gong_toward_2024,kang_quits_2025}.
|
||||
|
||||
% Reseach gap + our work
|
||||
|
||||
We observe a structural similarity between sliding-window decoding for
|
||||
\acp{dem} and window decoding for \ac{sc}-\acs{ldpc} codes.
|
||||
In contrast to the latter, however, where \ac{bp} messages are
|
||||
carried between windows \cite[Sec.~III.~C.]{hassan_fully_2016},
|
||||
the existing realizations of sliding-window decoding for \ac{qec}
|
||||
discard the soft information produced inside one window before moving
|
||||
to the next.
|
||||
We propose \emph{warm-start sliding-window decoding}, in which the
|
||||
\ac{bp} messages from the overlap region of the previous window are
|
||||
reused to initialize \ac{bp} in the current window in place of the
|
||||
standard cold-start initialization.
|
||||
We formulate the warm start first for plain \ac{bp} and then for
|
||||
\ac{bpgd}, a variant of \ac{bp} with better convergence properties
|
||||
for \ac{qec} codes.
|
||||
The decoders are evaluated by Monte Carlo simulation on the
|
||||
$\llbracket 144,12,12 \rrbracket$ \ac{bb} code under standard
|
||||
circuit-based depolarizing noise over $12$ syndrome extraction rounds.
|
||||
The main finding is that warm-starting yields a consistent
|
||||
improvement at low iteration budgets, which is the regime relevant for
|
||||
low-latency operation.
|
||||
|
||||
% Outline of the Thesis
|
||||
|
||||
\Cref{ch:Fundamentals} reviews the fundamentals of classical and
|
||||
quantum error correction.
|
||||
On the classical side, it covers binary linear block codes,
|
||||
\ac{ldpc} and \ac{sc}-\ac{ldpc} codes, and the \ac{bp} decoding
|
||||
algorithm.
|
||||
On the quantum side, it introduces the relevant quantum mechanical
|
||||
notation, stabilizer measurements, stabilizer codes, \acf{css} codes,
|
||||
\ac{qldpc} codes, and the \ac{bpgd} algorithm.
|
||||
|
||||
\Cref{ch:Fault tolerance} introduces fault-tolerant \ac{qec}.
|
||||
It formalizes the notion of fault tolerance, presents the noise
|
||||
models considered in this work, and develops the \ac{dem} formalism
|
||||
through the measurement syndrome matrix, the detector matrix, and the
|
||||
detector error matrix.
|
||||
The chapter closes with a discussion of practical considerations
|
||||
including the choice of noise model, the per-round \acf{ler}, and the
|
||||
Stim toolchain.
|
||||
|
||||
\Cref{ch:Decoding} considers practical aspects of decoding under \acp{dem}.
|
||||
It reviews the existing literature on sliding-window decoding for
|
||||
\ac{qec}, develops the formal windowing construction we build upon,
|
||||
introduces the proposed warm-start sliding-window decoder for
|
||||
plain \ac{bp} and for \ac{bpgd}, and reports numerical results on the
|
||||
$\llbracket 144,12,12 \rrbracket$ \ac{bb} code.
|
||||
|
||||
% TODO: Possibly extend to mention specific proposed research directions
|
||||
\Cref{ch:Conclusion} concludes the thesis and outlines directions for
|
||||
further research.
|
||||
|
||||
|
||||
File diff suppressed because it is too large
Load Diff
File diff suppressed because it is too large
Load Diff
File diff suppressed because it is too large
Load Diff
@@ -1 +1,129 @@
|
||||
\chapter{Conclusion and Outlook}
|
||||
\label{ch:Conclusion}
|
||||
|
||||
% Recap of motivation
|
||||
|
||||
This thesis investigated decoding under \acp{dem} for fault-tolerant
|
||||
\ac{qec}, with a focus on low-latency decoding methods for \ac{qldpc} codes.
|
||||
The repetition of the syndrome measurements, especially under
|
||||
consideration of circuit-level noise, leads to a significant increase
|
||||
in decoding complexity: in our experiments on the $\llbracket
|
||||
144,12,12 \rrbracket$ \ac{bb} code with $12$ syndrome extraction
|
||||
rounds, the check matrix grew from 144 \acp{vn} and 72
|
||||
\acp{cn} to 9504 \acp{vn} and 1008 \acp{cn}.
|
||||
|
||||
% Recap of research gap and own work
|
||||
|
||||
Sliding-window decoding addresses the latency constraint by
|
||||
exploiting the time-like locality of the syndrome extraction circuit,
|
||||
which manifests as a block-diagonal structure in the detector error
|
||||
matrix when detectors are defined as the difference of consecutive
|
||||
syndrome measurement rounds.
|
||||
We drew a comparison to windowed decoding for \ac{sc}-\ac{ldpc}
|
||||
codes, but noted that the existing realizations of sliding-window
|
||||
decoding discard the soft information produced inside one window
|
||||
before moving to the next.
|
||||
Building on this observation, we proposed 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 initialise
|
||||
the corresponding messages of the next window in place of the
|
||||
standard cold-start initialisation.
|
||||
|
||||
We formulated the warm start first for plain \ac{bp} and then for
|
||||
\ac{bpgd}, the latter being attractive as an inner decoder because it
|
||||
addresses the convergence problems caused by short cycles and
|
||||
degeneracy in \ac{qldpc} Tanner graphs.
|
||||
The decoders were evaluated by Monte Carlo simulation on the
|
||||
$\llbracket 144,12,12 \rrbracket$ \ac{bb} code over $12$ syndrome
|
||||
extraction rounds under standard circuit-based depolarizing noise.
|
||||
We focused on a qualitative analysis, refraining from further
|
||||
optimizations such as introducing a normalization parameter for the
|
||||
min-sum algorithm.
|
||||
|
||||
% Recap of experimental conclusions
|
||||
|
||||
For plain min-sum \ac{bp}, the warm start was consistently beneficial
|
||||
across the parameter ranges we examined. The size of the gain depended
|
||||
on the overlap between consecutive windows: enlarging $W$ or
|
||||
shrinking $F$, both of which enlarge the overlap, raised the
|
||||
warm-start performance increase.
|
||||
We argued that the underlying mechanism is an effective increase in
|
||||
the number of \ac{bp} iterations spent on the \acp{vn} in the overlap
|
||||
region: each such \ac{vn} is processed by multiple consecutive window
|
||||
invocations, and the warm start lets these invocations accumulate
|
||||
iterations on the same \acp{vn} rather than restarting from scratch.
|
||||
The gain was most pronounced at low numbers of maximum iterations, where
|
||||
every additional iteration carries proportionally more information.
|
||||
|
||||
For \ac{bpgd}, we noted that more information is available in the
|
||||
overlap region of a window: in addition to the \ac{bp} messages,
|
||||
there is information about which \acp{vn} were decimated and to what value.
|
||||
Passing this decimation information to the next window in addition to
|
||||
the messages turned out to worsen the performance considerably, which
|
||||
we attributed to a premature hard decision of the \acp{vn} in the
|
||||
overlap region.
|
||||
Restricting the warm start to the \ac{bp} messages alone, removed this effect.
|
||||
The resulting message-only warm start recovered a consistent
|
||||
improvement over cold-start that followed the same qualitative
|
||||
behaviour as for plain \ac{bp}: larger overlap, achieved by larger
|
||||
$W$ or smaller $F$, yielded a larger gain, and the
|
||||
performance difference was most pronounced at low numbers of maximum iterations.
|
||||
|
||||
% Implications from experimental results
|
||||
|
||||
These observations imply that the warm-start modification to
|
||||
sliding-window decoding provides a consistent improvement, as long as
|
||||
some care is taken with specifying the information to be passed to
|
||||
the subsequent window.
|
||||
Note that this comes at no additional cost to the decoding complexity,
|
||||
since the only difference between warm- and cold-start sliding-window
|
||||
decoding is the initialization of the \ac{bp} messages.
|
||||
We expect similar behavior with other inner decoders that support
|
||||
soft information initialization in the overlap region.
|
||||
|
||||
% Further research
|
||||
|
||||
Several directions for further research emerge from this work.
|
||||
The most immediate is an extension of the evaluation to other
|
||||
\ac{qldpc} code families, to other circuit-level noise models such as
|
||||
SI1000 or EM3, and to a range of code sizes.
|
||||
This would clarify the generality of the gain due to the warm-start
|
||||
initialization.
|
||||
We expect the qualitative findings to carry over, since the
|
||||
underlying mechanism is structural rather than code-specific, but
|
||||
quantifying the gain across code families and noise models is left to
|
||||
future work.
|
||||
|
||||
A second direction is a systematic study of inner decoders under the
|
||||
warm-start framework.
|
||||
We considered plain min-sum \ac{bp} and \ac{bpgd}, but other
|
||||
algorithms used for \ac{qldpc} decoding, such as automorphism
|
||||
ensemble decoding \cite{koutsioumpas_automorphism_2025} or neural
|
||||
\ac{bp} \cite{miao_quaternary_2025} may admit warm-start variants of their own.
|
||||
|
||||
A third direction is a softer treatment of the decimation state in \ac{bpgd}.
|
||||
Rather than discarding the decimation information of the previous
|
||||
window entirely, as in the message-only warm start used here, one
|
||||
could encode the decimation decisions as strong but finite biases on
|
||||
the channel \acp{llr} of the next window, allowing the new window's parity
|
||||
checks to override them if the syndrome calls for it.
|
||||
This would interpolate between the two warm-start variants studied here and
|
||||
might combine the benefits of both.
|
||||
A related question is whether the decimation schedule itself should
|
||||
be aware of the window structure, for instance by deferring
|
||||
decimation of \acp{vn} in the overlap region until they have been
|
||||
visited by the next window.
|
||||
|
||||
A final direction is suggested by the structural similarity between
|
||||
sliding-window decoding for \acp{dem} and windowed decoding for
|
||||
\ac{sc}-\ac{ldpc} codes.
|
||||
The current approach to generating the syndrome extraction circuitry
|
||||
necessarily leads to a coupling width of one between adjacent
|
||||
syndrome measurement rounds.
|
||||
A natural question is whether the coupling width could be
|
||||
increased, e.g., by interleaving two separate realizations of the
|
||||
syndrome measurement circuitry instead of always repeating the same one.
|
||||
Work in this direction would also be a step toward bringing
|
||||
sliding-window decoding under DEMs within the scope of the analytical
|
||||
machinery developed for SC-LDPC codes.
|
||||
|
||||
|
||||
56
src/thesis/chapters/abstract.tex
Normal file
56
src/thesis/chapters/abstract.tex
Normal file
@@ -0,0 +1,56 @@
|
||||
\chapter*{Abstract}
|
||||
|
||||
% Current state of the art
|
||||
|
||||
\Ac{qec} protects fragile quantum states against decoherence by
|
||||
encoding logical information into a larger number of physical qubits.
|
||||
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.
|
||||
Fault tolerance considerations and the syndrome extraction circuit
|
||||
are captured by \acp{dem}, which provide a unified framework for passing
|
||||
this information to the decoder.
|
||||
|
||||
Accounting for fault tolerance substantially inflates the
|
||||
decoding problem.
|
||||
At the same time, \ac{qec} imposes strict latency constraints due to
|
||||
the backlog problem, where syndrome data accumulates faster than it
|
||||
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
|
||||
decoded sequentially.
|
||||
This allows for an earlier start to the decoding process, before all
|
||||
syndrome measurements have been completed, thereby lowering the latency.
|
||||
|
||||
% 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
|
||||
(\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.
|
||||
|
||||
% 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
|
||||
\ac{bp} with guided decimation (\acs{bpgd}).
|
||||
For both plain min-sum \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
|
||||
variable nodes in the overlap regions: each such VN is processed by
|
||||
multiple consecutive windows, and warm-starting lets these
|
||||
invocations accumulate iterations rather than restart from scratch.
|
||||
Crucially, the warm-start modification incurs no additional
|
||||
computational cost relative to cold-start decoding, as it differs
|
||||
only in the initialization of the \ac{bp} messages.
|
||||
|
||||
111
src/thesis/clean_bibliography.sh
Executable file
111
src/thesis/clean_bibliography.sh
Executable file
@@ -0,0 +1,111 @@
|
||||
sed -i "s/Świerkowska/{\\\\'S}wierkowska/" bibliography.bib
|
||||
sed -i "s/Héctor/H{\\\\'e}ctor/" bibliography.bib
|
||||
sed -i "s/Bombín/Bomb{\\\\'i}n/" bibliography.bib
|
||||
sed -i "s/Zémor/Z{\\\\'e}mor/" bibliography.bib
|
||||
sed -Ezi "s/\s(abstract|note|urldate|url|keywords|file) = \{[^}]*(\{[^}]*\}[^}]*)*\},?\n//g" bibliography.bib
|
||||
|
||||
# Normalize arXiv-only entries to @misc with howpublished = {arXiv:<id>}.
|
||||
# Detection: doi matches 10.48550/arXiv.<id>. The IEEEtranSA .bst's @article
|
||||
# handler needs a journal field (which preprints lack) and ignores publisher,
|
||||
# so for arXiv preprints we coerce the type to @misc and add howpublished
|
||||
# (the field the .bst actually prints for @misc).
|
||||
python3 - <<'PY'
|
||||
import re
|
||||
|
||||
path = "bibliography.bib"
|
||||
with open(path) as f:
|
||||
text = f.read()
|
||||
|
||||
doi_re = re.compile(r"doi\s*=\s*\{10\.48550/arXiv\.([^}]+)\}")
|
||||
type_re = re.compile(r"^@([A-Za-z]+)\{", re.MULTILINE)
|
||||
howpublished_re = re.compile(r"^\s*howpublished\s*=\s*\{", re.MULTILINE)
|
||||
title_field_re = re.compile(r"\b(title|booktitle)\s*=\s*\{", re.IGNORECASE)
|
||||
inner_brace_re = re.compile(r"\{([A-Za-z0-9]+)\}")
|
||||
|
||||
# Split into entries by scanning for top-level "@type{...}" blocks. We walk
|
||||
# brace depth so that the closing "}" of the entry is matched correctly even
|
||||
# if internal fields contain braces.
|
||||
def split_entries(s):
|
||||
out, i, n = [], 0, len(s)
|
||||
while i < n:
|
||||
m = type_re.search(s, i)
|
||||
if not m:
|
||||
out.append(("text", s[i:]))
|
||||
break
|
||||
if m.start() > i:
|
||||
out.append(("text", s[i:m.start()]))
|
||||
depth, j = 0, m.start()
|
||||
while j < n:
|
||||
c = s[j]
|
||||
if c == "{":
|
||||
depth += 1
|
||||
elif c == "}":
|
||||
depth -= 1
|
||||
if depth == 0:
|
||||
j += 1
|
||||
break
|
||||
j += 1
|
||||
out.append(("entry", s[m.start():j]))
|
||||
i = j
|
||||
return out
|
||||
|
||||
def normalize_arxiv(entry):
|
||||
doi_m = doi_re.search(entry)
|
||||
if not doi_m:
|
||||
return entry
|
||||
arxiv_id = doi_m.group(1)
|
||||
entry = type_re.sub("@misc{", entry, count=1)
|
||||
if not howpublished_re.search(entry):
|
||||
# insert howpublished as the last field, before the entry-closing "}"
|
||||
entry = re.sub(
|
||||
r"(,?)(\s*)\}\s*$",
|
||||
lambda m: ("," if m.group(1) != "," else m.group(1))
|
||||
+ m.group(2) + "\thowpublished = {arXiv:" + arxiv_id + "},\n}",
|
||||
entry,
|
||||
count=1,
|
||||
)
|
||||
return entry
|
||||
|
||||
# Strip protective braces around words inside title/booktitle values.
|
||||
# BibTeX uses "{Word}" inside titles to preserve case against the bibliography
|
||||
# style's title-casing rules. We keep that protection only when every character
|
||||
# inside the braces is non-lowercase (e.g. acronyms like {NASA}); for ordinary
|
||||
# words like {Quantum} we drop the braces so the style's casing applies.
|
||||
def strip_title_braces(entry):
|
||||
out, i, n = [], 0, len(entry)
|
||||
while True:
|
||||
m = title_field_re.search(entry, i)
|
||||
if not m:
|
||||
out.append(entry[i:])
|
||||
break
|
||||
out.append(entry[i:m.end()])
|
||||
depth, j = 1, m.end()
|
||||
while j < n and depth > 0:
|
||||
c = entry[j]
|
||||
if c == "{":
|
||||
depth += 1
|
||||
elif c == "}":
|
||||
depth -= 1
|
||||
if depth == 0:
|
||||
break
|
||||
j += 1
|
||||
value = entry[m.end():j]
|
||||
cleaned = inner_brace_re.sub(
|
||||
lambda mm: mm.group(1) if any(c.islower() for c in mm.group(1)) else mm.group(0),
|
||||
value,
|
||||
)
|
||||
out.append(cleaned)
|
||||
if j < n:
|
||||
out.append(entry[j])
|
||||
i = j + 1
|
||||
return "".join(out)
|
||||
|
||||
def transform(entry):
|
||||
return strip_title_braces(normalize_arxiv(entry))
|
||||
|
||||
parts = split_entries(text)
|
||||
new_text = "".join(transform(p) if kind == "entry" else p for kind, p in parts)
|
||||
|
||||
with open(path, "w") as f:
|
||||
f.write(new_text)
|
||||
PY
|
||||
188
src/thesis/copy_sim_results.sh
Executable file
188
src/thesis/copy_sim_results.sh
Executable file
@@ -0,0 +1,188 @@
|
||||
#!/bin/bash
|
||||
|
||||
BASE_PATH="/home/andreas/workspace/private/ma-sw-results/outputs/"
|
||||
|
||||
# Copy BP param exploration results
|
||||
|
||||
function post_process_LERs() {
|
||||
local filename="$1"
|
||||
|
||||
python3 -c "
|
||||
import pandas as pd
|
||||
import numpy as np
|
||||
|
||||
df = pd.read_csv('${filename}')
|
||||
df['LER_per_round'] = 1 - (1 - df['LER'])**(1/12)
|
||||
df['num_errors'] = df['num_trials'] * df['LER']
|
||||
df.to_csv('${filename}', index=False)
|
||||
"
|
||||
}
|
||||
|
||||
i=1
|
||||
sp="/-\|"
|
||||
|
||||
# echo "Copying BP param exploration results..."
|
||||
# echo -n ' '
|
||||
# for decoder in "WindowingSyndromeMinSumDecoder" "WindowingSyndromeSpaDecoder"; do
|
||||
# for max_iter in 32 200 5000; do
|
||||
# for pass_soft_info in "True" "False"; do
|
||||
# for F in 1 2 3; do
|
||||
# for W in 3 4 5; do
|
||||
# SRC_PATH="${BASE_PATH}+rust_exp=soft_v_hard_bp,decoder.class_name=${decoder},decoder.max_iter=${max_iter},decoder.pass_soft_info=${pass_soft_info},system.F=${F},system.W=${W}/"
|
||||
# LATEST_RESULTS_DIR=$(ls -t ${SRC_PATH} | head -1)
|
||||
# SRC_FILE="${SRC_PATH}/${LATEST_RESULTS_DIR}/LERs.csv"
|
||||
# DEST_DIR="res/sim/WF/${decoder}/max_iter_${max_iter}/pass_soft_info_${pass_soft_info}/F_${F}/W_${W}/"
|
||||
# mkdir -p ${DEST_DIR}
|
||||
# DEST_FILE="${DEST_DIR}/LERs.csv"
|
||||
# cp ${SRC_FILE} ${DEST_FILE}
|
||||
# post_process_LERs ${DEST_FILE}
|
||||
# printf "\b${sp:i++%${#sp}:1}"
|
||||
# done
|
||||
# done
|
||||
# done
|
||||
# done
|
||||
# done
|
||||
#
|
||||
# # Copy BPGD param exploration results
|
||||
#
|
||||
# echo -e "\rCopying BPGD param exploration results..."
|
||||
# echo -n ' '
|
||||
# for max_iter in 32 200 5000; do
|
||||
# for pass_soft_info in "True" "False"; do
|
||||
# for F in 1 2 3; do
|
||||
# for W in 3 4 5; do
|
||||
# SRC_PATH="${BASE_PATH}/+rust_exp=soft_v_hard_bpgd,decoder.class_name=WindowingSyndromeSpaGdDecoder,decoder.max_iter=${max_iter},decoder.pass_soft_info=${pass_soft_info},system.F=${F},system.W=${W}/"
|
||||
# LATEST_RESULTS_DIR=$(ls -t ${SRC_PATH} | head -1)
|
||||
# SRC_FILE="${SRC_PATH}/${LATEST_RESULTS_DIR}/LERs.csv"
|
||||
# DEST_DIR="res/sim/WF/WindowingSyndromeSpaGdDecoder/max_iter_${max_iter}/pass_soft_info_${pass_soft_info}/F_${F}/W_${W}/"
|
||||
# mkdir -p ${DEST_DIR}
|
||||
# DEST_FILE="${DEST_DIR}/LERs.csv"
|
||||
# cp ${SRC_FILE} ${DEST_FILE}
|
||||
# post_process_LERs ${DEST_FILE}
|
||||
# printf "\b${sp:i++%${#sp}:1}"
|
||||
# done
|
||||
# done
|
||||
# done
|
||||
# done
|
||||
#
|
||||
# # Copy BP over max iter. results
|
||||
#
|
||||
# echo -e "\rCopying BP over max. iter. results..."
|
||||
# echo -n ' '
|
||||
# for decoder in "WindowingSyndromeMinSumDecoder" "WindowingSyndromeSpaDecoder"; do
|
||||
# for p in 0.001 0.0025 0.004; do
|
||||
# for pass_soft_info in "True" "False"; do
|
||||
# for F in 1 2 3; do
|
||||
# for W in 3 4 5; do
|
||||
# SRC_PATH="${BASE_PATH}+rust_exp=max_iter_bp,decoder.class_name=${decoder},decoder.pass_soft_info=${pass_soft_info},simulation.phy_err_rate=${p},system.F=${F},system.W=${W}/"
|
||||
# LATEST_RESULTS_DIR=$(ls -t ${SRC_PATH} | head -1)
|
||||
# SRC_FILE="${SRC_PATH}/${LATEST_RESULTS_DIR}/LERs.csv"
|
||||
# DEST_DIR="res/sim/max_iter/${decoder}/p_${p}/pass_soft_info_${pass_soft_info}/F_${F}/W_${W}"
|
||||
# mkdir -p ${DEST_DIR}
|
||||
# DEST_FILE="${DEST_DIR}/LERs.csv"
|
||||
# cp ${SRC_FILE} ${DEST_FILE}
|
||||
# post_process_LERs ${DEST_FILE}
|
||||
# printf "\b${sp:i++%${#sp}:1}"
|
||||
# done
|
||||
# done
|
||||
# done
|
||||
# done
|
||||
# done
|
||||
#
|
||||
# # Copy BPGD over max iter. results
|
||||
#
|
||||
# echo -e "\rCopying BPGD over max. iter. results..."
|
||||
# echo -n ' '
|
||||
# for p in 0.001 0.0025 0.004; do
|
||||
# for pass_soft_info in "True" "False"; do
|
||||
# for F in 1 2 3; do
|
||||
# for W in 3 4 5; do
|
||||
# SRC_PATH="${BASE_PATH}+rust_exp=max_iter_bpgd,decoder.class_name=WindowingSyndromeSpaGdDecoder,decoder.pass_soft_info=${pass_soft_info},simulation.phy_err_rate=${p},system.F=${F},system.W=${W}/"
|
||||
# LATEST_RESULTS_DIR=$(ls -t ${SRC_PATH} | head -1)
|
||||
# SRC_FILE="${SRC_PATH}/${LATEST_RESULTS_DIR}/LERs.csv"
|
||||
# DEST_DIR="res/sim/max_iter/WindowingSyndromeSpaGdDecoder/p_${p}/pass_soft_info_${pass_soft_info}/F_${F}/W_${W}"
|
||||
# mkdir -p ${DEST_DIR}
|
||||
# DEST_FILE="${DEST_DIR}/LERs.csv"
|
||||
# cp ${SRC_FILE} ${DEST_FILE}
|
||||
# post_process_LERs ${DEST_FILE}
|
||||
# printf "\b${sp:i++%${#sp}:1}"
|
||||
# done
|
||||
# done
|
||||
# done
|
||||
# done
|
||||
#
|
||||
# # Copy BP over max iter. results
|
||||
#
|
||||
# echo -e "\rCopying one-shot simulation results..."
|
||||
# echo -n ' '
|
||||
# for decoder in "SyndromeMinSumDecoder" "SyndromeSpaDecoder" "SyndromeSpaGdDecoder"; do
|
||||
# for max_iter in 32 200 5000; do
|
||||
# SRC_PATH="${BASE_PATH}+rust_exp=whole_bp_bpgd,decoder.class_name=${decoder},decoder.max_iter=${max_iter},system.F=1,system.W=5/"
|
||||
# LATEST_RESULTS_DIR=$(ls -t ${SRC_PATH} | head -1)
|
||||
# SRC_FILE="${SRC_PATH}/${LATEST_RESULTS_DIR}/LERs.csv"
|
||||
# DEST_DIR="res/sim/one-shot/${decoder}/max_iter_${max_iter}/"
|
||||
# mkdir -p ${DEST_DIR}
|
||||
# DEST_FILE="${DEST_DIR}/LERs.csv"
|
||||
# cp ${SRC_FILE} ${DEST_FILE}
|
||||
# post_process_LERs ${DEST_FILE}
|
||||
# printf "\b${sp:i++%${#sp}:1}"
|
||||
# done
|
||||
# done
|
||||
|
||||
# Copy whole BP over max iter. results
|
||||
|
||||
echo -e "\rCopying whole over max_iter simulation results..."
|
||||
echo -n ' '
|
||||
for decoder in "SyndromeMinSumDecoder"; do
|
||||
for p in 0.001 0.0025 0.004; do
|
||||
SRC_PATH="${BASE_PATH}+rust_exp=max_iter_bp,decoder.class_name=${decoder},simulation.phy_err_rate=${p}/"
|
||||
LATEST_RESULTS_DIR=$(ls -t ${SRC_PATH} | head -1)
|
||||
SRC_FILE="${SRC_PATH}/${LATEST_RESULTS_DIR}/LERs.csv"
|
||||
DEST_DIR="res/sim/max_iter/${decoder}/p_${p}/"
|
||||
mkdir -p ${DEST_DIR}
|
||||
DEST_FILE="${DEST_DIR}/LERs.csv"
|
||||
cp ${SRC_FILE} ${DEST_FILE}
|
||||
post_process_LERs ${DEST_FILE}
|
||||
printf "\b${sp:i++%${#sp}:1}"
|
||||
done
|
||||
done
|
||||
|
||||
# # Copy BPGD decimation passing
|
||||
#
|
||||
# echo -e "\rCopying BPGD param exploration results..."
|
||||
# echo -n ' '
|
||||
# for max_iter in 32 200 5000; do
|
||||
# for F in 1 2 3; do
|
||||
# for W in 3 4 5; do
|
||||
# SRC_PATH="${BASE_PATH}+rust_exp=soft_v_hard_bpgd_pass_channel,decoder.class_name=WindowingSyndromeSpaGdDecoder,decoder.max_iter=${max_iter},decoder.pass_soft_info=True,system.F=${F},system.W=${W}"
|
||||
# LATEST_RESULTS_DIR=$(ls -t ${SRC_PATH} | head -1)
|
||||
# SRC_FILE="${SRC_PATH}/${LATEST_RESULTS_DIR}/LERs.csv"
|
||||
# DEST_DIR="res/sim/WF/WindowingSyndromeSpaGdDecoderPassDecimation/max_iter_${max_iter}/pass_soft_info_True/F_${F}/W_${W}/"
|
||||
# mkdir -p ${DEST_DIR}
|
||||
# DEST_FILE="${DEST_DIR}/LERs.csv"
|
||||
# cp ${SRC_FILE} ${DEST_FILE}
|
||||
# post_process_LERs ${DEST_FILE}
|
||||
# printf "\b${sp:i++%${#sp}:1}"
|
||||
# done
|
||||
# done
|
||||
# done
|
||||
|
||||
# Copy BPGD with decimation info passing over max iter. results
|
||||
|
||||
# echo -e "\rCopying BPGD over max. iter. results..."
|
||||
# echo -n ' '
|
||||
# for pass_soft_info in "True" "False"; do
|
||||
# for F in 1 2 3; do
|
||||
# for W in 3 4 5; do
|
||||
# SRC_PATH="${BASE_PATH}+rust_exp=max_iter_bpgd_pass_channel,decoder.class_name=WindowingSyndromeSpaGdDecoder,decoder.pass_soft_info=${pass_soft_info},simulation.phy_err_rate=0.0025,system.F=${F},system.W=${W}/"
|
||||
# LATEST_RESULTS_DIR=$(ls -t ${SRC_PATH} | head -1)
|
||||
# SRC_FILE="${SRC_PATH}/${LATEST_RESULTS_DIR}/LERs.csv"
|
||||
# DEST_DIR="res/sim/max_iter/WindowingSyndromeSpaGdDecoderPassDecimation/p_0.0025/pass_soft_info_${pass_soft_info}/F_${F}/W_${W}"
|
||||
# mkdir -p ${DEST_DIR}
|
||||
# DEST_FILE="${DEST_DIR}/LERs.csv"
|
||||
# cp ${SRC_FILE} ${DEST_FILE}
|
||||
# post_process_LERs ${DEST_FILE}
|
||||
# printf "\b${sp:i++%${#sp}:1}"
|
||||
# done
|
||||
# done
|
||||
# done
|
||||
@@ -6,27 +6,44 @@
|
||||
\usepackage{amsfonts}
|
||||
\usepackage{mleftright}
|
||||
\usepackage{bm}
|
||||
\usepackage{bbm}
|
||||
\usepackage{tikz}
|
||||
\usepackage{xcolor}
|
||||
\usepackage{pgfplots}
|
||||
\pgfplotsset{compat=newest}
|
||||
\usepackage{acro}
|
||||
\usepackage{braket}
|
||||
\usepackage{listings}
|
||||
\usepackage{caption}
|
||||
% \usepackage[
|
||||
% backend=biber,
|
||||
% style=ieee,
|
||||
% sorting=nty,
|
||||
% ]{biblatex}
|
||||
\usepackage{todonotes}
|
||||
% \usepackage{todonotes}
|
||||
\usepackage{quantikz}
|
||||
\usepackage{stmaryrd}
|
||||
\usepackage{algorithm}
|
||||
\usepackage[noEnd=false]{algpseudocodex}
|
||||
\usepackage{nicematrix}
|
||||
\usepackage{colortbl}
|
||||
\usepackage{cleveref}
|
||||
\usepackage{lipsum}
|
||||
|
||||
\usetikzlibrary{calc, positioning, arrows, fit}
|
||||
|
||||
\usetikzlibrary{external}
|
||||
\tikzexternalize
|
||||
|
||||
\makeatletter
|
||||
\renewcommand{\todo}[2][]{\tikzexternaldisable\@todo[#1]{#2}\tikzexternalenable}
|
||||
\makeatother
|
||||
% \makeatletter
|
||||
% \renewcommand{\todo}[2][]{\tikzexternaldisable\@todo[#1]{#2}\tikzexternalenable}
|
||||
% \makeatother
|
||||
|
||||
\setcounter{MaxMatrixCols}{20}
|
||||
|
||||
\Crefname{equation}{}{}
|
||||
\Crefname{section}{Section}{Sections}
|
||||
\Crefname{subsection}{Section}{Sections}
|
||||
\Crefname{figure}{Figure}{Figures}
|
||||
|
||||
%
|
||||
%
|
||||
@@ -35,6 +52,8 @@
|
||||
%
|
||||
|
||||
\newcommand{\red}[1]{\textcolor{red}{#1}}
|
||||
\newcommand{\content}[1]{\noindent\indent\red{[#1]\\}}
|
||||
|
||||
\newcommand{\figwidth}{10cm}
|
||||
\newcommand{\figheight}{7.5cm}
|
||||
|
||||
@@ -70,10 +89,12 @@
|
||||
% \thesisHeadOfInstitute{Prof. Dr.-Ing. Peter Rost}
|
||||
%\thesisHeadOfInstitute{Prof. Dr.-Ing. Peter Rost\\Prof. Dr.-Ing.
|
||||
% Laurent Schmalen}
|
||||
\thesisSupervisor{Jonathan Mandelbaum}
|
||||
\thesisSupervisor{M.Sc. Jonathan Mandelbaum}
|
||||
\thesisStartDate{01.11.2025}
|
||||
\thesisEndDate{04.05.2026}
|
||||
\thesisSignatureDate{Signature date}
|
||||
\thesisSignatureDate{04.05.2026}
|
||||
\thesisSignature{res/Unterschrift_AT_blue.png}
|
||||
\thesisSignatureHeight{2.4cm}
|
||||
\thesisLanguage{english}
|
||||
|
||||
\begin{document}
|
||||
@@ -82,7 +103,7 @@
|
||||
\maketitle
|
||||
\newpage
|
||||
|
||||
% \include{chapters/abstract}
|
||||
\include{chapters/abstract}
|
||||
|
||||
\cleardoublepage
|
||||
\pagenumbering{arabic}
|
||||
|
||||
BIN
src/thesis/res/72_bb_dem.pdf
Normal file
BIN
src/thesis/res/72_bb_dem.pdf
Normal file
Binary file not shown.
BIN
src/thesis/res/Unterschrift_AT_blue.png
Normal file
BIN
src/thesis/res/Unterschrift_AT_blue.png
Normal file
Binary file not shown.
|
After Width: | Height: | Size: 181 KiB |
@@ -0,0 +1,8 @@
|
||||
physical_p,num_trials,LER,LER_per_round,num_errors
|
||||
0.001,12000,0.01675,0.0014066653566989773,201.0
|
||||
0.0015,6000,0.048,0.004090796817048492,288.0
|
||||
0.002,2000,0.124,0.010971798240880681,248.0
|
||||
0.0025,2000,0.258,0.024560528611376475,516.0
|
||||
0.003,2000,0.441,0.04731136584915907,882.0
|
||||
0.0035,2000,0.6485,0.08344096230884013,1297.0
|
||||
0.004,2000,0.8085,0.1286738833656923,1617.0
|
||||
|
@@ -0,0 +1,8 @@
|
||||
physical_p,num_trials,LER,LER_per_round,num_errors
|
||||
0.001,50000,0.004,0.0003339460107422143,200.0
|
||||
0.0015,14000,0.016,0.0013432122426282334,224.0
|
||||
0.002,6000,0.0538333333333333,0.004600762670813663,322.99999999999983
|
||||
0.0025,2000,0.1515,0.01359714508496701,303.0
|
||||
0.003,2000,0.29,0.028137416075114108,580.0
|
||||
0.0035,2000,0.485,0.05379783863208576,970.0
|
||||
0.004,2000,0.657,0.08530878077130555,1314.0
|
||||
|
@@ -0,0 +1,8 @@
|
||||
physical_p,num_trials,LER,LER_per_round,num_errors
|
||||
0.001,74000,0.0027837837837837,0.000232278495492233,205.9999999999938
|
||||
0.0015,20000,0.01065,0.0008918618165982828,213.0
|
||||
0.002,6000,0.0386666666666666,0.003280778882142177,231.9999999999996
|
||||
0.0025,2000,0.1005,0.008787514236290539,201.0
|
||||
0.003,2000,0.2145,0.019918520513549032,429.0
|
||||
0.0035,2000,0.3975,0.041343353576980935,795.0
|
||||
0.004,2000,0.5975,0.07303396011007879,1195.0
|
||||
|
@@ -0,0 +1,8 @@
|
||||
physical_p,num_trials,LER,LER_per_round,num_errors
|
||||
0.001,4000,0.05975,0.005120966383739489,239.0
|
||||
0.0015,2000,0.12,0.010596241035318976,240.0
|
||||
0.002,2000,0.2925,0.02842304828215303,585.0
|
||||
0.0025,2000,0.457,0.049614097064849094,914.0
|
||||
0.003,2000,0.6565,0.08519774084658893,1313.0
|
||||
0.0035,2000,0.807,0.12810716433630664,1614.0
|
||||
0.004,2000,0.927,0.19596138832598886,1854.0
|
||||
|
@@ -0,0 +1,8 @@
|
||||
physical_p,num_trials,LER,LER_per_round,num_errors
|
||||
0.001,30000,0.0074,0.0006187681363896136,222.0
|
||||
0.0015,8000,0.027375,0.002310383366790014,219.0
|
||||
0.002,4000,0.081,0.007014379974311313,324.0
|
||||
0.0025,2000,0.1935,0.01776132322220747,387.0
|
||||
0.003,2000,0.3505,0.03532372820929974,701.0
|
||||
0.0035,2000,0.549,0.06420358199217457,1098.0
|
||||
0.004,2000,0.736,0.10504679589131227,1472.0
|
||||
|
@@ -0,0 +1,8 @@
|
||||
physical_p,num_trials,LER,LER_per_round,num_errors
|
||||
0.001,56000,0.0035892857142857,0.0002996003321397156,200.99999999999918
|
||||
0.0015,16000,0.0141875,0.001190050056010028,227.0
|
||||
0.002,6000,0.0458333333333333,0.003902110220303623,274.99999999999983
|
||||
0.0025,2000,0.127,0.011254499159800035,254.0
|
||||
0.003,2000,0.255,0.024232483954962025,510.0
|
||||
0.0035,2000,0.455,0.049322879977013234,910.0
|
||||
0.004,2000,0.629,0.07930773938046853,1258.0
|
||||
|
@@ -0,0 +1,8 @@
|
||||
physical_p,num_trials,LER,LER_per_round,num_errors
|
||||
0.001,2000,0.632,0.07993046327730713,1264.0
|
||||
0.0015,2000,0.7685,0.11479080536457342,1537.0
|
||||
0.002,2000,0.8905,0.16832973055592892,1781.0
|
||||
0.0025,2000,0.9405,0.2095463416012857,1881.0
|
||||
0.003,2000,0.9765,0.26843039175484296,1953.0
|
||||
0.0035,2000,0.993,0.33865993052589327,1986.0
|
||||
0.004,2000,0.995,0.3569459165824279,1990.0
|
||||
|
@@ -0,0 +1,8 @@
|
||||
physical_p,num_trials,LER,LER_per_round,num_errors
|
||||
0.001,6000,0.0361666666666666,0.003065034000747535,216.99999999999957
|
||||
0.0015,4000,0.08675,0.007533613442062825,347.0
|
||||
0.002,2000,0.183,0.01670196477645869,366.0
|
||||
0.0025,2000,0.3605,0.036570265848455796,721.0
|
||||
0.003,2000,0.5385,0.062407102537387016,1077.0
|
||||
0.0035,2000,0.7385,0.10575612450061989,1477.0
|
||||
0.004,2000,0.8635,0.15291357705621333,1727.0
|
||||
|
@@ -0,0 +1,8 @@
|
||||
physical_p,num_trials,LER,LER_per_round,num_errors
|
||||
0.001,32000,0.0065,0.0005432871152698526,208.0
|
||||
0.0015,10000,0.0211,0.0017755706988360487,211.0
|
||||
0.002,4000,0.067,0.005762505879780444,268.0
|
||||
0.0025,2000,0.1555,0.013985493383097625,311.0
|
||||
0.003,2000,0.2855,0.02762559348483462,571.0
|
||||
0.0035,2000,0.4885,0.05433539011619826,977.0
|
||||
0.004,2000,0.678,0.09011189125403751,1356.0
|
||||
|
@@ -0,0 +1,8 @@
|
||||
physical_p,num_trials,LER,LER_per_round,num_errors
|
||||
0.001,16000,0.01375,0.0011531185491073792,220.0
|
||||
0.0015,6000,0.0416666666666666,0.0035403526553423603,249.9999999999996
|
||||
0.002,2000,0.11,0.009664150391878956,220.0
|
||||
0.0025,2000,0.2535,0.024068915462335805,507.0
|
||||
0.003,2000,0.4185,0.04417333224775788,837.0
|
||||
0.0035,2000,0.62,0.0774668808446417,1240.0
|
||||
0.004,2000,0.792,0.12265189055421477,1584.0
|
||||
|
@@ -0,0 +1,8 @@
|
||||
physical_p,num_trials,LER,LER_per_round,num_errors
|
||||
0.001,62000,0.0032903225806451,0.0002746079212814223,203.99999999999622
|
||||
0.0015,16000,0.0134375,0.0011267480946226538,215.0
|
||||
0.002,6000,0.0453333333333333,0.0038586229394146354,271.99999999999983
|
||||
0.0025,2000,0.1265,0.011207320558933254,253.0
|
||||
0.003,2000,0.252,0.02390564797425576,504.0
|
||||
0.0035,2000,0.453,0.04903264087587211,906.0
|
||||
0.004,2000,0.6265,0.07879231884746019,1253.0
|
||||
|
@@ -0,0 +1,8 @@
|
||||
physical_p,num_trials,LER,LER_per_round,num_errors
|
||||
0.001,100000,0.00162,0.00013510034136854365,162.0
|
||||
0.0015,26000,0.0079615384615384,0.00066589492156377,206.9999999999984
|
||||
0.002,8000,0.027,0.0022783337152086913,216.0
|
||||
0.0025,4000,0.0855,0.0074204821894011674,342.0
|
||||
0.003,2000,0.1795,0.016351617556473186,359.0
|
||||
0.0035,2000,0.345,0.034645612003118,690.0
|
||||
0.004,2000,0.5415,0.06291652725715624,1083.0
|
||||
|
@@ -0,0 +1,8 @@
|
||||
physical_p,num_trials,LER,LER_per_round,num_errors
|
||||
0.001,4000,0.057,0.004878809452940613,228.0
|
||||
0.0015,2000,0.1345,0.011965166585961362,269.0
|
||||
0.002,2000,0.2835,0.02739906464725228,567.0
|
||||
0.0025,2000,0.4645,0.050714990274915994,929.0
|
||||
0.003,2000,0.649,0.08354968174320077,1298.0
|
||||
0.0035,2000,0.799,0.125151191269673,1598.0
|
||||
0.004,2000,0.923,0.19237907929568254,1846.0
|
||||
|
@@ -0,0 +1,8 @@
|
||||
physical_p,num_trials,LER,LER_per_round,num_errors
|
||||
0.001,28000,0.0072857142857142,0.0006091797682086231,203.9999999999976
|
||||
0.0015,8000,0.026875,0.0022676530141574336,215.0
|
||||
0.002,4000,0.07125,0.006140708552619056,285.0
|
||||
0.0025,2000,0.181,0.016501598292156028,362.0
|
||||
0.003,2000,0.343,0.0344003178522726,686.0
|
||||
0.0035,2000,0.539,0.06249179545899253,1078.0
|
||||
0.004,2000,0.734,0.10448375252924946,1468.0
|
||||
|
@@ -0,0 +1,8 @@
|
||||
physical_p,num_trials,LER,LER_per_round,num_errors
|
||||
0.001,66000,0.0031060606060606,0.0002592076019299894,204.9999999999996
|
||||
0.0015,16000,0.0130625,0.0010951136545078732,209.0
|
||||
0.002,6000,0.0398333333333333,0.003381635886214096,238.99999999999977
|
||||
0.0025,2000,0.108,0.009478884979367552,216.0
|
||||
0.003,2000,0.241,0.022717441549556572,482.0
|
||||
0.0035,2000,0.427,0.04534551221126004,854.0
|
||||
0.004,2000,0.616,0.07666151943586219,1232.0
|
||||
|
@@ -0,0 +1,8 @@
|
||||
physical_p,num_trials,LER,LER_per_round,num_errors
|
||||
0.001,2000,0.632,0.07993046327730713,1264.0
|
||||
0.0015,2000,0.7685,0.11479080536457342,1537.0
|
||||
0.002,2000,0.8905,0.16832973055592892,1781.0
|
||||
0.0025,2000,0.9405,0.2095463416012857,1881.0
|
||||
0.003,2000,0.9765,0.26843039175484296,1953.0
|
||||
0.0035,2000,0.993,0.33865993052589327,1986.0
|
||||
0.004,2000,0.995,0.3569459165824279,1990.0
|
||||
|
@@ -0,0 +1,8 @@
|
||||
physical_p,num_trials,LER,LER_per_round,num_errors
|
||||
0.001,6000,0.0343333333333333,0.0029071468641445053,205.9999999999998
|
||||
0.0015,4000,0.09775,0.008535335041573222,391.0
|
||||
0.002,2000,0.2005,0.018474608554528427,401.0
|
||||
0.0025,2000,0.347,0.03489159369123396,694.0
|
||||
0.003,2000,0.559,0.06595052116772404,1118.0
|
||||
0.0035,2000,0.735,0.1047647873005133,1470.0
|
||||
0.004,2000,0.867,0.15474521742325598,1734.0
|
||||
|
@@ -0,0 +1,8 @@
|
||||
physical_p,num_trials,LER,LER_per_round,num_errors
|
||||
0.001,34000,0.0061176470588235,0.0005112389838239917,207.999999999999
|
||||
0.0015,12000,0.0199166666666666,0.0016750685805796417,238.9999999999992
|
||||
0.002,4000,0.05925,0.005076889602981138,237.0
|
||||
0.0025,2000,0.1465,0.013114062821618089,293.0
|
||||
0.003,2000,0.297,0.028939525764745788,594.0
|
||||
0.0035,2000,0.4765,0.05250617012872005,953.0
|
||||
0.004,2000,0.664,0.08687912132657749,1328.0
|
||||
|
@@ -0,0 +1,8 @@
|
||||
physical_p,num_trials,LER,LER_per_round,num_errors
|
||||
0.001,4000,0.08375,0.0072623363421430165,335.0
|
||||
0.0015,2000,0.17,0.015407535303274322,340.0
|
||||
0.002,2000,0.333,0.03318402118027908,666.0
|
||||
0.0025,2000,0.5225,0.05974038898813494,1045.0
|
||||
0.003,2000,0.7125,0.09866447739264284,1425.0
|
||||
0.0035,2000,0.8475,0.14505307692276814,1695.0
|
||||
0.004,2000,0.936,0.20472927123294937,1872.0
|
||||
|
@@ -0,0 +1,8 @@
|
||||
physical_p,num_trials,LER,LER_per_round,num_errors
|
||||
0.001,4000,0.05375,0.00459345717599724,215.0
|
||||
0.0015,2000,0.137,0.012203310556051061,274.0
|
||||
0.002,2000,0.248,0.023471730814805247,496.0
|
||||
0.0025,2000,0.424,0.044929992453897394,848.0
|
||||
0.003,2000,0.6005,0.07361169169753423,1201.0
|
||||
0.0035,2000,0.7845,0.12005821823758633,1569.0
|
||||
0.004,2000,0.9005,0.1749405238157723,1801.0
|
||||
|
@@ -0,0 +1,8 @@
|
||||
physical_p,num_trials,LER,LER_per_round,num_errors
|
||||
0.001,4000,0.0555,0.004746996564855888,222.0
|
||||
0.0015,2000,0.122,0.010783823589648356,244.0
|
||||
0.002,2000,0.228,0.02133338177466315,456.0
|
||||
0.0025,2000,0.3975,0.041343353576980935,795.0
|
||||
0.003,2000,0.577,0.06918859214518802,1154.0
|
||||
0.0035,2000,0.7605,0.11228111333332969,1521.0
|
||||
0.004,2000,0.8835,0.16402396604923497,1767.0
|
||||
|
@@ -0,0 +1,8 @@
|
||||
physical_p,num_trials,LER,LER_per_round,num_errors
|
||||
0.001,2000,0.1275,0.011301702536387737,255.0
|
||||
0.0015,2000,0.2445,0.023093785381261167,489.0
|
||||
0.002,2000,0.471,0.05168059078836085,942.0
|
||||
0.0025,2000,0.6925,0.09359889423026135,1385.0
|
||||
0.003,2000,0.83,0.13727825732341103,1660.0
|
||||
0.0035,2000,0.927,0.19596138832598886,1854.0
|
||||
0.004,2000,0.9745,0.2634339765587691,1949.0
|
||||
|
@@ -0,0 +1,8 @@
|
||||
physical_p,num_trials,LER,LER_per_round,num_errors
|
||||
0.001,4000,0.05525,0.004725046408614819,221.0
|
||||
0.0015,2000,0.133,0.011822582694107964,266.0
|
||||
0.002,2000,0.2755,0.026498707449347236,551.0
|
||||
0.0025,2000,0.462,0.050346464045528894,924.0
|
||||
0.003,2000,0.641,0.08182695829978004,1282.0
|
||||
0.0035,2000,0.8035,0.12680036354194668,1607.0
|
||||
0.004,2000,0.9095,0.18143334698302127,1819.0
|
||||
|
@@ -0,0 +1,8 @@
|
||||
physical_p,num_trials,LER,LER_per_round,num_errors
|
||||
0.001,6000,0.048,0.004090796817048492,288.0
|
||||
0.0015,2000,0.115,0.010128988904076097,230.0
|
||||
0.002,2000,0.2155,0.02002255762528382,431.0
|
||||
0.0025,2000,0.402,0.04194208019539358,804.0
|
||||
0.003,2000,0.577,0.06918859214518802,1154.0
|
||||
0.0035,2000,0.764,0.11336949998487811,1528.0
|
||||
0.004,2000,0.897,0.17256014533992214,1794.0
|
||||
|
@@ -0,0 +1,8 @@
|
||||
physical_p,num_trials,LER,LER_per_round,num_errors
|
||||
0.001,2000,0.6955,0.09433912151694923,1391.0
|
||||
0.0015,2000,0.816,0.13156999840650407,1632.0
|
||||
0.002,2000,0.9215,0.19107956872744314,1843.0
|
||||
0.0025,2000,0.9595,0.2344834483240309,1919.0
|
||||
0.003,2000,0.9895,0.31593226271987895,1979.0
|
||||
0.0035,2000,0.997,0.3837454986270925,1994.0
|
||||
0.004,2000,0.999,0.4376586748096508,1998.0
|
||||
|
@@ -0,0 +1,8 @@
|
||||
physical_p,num_trials,LER,LER_per_round,num_errors
|
||||
0.001,4000,0.09425,0.0082153967557419,377.0
|
||||
0.0015,2000,0.206,0.019039074473767514,412.0
|
||||
0.002,2000,0.371,0.03789851025936897,742.0
|
||||
0.0025,2000,0.5865,0.07094884804525436,1173.0
|
||||
0.003,2000,0.7685,0.11479080536457342,1537.0
|
||||
0.0035,2000,0.8965,0.17222616291377513,1793.0
|
||||
0.004,2000,0.9575,0.2314023053376273,1915.0
|
||||
|
@@ -0,0 +1,8 @@
|
||||
physical_p,num_trials,LER,LER_per_round,num_errors
|
||||
0.001,6000,0.0488333333333333,0.004163473418041463,292.9999999999998
|
||||
0.0015,2000,0.1225,0.01083078042647323,245.0
|
||||
0.002,2000,0.2435,0.022986095764761516,487.0
|
||||
0.0025,2000,0.4055,0.042410618607193085,811.0
|
||||
0.003,2000,0.5965,0.07284225986971693,1193.0
|
||||
0.0035,2000,0.7945,0.12353552306518623,1589.0
|
||||
0.004,2000,0.9,0.1745958147319816,1800.0
|
||||
|
@@ -0,0 +1,8 @@
|
||||
physical_p,num_trials,LER,LER_per_round,num_errors
|
||||
0.001,8000,0.033,0.0027924923467828044,264.0
|
||||
0.0015,4000,0.0885,0.0076922358935922475,354.0
|
||||
0.002,2000,0.189,0.01730577346851303,378.0
|
||||
0.0025,2000,0.386,0.039831698576282215,772.0
|
||||
0.003,2000,0.5745,0.06873139184884758,1149.0
|
||||
0.0035,2000,0.7675,0.11447278468704636,1535.0
|
||||
0.004,2000,0.8925,0.16960631326972486,1785.0
|
||||
|
@@ -0,0 +1,8 @@
|
||||
physical_p,num_trials,LER,LER_per_round,num_errors
|
||||
0.001,16000,0.013375,0.0011214749225721965,214.0
|
||||
0.0015,6000,0.0436666666666666,0.0037138159693325123,261.9999999999996
|
||||
0.002,2000,0.1125,0.009896269575755956,225.0
|
||||
0.0025,2000,0.2375,0.022342685193895928,475.0
|
||||
0.003,2000,0.4105,0.04308436449639608,821.0
|
||||
0.0035,2000,0.621,0.07766943516436708,1242.0
|
||||
0.004,2000,0.799,0.125151191269673,1598.0
|
||||
|
@@ -0,0 +1,8 @@
|
||||
physical_p,num_trials,LER,LER_per_round,num_errors
|
||||
0.001,20000,0.01,0.0008371773591205889,200.0
|
||||
0.0015,8000,0.02975,0.002513627927773654,238.0
|
||||
0.002,4000,0.08025,0.0069468735550100025,321.0
|
||||
0.0025,2000,0.2055,0.018987611527110704,411.0
|
||||
0.003,2000,0.3465,0.03483003359216841,693.0
|
||||
0.0035,2000,0.556,0.06542265847616091,1112.0
|
||||
0.004,2000,0.738,0.1056137629395989,1476.0
|
||||
|
@@ -0,0 +1,8 @@
|
||||
physical_p,num_trials,LER,LER_per_round,num_errors
|
||||
0.001,4000,0.102,0.008925364554660087,408.0
|
||||
0.0015,2000,0.234,0.02196950237720341,468.0
|
||||
0.002,2000,0.433,0.04618256897389805,866.0
|
||||
0.0025,2000,0.6455,0.08279160735454238,1291.0
|
||||
0.003,2000,0.82,0.13315913781420163,1640.0
|
||||
0.0035,2000,0.922,0.19151019058730434,1844.0
|
||||
0.004,2000,0.9805,0.2797174651647023,1961.0
|
||||
|
@@ -0,0 +1,8 @@
|
||||
physical_p,num_trials,LER,LER_per_round,num_errors
|
||||
0.001,6000,0.0355,0.0030075886692517706,212.99999999999997
|
||||
0.0015,4000,0.0835,0.007239766684647431,334.0
|
||||
0.002,2000,0.2025,0.018679455867679495,405.0
|
||||
0.0025,2000,0.3635,0.036947712076332184,727.0
|
||||
0.003,2000,0.5605,0.06621568805942701,1121.0
|
||||
0.0035,2000,0.749,0.10880485867108969,1498.0
|
||||
0.004,2000,0.8895,0.1676994342621433,1779.0
|
||||
|
@@ -0,0 +1,8 @@
|
||||
physical_p,num_trials,LER,LER_per_round,num_errors
|
||||
0.001,12000,0.0174166666666666,0.0014631053822830031,208.9999999999992
|
||||
0.0015,4000,0.051,0.004352706093600722,204.0
|
||||
0.002,2000,0.1315,0.011680224751058454,263.0
|
||||
0.0025,2000,0.281,0.02711671729858034,562.0
|
||||
0.003,2000,0.46,0.050052771570453625,920.0
|
||||
0.0035,2000,0.662,0.08642741539493726,1324.0
|
||||
0.004,2000,0.8145,0.13098222531638515,1629.0
|
||||
|
@@ -0,0 +1,8 @@
|
||||
physical_p,num_trials,LER,LER_per_round,num_errors
|
||||
0.001,2000,0.6955,0.09433912151694923,1391.0
|
||||
0.0015,2000,0.816,0.13156999840650407,1632.0
|
||||
0.002,2000,0.9215,0.19107956872744314,1843.0
|
||||
0.0025,2000,0.9595,0.2344834483240309,1919.0
|
||||
0.003,2000,0.9895,0.31593226271987895,1979.0
|
||||
0.0035,2000,0.997,0.3837454986270925,1994.0
|
||||
0.004,2000,0.999,0.4376586748096508,1998.0
|
||||
|
@@ -0,0 +1,8 @@
|
||||
physical_p,num_trials,LER,LER_per_round,num_errors
|
||||
0.001,4000,0.087,0.0075562567245422985,348.0
|
||||
0.0015,2000,0.2025,0.018679455867679495,405.0
|
||||
0.002,2000,0.3515,0.035447587291447924,703.0
|
||||
0.0025,2000,0.5605,0.06621568805942701,1121.0
|
||||
0.003,2000,0.766,0.11399809680348838,1532.0
|
||||
0.0035,2000,0.896,0.1718936562142762,1792.0
|
||||
0.004,2000,0.9535,0.22561949205779908,1907.0
|
||||
|
@@ -0,0 +1,8 @@
|
||||
physical_p,num_trials,LER,LER_per_round,num_errors
|
||||
0.001,6000,0.0341666666666666,0.0028928071163165647,204.9999999999996
|
||||
0.0015,4000,0.0915,0.007964810720254789,366.0
|
||||
0.002,2000,0.202,0.018628199928893086,404.0
|
||||
0.0025,2000,0.3685,0.03758042822058505,737.0
|
||||
0.003,2000,0.562,0.06648168584179992,1124.0
|
||||
0.0035,2000,0.7435,0.10719362881586803,1487.0
|
||||
0.004,2000,0.876,0.15966624844871136,1752.0
|
||||
|
@@ -0,0 +1,8 @@
|
||||
physical_p,num_trials,LER,LER_per_round,num_errors
|
||||
0.001,24000,0.008875,0.0007426089118820478,212.99999999999997
|
||||
0.0015,8000,0.027375,0.002310383366790014,219.0
|
||||
0.002,4000,0.0805,0.006969370086301163,322.0
|
||||
0.0025,2000,0.1765,0.016052408593168255,353.0
|
||||
0.003,2000,0.321,0.03174633874742727,642.0
|
||||
0.0035,2000,0.5295,0.06089683913260491,1059.0
|
||||
0.004,2000,0.703,0.09621935287123151,1406.0
|
||||
|
@@ -0,0 +1,8 @@
|
||||
physical_p,num_trials,LER,LER_per_round,num_errors
|
||||
0.001,100000,0.0018,0.00015012389249957625,180.0
|
||||
0.0015,30000,0.0071666666666666,0.000599192960614614,214.999999999998
|
||||
0.002,8000,0.026125,0.0022035952056765895,209.0
|
||||
0.0025,4000,0.08375,0.0072623363421430165,335.0
|
||||
0.003,2000,0.184,0.016802316683105167,368.0
|
||||
0.0035,2000,0.344,0.0345228792367418,688.0
|
||||
0.004,2000,0.5175,0.058923829667395955,1035.0
|
||||
|
@@ -0,0 +1,8 @@
|
||||
physical_p,num_trials,LER,LER_per_round,num_errors
|
||||
0.001,100000,0.0007,5.83520569852336e-05,70.0
|
||||
0.0015,62000,0.003258064516129,0.0002719116557121648,201.999999999998
|
||||
0.002,16000,0.013,0.0010898423190723872,208.0
|
||||
0.0025,6000,0.0468333333333333,0.0039891474854014675,280.99999999999983
|
||||
0.003,2000,0.1165,0.010268909922777514,233.0
|
||||
0.0035,2000,0.2525,0.023960037096822373,505.0
|
||||
0.004,2000,0.4255,0.04513750370753944,851.0
|
||||
|
@@ -0,0 +1,8 @@
|
||||
physical_p,num_trials,LER,LER_per_round,num_errors
|
||||
0.001,6000,0.0453333333333333,0.0038586229394146354,271.99999999999983
|
||||
0.0015,4000,0.09175,0.007987562516493574,367.0
|
||||
0.002,2000,0.199,0.018321281103642173,398.0
|
||||
0.0025,2000,0.362,0.036758785596775034,724.0
|
||||
0.003,2000,0.5155,0.058599376123828484,1031.0
|
||||
0.0035,2000,0.7085,0.09762605599754803,1417.0
|
||||
0.004,2000,0.856,0.149129354542893,1712.0
|
||||
|
@@ -0,0 +1,8 @@
|
||||
physical_p,num_trials,LER,LER_per_round,num_errors
|
||||
0.001,44000,0.0045454545454545,0.00037957931952325996,199.999999999998
|
||||
0.0015,16000,0.014625,0.001226996590199092,234.0
|
||||
0.002,6000,0.046,0.003916610622698213,276.0
|
||||
0.0025,2000,0.128,0.011348930715916694,256.0
|
||||
0.003,2000,0.239,0.022503101573992157,478.0
|
||||
0.0035,2000,0.4195,0.044310417497246735,839.0
|
||||
0.004,2000,0.5965,0.07284225986971693,1193.0
|
||||
|
@@ -0,0 +1,8 @@
|
||||
physical_p,num_trials,LER,LER_per_round,num_errors
|
||||
0.001,100000,0.00122,0.00010172355962756452,122.0
|
||||
0.0015,42000,0.0047857142857142,0.0003996869775206857,200.9999999999964
|
||||
0.002,12000,0.0196666666666666,0.001653849971735899,235.9999999999992
|
||||
0.0025,4000,0.066,0.0056737465539274945,264.0
|
||||
0.003,2000,0.1485,0.01330698362831062,297.0
|
||||
0.0035,2000,0.3085,0.03027331056488236,617.0
|
||||
0.004,2000,0.473,0.05197988715416113,946.0
|
||||
|
@@ -0,0 +1,8 @@
|
||||
physical_p,num_trials,LER,LER_per_round,num_errors
|
||||
0.001,2000,0.626,0.07868961436921773,1252.0
|
||||
0.0015,2000,0.7655,0.11384048722645845,1531.0
|
||||
0.002,2000,0.8745,0.15882379851291006,1749.0
|
||||
0.0025,2000,0.933,0.20168755384893544,1866.0
|
||||
0.003,2000,0.972,0.2576708709890312,1944.0
|
||||
0.0035,2000,0.985,0.29529459105967726,1970.0
|
||||
0.004,2000,0.994,0.3471010990626149,1988.0
|
||||
|
@@ -0,0 +1,8 @@
|
||||
physical_p,num_trials,LER,LER_per_round,num_errors
|
||||
0.001,8000,0.026875,0.0022676530141574336,215.0
|
||||
0.0015,4000,0.06075,0.005209184439765924,243.0
|
||||
0.002,2000,0.1275,0.011301702536387737,255.0
|
||||
0.0025,2000,0.2435,0.022986095764761516,487.0
|
||||
0.003,2000,0.4095,0.04294919734292335,819.0
|
||||
0.0035,2000,0.605,0.07448578964497943,1210.0
|
||||
0.004,2000,0.767,0.11431424426031134,1534.0
|
||||
|
@@ -0,0 +1,8 @@
|
||||
physical_p,num_trials,LER,LER_per_round,num_errors
|
||||
0.001,68000,0.0030882352941176,0.00025771792946360783,209.9999999999968
|
||||
0.0015,22000,0.0100454545454545,0.0008410003766037288,220.999999999999
|
||||
0.002,6000,0.0353333333333333,0.0029932330235841187,211.9999999999998
|
||||
0.0025,4000,0.08725,0.007578905691289939,349.0
|
||||
0.003,2000,0.191,0.017507953228264928,382.0
|
||||
0.0035,2000,0.3535,0.03569583157768186,707.0
|
||||
0.004,2000,0.5215,0.059576452112257594,1043.0
|
||||
|
@@ -0,0 +1,8 @@
|
||||
physical_p,num_trials,LER,LER_per_round,num_errors
|
||||
0.001,24000,0.00875,0.0007321073812772694,210.00000000000003
|
||||
0.0015,8000,0.025125,0.00211825510203556,201.0
|
||||
0.002,4000,0.0815,0.0070594123157259325,326.0
|
||||
0.0025,2000,0.174,0.015803830077221748,348.0
|
||||
0.003,2000,0.319,0.03150899241712146,638.0
|
||||
0.0035,2000,0.5135,0.05827614798780856,1027.0
|
||||
0.004,2000,0.7075,0.09736849218423416,1415.0
|
||||
|
@@ -0,0 +1,8 @@
|
||||
physical_p,num_trials,LER,LER_per_round,num_errors
|
||||
0.001,100000,0.00146,0.00012174815796772709,146.0
|
||||
0.0015,32000,0.0064375,0.000538047705478828,206.0
|
||||
0.002,10000,0.0229,0.0019286609080385597,229.0
|
||||
0.0025,4000,0.07525,0.006498116023036737,301.0
|
||||
0.003,2000,0.1585,0.01427786270551501,317.0
|
||||
0.0035,2000,0.3395,0.033972695445756096,679.0
|
||||
0.004,2000,0.4985,0.055890042576412724,997.0
|
||||
|
@@ -0,0 +1,8 @@
|
||||
physical_p,num_trials,LER,LER_per_round,num_errors
|
||||
0.001,100000,0.0004,3.3339446006586115e-05,40.0
|
||||
0.0015,72000,0.0027916666666666,0.0002329370855657098,200.9999999999952
|
||||
0.002,18000,0.0121666666666666,0.0010195870693898712,218.9999999999988
|
||||
0.0025,6000,0.0435,0.0036993479983105093,261.0
|
||||
0.003,4000,0.097,0.00846668118140581,388.0
|
||||
0.0035,2000,0.2385,0.022449597267178878,477.0
|
||||
0.004,2000,0.4015,0.04187535144908072,803.0
|
||||
|
@@ -0,0 +1,8 @@
|
||||
physical_p,num_trials,LER,LER_per_round,num_errors
|
||||
0.001,6000,0.038,0.003223196672329065,228.0
|
||||
0.0015,4000,0.098,0.008558231287084661,392.0
|
||||
0.002,2000,0.206,0.019039074473767514,412.0
|
||||
0.0025,2000,0.3485,0.035076533583668024,697.0
|
||||
0.003,2000,0.5245,0.060069209055131356,1049.0
|
||||
0.0035,2000,0.6985,0.09508606438098832,1397.0
|
||||
0.004,2000,0.8495,0.14599310907967555,1699.0
|
||||
|
@@ -0,0 +1,8 @@
|
||||
physical_p,num_trials,LER,LER_per_round,num_errors
|
||||
0.001,46000,0.004391304347826,0.0003666806266127143,201.99999999999602
|
||||
0.0015,14000,0.0164285714285714,0.001379465734122176,229.9999999999996
|
||||
0.002,6000,0.0438333333333333,0.003728286251850954,262.99999999999983
|
||||
0.0025,2000,0.118,0.010409048871669824,236.0
|
||||
0.003,2000,0.228,0.02133338177466315,456.0
|
||||
0.0035,2000,0.4185,0.04417333224775788,837.0
|
||||
0.004,2000,0.594,0.07236490793227202,1188.0
|
||||
|
@@ -0,0 +1,8 @@
|
||||
physical_p,num_trials,LER,LER_per_round,num_errors
|
||||
0.001,100000,0.00095,7.920115808901507e-05,95.0
|
||||
0.0015,42000,0.0050238095238095,0.00041961787574185117,210.999999999999
|
||||
0.002,12000,0.01975,0.0016609222901676768,237.0
|
||||
0.0025,4000,0.062,0.005319578163374583,248.0
|
||||
0.003,2000,0.159,0.014326683792962536,318.0
|
||||
0.0035,2000,0.313,0.030800767790453154,626.0
|
||||
0.004,2000,0.47,0.0515313313739999,940.0
|
||||
|
@@ -0,0 +1,8 @@
|
||||
physical_p,num_trials,LER,LER_per_round,num_errors
|
||||
0.001,2000,0.626,0.07868961436921773,1252.0
|
||||
0.0015,2000,0.7655,0.11384048722645845,1531.0
|
||||
0.002,2000,0.8745,0.15882379851291006,1749.0
|
||||
0.0025,2000,0.933,0.20168755384893544,1866.0
|
||||
0.003,2000,0.972,0.2576708709890312,1944.0
|
||||
0.0035,2000,0.985,0.29529459105967726,1970.0
|
||||
0.004,2000,0.994,0.3471010990626149,1988.0
|
||||
|
@@ -0,0 +1,8 @@
|
||||
physical_p,num_trials,LER,LER_per_round,num_errors
|
||||
0.001,8000,0.026125,0.0022035952056765895,209.0
|
||||
0.0015,4000,0.06075,0.005209184439765924,243.0
|
||||
0.002,2000,0.136,0.012107977177767903,272.0
|
||||
0.0025,2000,0.254,0.02412340479098629,508.0
|
||||
0.003,2000,0.4115,0.043219741997103434,823.0
|
||||
0.0035,2000,0.6,0.07351512752093081,1200.0
|
||||
0.004,2000,0.7645,0.11352619006706066,1529.0
|
||||
|
@@ -0,0 +1,8 @@
|
||||
physical_p,num_trials,LER,LER_per_round,num_errors
|
||||
0.001,72000,0.0027777777777777,0.00023177671578233916,199.9999999999944
|
||||
0.0015,20000,0.0105,0.0008792394039432994,210.0
|
||||
0.002,8000,0.032125,0.0027173290492218394,257.0
|
||||
0.0025,4000,0.08575,0.007443097095222506,343.0
|
||||
0.003,2000,0.186,0.01700335914772977,372.0
|
||||
0.0035,2000,0.356,0.03600712878727563,712.0
|
||||
0.004,2000,0.529,0.06081371425997428,1058.0
|
||||
|
@@ -0,0 +1,8 @@
|
||||
physical_p,num_trials,LER,LER_per_round,num_errors
|
||||
0.001,6000,0.0453333333333333,0.0038586229394146354,271.99999999999983
|
||||
0.0015,2000,0.1245,0.011018853369859305,249.0
|
||||
0.002,2000,0.2185,0.02033539996612399,437.0
|
||||
0.0025,2000,0.3975,0.041343353576980935,795.0
|
||||
0.003,2000,0.5945,0.07246016235632424,1189.0
|
||||
0.0035,2000,0.735,0.1047647873005133,1470.0
|
||||
0.004,2000,0.8745,0.15882379851291006,1749.0
|
||||
|
@@ -0,0 +1,8 @@
|
||||
physical_p,num_trials,LER,LER_per_round,num_errors
|
||||
0.001,8000,0.030875,0.00261006088942628,247.0
|
||||
0.0015,4000,0.07825,0.006767102824702054,313.0
|
||||
0.002,2000,0.141,0.012585659483247746,282.0
|
||||
0.0025,2000,0.279,0.02689148662280816,558.0
|
||||
0.003,2000,0.4385,0.046957034683799304,877.0
|
||||
0.0035,2000,0.633,0.08013907230132367,1266.0
|
||||
0.004,2000,0.793,0.12300416913096102,1586.0
|
||||
|
@@ -0,0 +1,8 @@
|
||||
physical_p,num_trials,LER,LER_per_round,num_errors
|
||||
0.001,8000,0.027625,0.0023317560946333193,221.0
|
||||
0.0015,4000,0.06525,0.005607234208600653,261.0
|
||||
0.002,2000,0.122,0.010783823589648356,244.0
|
||||
0.0025,2000,0.2335,0.021916318194268203,467.0
|
||||
0.003,2000,0.385,0.03970147975050575,770.0
|
||||
0.0035,2000,0.569,0.0677341570379616,1138.0
|
||||
0.004,2000,0.729,0.10309294344737896,1458.0
|
||||
|
@@ -0,0 +1,8 @@
|
||||
physical_p,num_trials,LER,LER_per_round,num_errors
|
||||
0.001,2000,0.122,0.010783823589648356,244.0
|
||||
0.0015,2000,0.2475,0.02341764001219704,495.0
|
||||
0.002,2000,0.38,0.039053282833609426,760.0
|
||||
0.0025,2000,0.5705,0.06800496801270284,1141.0
|
||||
0.003,2000,0.7255,0.10213330493021633,1451.0
|
||||
0.0035,2000,0.846,0.14435544028130065,1692.0
|
||||
0.004,2000,0.944,0.2135296839449985,1888.0
|
||||
|
@@ -0,0 +1,8 @@
|
||||
physical_p,num_trials,LER,LER_per_round,num_errors
|
||||
0.001,6000,0.0375,0.00318003401506195,225.0
|
||||
0.0015,4000,0.08775,0.007624220689530503,351.0
|
||||
0.002,2000,0.169,0.015308735184581312,338.0
|
||||
0.0025,2000,0.3185,0.03144975567894859,637.0
|
||||
0.003,2000,0.4945,0.055264800927331104,989.0
|
||||
0.0035,2000,0.6715,0.08859526368715209,1343.0
|
||||
0.004,2000,0.8295,0.13706709042620446,1659.0
|
||||
|
@@ -0,0 +1,8 @@
|
||||
physical_p,num_trials,LER,LER_per_round,num_errors
|
||||
0.001,8000,0.029125,0.0024600983395249854,233.0
|
||||
0.0015,4000,0.06525,0.005607234208600653,261.0
|
||||
0.002,2000,0.129,0.011443461592906767,258.0
|
||||
0.0025,2000,0.2545,0.02417792760750781,509.0
|
||||
0.003,2000,0.416,0.043831562260356005,832.0
|
||||
0.0035,2000,0.5905,0.07170112206446477,1181.0
|
||||
0.004,2000,0.763,0.1130570306237979,1526.0
|
||||
|
@@ -0,0 +1,8 @@
|
||||
physical_p,num_trials,LER,LER_per_round,num_errors
|
||||
0.001,2000,0.789,0.12160429293407071,1578.0
|
||||
0.0015,2000,0.9,0.1745958147319816,1800.0
|
||||
0.002,2000,0.9465,0.21651717275071503,1893.0
|
||||
0.0025,2000,0.967,0.24743705884517853,1934.0
|
||||
0.003,2000,0.9905,0.32161385879719506,1981.0
|
||||
0.0035,2000,0.9965,0.3757780964762649,1993.0
|
||||
0.004,2000,0.9995,0.4692204681934514,1999.0
|
||||
|
@@ -0,0 +1,8 @@
|
||||
physical_p,num_trials,LER,LER_per_round,num_errors
|
||||
0.001,4000,0.09675,0.008443808176524459,387.0
|
||||
0.0015,2000,0.1775,0.01615203373482954,355.0
|
||||
0.002,2000,0.322,0.03186525232867321,644.0
|
||||
0.0025,2000,0.4605,0.050126101092695885,921.0
|
||||
0.003,2000,0.653,0.08442458415488852,1306.0
|
||||
0.0035,2000,0.798,0.12478930891509032,1596.0
|
||||
0.004,2000,0.912,0.18334199643064264,1824.0
|
||||
|
@@ -0,0 +1,8 @@
|
||||
physical_p,num_trials,LER,LER_per_round,num_errors
|
||||
0.001,6000,0.0365,0.0030937703263473892,219.0
|
||||
0.0015,4000,0.0795,0.006879417576947544,318.0
|
||||
0.002,2000,0.1575,0.01418030025167627,315.0
|
||||
0.0025,2000,0.29,0.028137416075114108,580.0
|
||||
0.003,2000,0.4455,0.04795283848945675,891.0
|
||||
0.0035,2000,0.6305,0.07961852200020059,1261.0
|
||||
0.004,2000,0.7825,0.11938055324065988,1565.0
|
||||
|
@@ -0,0 +1,8 @@
|
||||
physical_p,num_trials,LER,LER_per_round,num_errors
|
||||
0.001,6000,0.0343333333333333,0.0029071468641445053,205.9999999999998
|
||||
0.0015,4000,0.0885,0.0076922358935922475,354.0
|
||||
0.002,2000,0.177,0.0161022072935475,354.0
|
||||
0.0025,2000,0.3325,0.03312364612025187,665.0
|
||||
0.003,2000,0.501,0.05628314409130197,1002.0
|
||||
0.0035,2000,0.682,0.09105921022136998,1364.0
|
||||
0.004,2000,0.8345,0.13920480678485292,1669.0
|
||||
|
@@ -0,0 +1,8 @@
|
||||
physical_p,num_trials,LER,LER_per_round,num_errors
|
||||
0.001,10000,0.0225,0.0018946185336699006,225.0
|
||||
0.0015,4000,0.05,0.004265318777560645,200.0
|
||||
0.002,2000,0.1095,0.009617798287998358,219.0
|
||||
0.0025,2000,0.214,0.01986654747829364,428.0
|
||||
0.003,2000,0.364,0.03701077827175081,728.0
|
||||
0.0035,2000,0.5525,0.06481093518102832,1105.0
|
||||
0.004,2000,0.7365,0.10518816757921234,1473.0
|
||||
|
@@ -0,0 +1,8 @@
|
||||
physical_p,num_trials,LER,LER_per_round,num_errors
|
||||
0.001,12000,0.0199166666666666,0.0016750685805796417,238.9999999999992
|
||||
0.0015,6000,0.0413333333333333,0.0035114743705089158,247.9999999999998
|
||||
0.002,4000,0.082,0.007104467133977943,328.0
|
||||
0.0025,2000,0.194,0.01781208360090769,388.0
|
||||
0.003,2000,0.321,0.03174633874742727,642.0
|
||||
0.0035,2000,0.4975,0.055733304754966406,995.0
|
||||
0.004,2000,0.6875,0.0923797676224748,1375.0
|
||||
|
@@ -0,0 +1,8 @@
|
||||
physical_p,num_trials,LER,LER_per_round,num_errors
|
||||
0.001,2000,0.124,0.010971798240880681,248.0
|
||||
0.0015,2000,0.2365,0.0222359015716157,473.0
|
||||
0.002,2000,0.3665,0.037326792598442404,733.0
|
||||
0.0025,2000,0.5595,0.06603881814539603,1119.0
|
||||
0.003,2000,0.73,0.10336921268218224,1460.0
|
||||
0.0035,2000,0.837,0.14029596115963894,1674.0
|
||||
0.004,2000,0.9355,0.20421336158924952,1871.0
|
||||
|
@@ -0,0 +1,8 @@
|
||||
physical_p,num_trials,LER,LER_per_round,num_errors
|
||||
0.001,8000,0.0295,0.002492212300538421,236.0
|
||||
0.0015,4000,0.07525,0.006498116023036737,301.0
|
||||
0.002,2000,0.154,0.013839665569208792,308.0
|
||||
0.0025,2000,0.293,0.02848028572607786,586.0
|
||||
0.003,2000,0.4585,0.04983315584200687,917.0
|
||||
0.0035,2000,0.6525,0.08431471728347295,1305.0
|
||||
0.004,2000,0.802,0.1262468270496201,1604.0
|
||||
|
@@ -0,0 +1,8 @@
|
||||
physical_p,num_trials,LER,LER_per_round,num_errors
|
||||
0.001,8000,0.025875,0.0021822526517427665,207.0
|
||||
0.0015,4000,0.0535,0.004571544229555857,214.0
|
||||
0.002,2000,0.1165,0.010268909922777514,233.0
|
||||
0.0025,2000,0.231,0.021650873371036106,462.0
|
||||
0.003,2000,0.3665,0.037326792598442404,733.0
|
||||
0.0035,2000,0.552,0.06472390440895348,1104.0
|
||||
0.004,2000,0.742,0.10675969983223876,1484.0
|
||||
|
@@ -0,0 +1,8 @@
|
||||
physical_p,num_trials,LER,LER_per_round,num_errors
|
||||
0.001,2000,0.789,0.12160429293407071,1578.0
|
||||
0.0015,2000,0.9,0.1745958147319816,1800.0
|
||||
0.002,2000,0.9465,0.21651717275071503,1893.0
|
||||
0.0025,2000,0.967,0.24743705884517853,1934.0
|
||||
0.003,2000,0.9905,0.32161385879719506,1981.0
|
||||
0.0035,2000,0.9965,0.3757780964762649,1993.0
|
||||
0.004,2000,0.9995,0.4692204681934514,1999.0
|
||||
|
@@ -0,0 +1,8 @@
|
||||
physical_p,num_trials,LER,LER_per_round,num_errors
|
||||
0.001,4000,0.0915,0.007964810720254789,366.0
|
||||
0.0015,2000,0.18,0.016401583188387914,360.0
|
||||
0.002,2000,0.307,0.03009819055291696,614.0
|
||||
0.0025,2000,0.4545,0.04925022878399943,909.0
|
||||
0.003,2000,0.649,0.08354968174320077,1298.0
|
||||
0.0035,2000,0.793,0.12300416913096102,1586.0
|
||||
0.004,2000,0.9115,0.18295632456593924,1823.0
|
||||
|
@@ -0,0 +1,8 @@
|
||||
physical_p,num_trials,LER,LER_per_round,num_errors
|
||||
0.001,8000,0.030125,0.002545760854709589,241.0
|
||||
0.0015,4000,0.067,0.005762505879780444,268.0
|
||||
0.002,2000,0.1355,0.012060348411758404,271.0
|
||||
0.0025,2000,0.2805,0.027060355839749417,561.0
|
||||
0.003,2000,0.4395,0.0470985932750948,879.0
|
||||
0.0035,2000,0.619,0.07726481455474521,1238.0
|
||||
0.004,2000,0.7745,0.11672579914287295,1549.0
|
||||
|
@@ -0,0 +1,8 @@
|
||||
physical_p,num_trials,LER,LER_per_round,num_errors
|
||||
0.001,2000,0.115,0.010128988904076097,230.0
|
||||
0.0015,2000,0.2165,0.020126716372619535,433.0
|
||||
0.002,2000,0.3575,0.0361944392516631,715.0
|
||||
0.0025,2000,0.5255,0.06023409479070929,1051.0
|
||||
0.003,2000,0.6935,0.09384489827464226,1387.0
|
||||
0.0035,2000,0.816,0.13156999840650407,1632.0
|
||||
0.004,2000,0.9105,0.1821909360735222,1821.0
|
||||
|
@@ -0,0 +1,8 @@
|
||||
physical_p,num_trials,LER,LER_per_round,num_errors
|
||||
0.001,4000,0.0975,0.008512444610847103,390.0
|
||||
0.0015,2000,0.1915,0.017558569754261066,383.0
|
||||
0.002,2000,0.2765,0.02661075227253118,553.0
|
||||
0.0025,2000,0.448,0.04831127709115113,896.0
|
||||
0.003,2000,0.5865,0.07094884804525436,1173.0
|
||||
0.0035,2000,0.7455,0.10777583350900755,1491.0
|
||||
0.004,2000,0.8585,0.15037026489320615,1717.0
|
||||
|
@@ -0,0 +1,8 @@
|
||||
physical_p,num_trials,LER,LER_per_round,num_errors
|
||||
0.001,4000,0.0925,0.008055852365631777,370.0
|
||||
0.0015,2000,0.1735,0.015754197146499838,347.0
|
||||
0.002,2000,0.265,0.025330719468954155,530.0
|
||||
0.0025,2000,0.427,0.04534551221126004,854.0
|
||||
0.003,2000,0.571,0.0680954310203834,1142.0
|
||||
0.0035,2000,0.7105,0.09814362266376564,1421.0
|
||||
0.004,2000,0.8315,0.1379151915045972,1663.0
|
||||
|
@@ -0,0 +1,8 @@
|
||||
physical_p,num_trials,LER,LER_per_round,num_errors
|
||||
0.001,2000,0.189,0.01730577346851303,378.0
|
||||
0.0015,2000,0.334,0.03330489586414709,668.0
|
||||
0.002,2000,0.462,0.050346464045528894,924.0
|
||||
0.0025,2000,0.67,0.088249181932055,1340.0
|
||||
0.003,2000,0.8035,0.12680036354194668,1607.0
|
||||
0.0035,2000,0.8915,0.1689653255579383,1783.0
|
||||
0.004,2000,0.965,0.2437378987592076,1930.0
|
||||
|
@@ -0,0 +1,8 @@
|
||||
physical_p,num_trials,LER,LER_per_round,num_errors
|
||||
0.001,4000,0.092,0.008010320054115394,368.0
|
||||
0.0015,2000,0.182,0.016601725400650635,364.0
|
||||
0.002,2000,0.2885,0.027966478964539188,577.0
|
||||
0.0025,2000,0.468,0.05123358540561418,936.0
|
||||
0.003,2000,0.6195,0.07736578684966466,1239.0
|
||||
0.0035,2000,0.7805,0.11870857647232991,1561.0
|
||||
0.004,2000,0.8815,0.16283731439217686,1763.0
|
||||
|
@@ -0,0 +1,8 @@
|
||||
physical_p,num_trials,LER,LER_per_round,num_errors
|
||||
0.001,4000,0.0825,0.007149544452537682,330.0
|
||||
0.0015,2000,0.1585,0.01427786270551501,317.0
|
||||
0.002,2000,0.2535,0.024068915462335805,507.0
|
||||
0.0025,2000,0.4035,0.042142573743546796,807.0
|
||||
0.003,2000,0.5605,0.06621568805942701,1121.0
|
||||
0.0035,2000,0.729,0.10309294344737896,1458.0
|
||||
0.004,2000,0.8435,0.14320643674428069,1687.0
|
||||
|
@@ -0,0 +1,8 @@
|
||||
physical_p,num_trials,LER,LER_per_round,num_errors
|
||||
0.001,2000,0.818,0.13236056607309032,1636.0
|
||||
0.0015,2000,0.901,0.17528682442801136,1802.0
|
||||
0.002,2000,0.9565,0.2299112633774043,1913.0
|
||||
0.0025,2000,0.969,0.25134773793289455,1938.0
|
||||
0.003,2000,0.9945,0.3518181130178767,1989.0
|
||||
0.0035,2000,0.997,0.3837454986270925,1994.0
|
||||
0.004,2000,0.9995,0.4692204681934514,1999.0
|
||||
|
@@ -0,0 +1,8 @@
|
||||
physical_p,num_trials,LER,LER_per_round,num_errors
|
||||
0.001,2000,0.146,0.013065897372720348,292.0
|
||||
0.0015,2000,0.2805,0.027060355839749417,561.0
|
||||
0.002,2000,0.415,0.043695229663312296,830.0
|
||||
0.0025,2000,0.578,0.06937216612000952,1156.0
|
||||
0.003,2000,0.746,0.10792203989196847,1492.0
|
||||
0.0035,2000,0.8665,0.15448086847325826,1733.0
|
||||
0.004,2000,0.9405,0.2095463416012857,1881.0
|
||||
|
@@ -0,0 +1,8 @@
|
||||
physical_p,num_trials,LER,LER_per_round,num_errors
|
||||
0.001,4000,0.082,0.007104467133977943,328.0
|
||||
0.0015,2000,0.1555,0.013985493383097625,311.0
|
||||
0.002,2000,0.26,0.024779901164930007,520.0
|
||||
0.0025,2000,0.434,0.04632286722747814,868.0
|
||||
0.003,2000,0.603,0.07409618065132939,1206.0
|
||||
0.0035,2000,0.7465,0.10806851033720544,1493.0
|
||||
0.004,2000,0.859,0.1506208564330962,1718.0
|
||||
|
@@ -0,0 +1,8 @@
|
||||
physical_p,num_trials,LER,LER_per_round,num_errors
|
||||
0.001,4000,0.058,0.004966791530059078,232.0
|
||||
0.0015,2000,0.129,0.011443461592906767,258.0
|
||||
0.002,2000,0.241,0.022717441549556572,482.0
|
||||
0.0025,2000,0.4295,0.04569330484413092,859.0
|
||||
0.003,2000,0.593,0.07217472124714996,1186.0
|
||||
0.0035,2000,0.744,0.10733878882764858,1488.0
|
||||
0.004,2000,0.871,0.15689342561956476,1742.0
|
||||
|
@@ -0,0 +1,8 @@
|
||||
physical_p,num_trials,LER,LER_per_round,num_errors
|
||||
0.001,6000,0.0401666666666666,0.0034104728062255285,240.9999999999996
|
||||
0.0015,4000,0.08925,0.007760302417565645,357.0
|
||||
0.002,2000,0.156,0.014034155420617034,312.0
|
||||
0.0025,2000,0.3135,0.030859569505892193,627.0
|
||||
0.003,2000,0.445,0.0478813285765477,890.0
|
||||
0.0035,2000,0.63,0.07951479949867513,1260.0
|
||||
0.004,2000,0.795,0.12371343129766765,1590.0
|
||||
|
@@ -0,0 +1,8 @@
|
||||
physical_p,num_trials,LER,LER_per_round,num_errors
|
||||
0.001,8000,0.032,0.002706596520449467,256.0
|
||||
0.0015,4000,0.074,0.006386274207228704,296.0
|
||||
0.002,2000,0.1445,0.012921555968088194,289.0
|
||||
0.0025,2000,0.275,0.02644273818893983,550.0
|
||||
0.003,2000,0.411,0.043152026910574515,822.0
|
||||
0.0035,2000,0.5955,0.07265099463809832,1191.0
|
||||
0.004,2000,0.7595,0.11197282364335293,1519.0
|
||||
|
@@ -0,0 +1,8 @@
|
||||
physical_p,num_trials,LER,LER_per_round,num_errors
|
||||
0.001,2000,0.1595,0.014375531494479343,319.0
|
||||
0.0015,2000,0.3005,0.029343329924881867,601.0
|
||||
0.002,2000,0.4525,0.04896023310758335,905.0
|
||||
0.0025,2000,0.6415,0.08193359243128073,1283.0
|
||||
0.003,2000,0.7785,0.11804218900471797,1557.0
|
||||
0.0035,2000,0.879,0.16137955205786958,1758.0
|
||||
0.004,2000,0.9555,0.22845131704956945,1911.0
|
||||
|
Some files were not shown because too many files have changed in this diff Show More
Reference in New Issue
Block a user