Last changes

src/thesis/acronyms.tex

@@ -3,6 +3,16 @@
     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
@@ -13,11 +23,26 @@
     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
@@ -102,3 +127,18 @@
     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
+}

src/thesis/bibliography.bib

@@ -7,19 +7,20 @@
 	language = {en},
 	number = {3},
 	journal = {Mathematical Proceedings of the Cambridge Philosophical Society},
-	author = {Dirac, P. a. M.},
+	author = {Dirac, P. A. M.},
 	month = jul,
 	year = {1939},
 	pages = {416--418},
 }
 
-@article{huang_improved_2023,
-	title = {Improved {Noisy} {Syndrome} {Decoding} of {Quantum} {LDPC} {Codes} with {Sliding} {Window}},
+@misc{huang_improved_2023,
+	title = {Improved Noisy Syndrome Decoding of Quantum {LDPC} Codes with Sliding Window},
 	doi = {10.48550/arXiv.2311.03307},
 	publisher = {arXiv},
 	author = {Huang, Shilin and Puri, Shruti},
 	month = nov,
 	year = {2023},
+	howpublished = {arXiv:2311.03307},
 }
 
 @article{huang_increasing_2024,
@@ -35,17 +36,18 @@
 	pages = {012453},
 }
 
-@article{xu_batched_2025,
+@misc{xu_batched_2025,
 	title = {Batched high-rate logical operations for quantum {LDPC} codes},
 	doi = {10.48550/arXiv.2510.06159},
 	publisher = {arXiv},
 	author = {Xu, Qian and Zhou, Hengyun and Bluvstein, Dolev and Cain, Madelyn and Kalinowski, Marcin and Preskill, John and Lukin, Mikhail D. and Maskara, Nishad},
 	month = oct,
 	year = {2025},
+	howpublished = {arXiv:2510.06159},
 }
 
 @article{gidney_stability_2022,
-	title = {Stability {Experiments}: {The} {Overlooked} {Dual} of {Memory} {Experiments}},
+	title = {Stability Experiments: The Overlooked Dual of Memory Experiments},
 	volume = {6},
 	issn = {2521-327X},
 	shorttitle = {Stability {Experiments}},
@@ -57,30 +59,33 @@
 	pages = {786},
 }
 
-@article{koutsioumpas_colour_2025,
-	title = {Colour {Codes} {Reach} {Surface} {Code} {Performance} using {Vibe} {Decoding}},
+@misc{koutsioumpas_colour_2025,
+	title = {Colour Codes Reach Surface Code Performance using Vibe Decoding},
 	doi = {10.48550/arXiv.2508.15743},
 	publisher = {arXiv},
 	author = {Koutsioumpas, Stergios and Noszko, Tamas and Sayginel, Hasan and Webster, Mark and Roffe, Joschka},
 	month = aug,
 	year = {2025},
+	howpublished = {arXiv:2508.15743},
 }
 
-@article{koutsioumpas_automorphism_2025,
-	title = {Automorphism {Ensemble} {Decoding} of {Quantum} {LDPC} {Codes}},
+@misc{koutsioumpas_automorphism_2025,
+	title = {Automorphism Ensemble Decoding of Quantum {LDPC} Codes},
 	language = {en},
 	author = {Koutsioumpas, Stergios and Sayginel, Hasan and Webster, Mark and Browne, Dan E},
 	month = mar,
 	year = {2025},
+        howpublished = {arXiv:2503.01738},
 }
 
-@article{gottesman_heisenberg_1998,
-	title = {The {Heisenberg} {Representation} of {Quantum} {Computers}},
+@misc{gottesman_heisenberg_1998,
+	title = {The Heisenberg Representation of Quantum Computers},
 	doi = {10.48550/arXiv.quant-ph/9807006},
 	publisher = {arXiv},
 	author = {Gottesman, Daniel},
 	month = jul,
 	year = {1998},
+	howpublished = {arXiv:quant-ph/9807006},
 }
 
 @article{gidney_stim_2021,
@@ -98,8 +103,8 @@
 }
 
 @phdthesis{higgott_practical_2024,
-	type = {Doctoral},
-	title = {Practical and {Efficient} {Quantum} {Error} {Correction}},
+	type = {Ph.D. {Thesis}},
+	title = {Practical and Efficient Quantum Error Correction},
 	copyright = {open},
 	language = {eng},
 	school = {UCL (University College London)},
@@ -117,16 +122,17 @@
 }
 
 @misc{gong_toward_2024,
-	title = {Toward {Low}-latency {Iterative} {Decoding} of {QLDPC} {Codes} {Under} {Circuit}-{Level} {Noise}},
+	title = {Toward Low-latency Iterative Decoding of {QLDPC} Codes Under Circuit-Level Noise},
 	language = {en},
 	journal = {arXiv.org},
 	author = {Gong, Anqi and Cammerer, Sebastian and Renes, Joseph M.},
 	month = mar,
+	howpublished = {arXiv:2403.18901},
 	year = {2024},
 }
 
 @article{miao_quaternary_2025,
-	title = {Quaternary {Neural} {Belief} {Propagation} {Decoding} of {Quantum} {LDPC} {Codes} with {Overcomplete} {Check} {Matrices}},
+	title = {Quaternary Neural Belief Propagation Decoding of Quantum {LDPC} Codes with Overcomplete Check Matrices},
 	volume = {13},
 	issn = {2169-3536},
 	doi = {10.1109/ACCESS.2025.3539475},
@@ -138,7 +144,7 @@
 }
 
 @misc{tsouchlos_ccam_2024,
-	title = {{CCAM} {Summary}},
+	title = {{CCAM} Summary},
 	author = {Tsouchlos, Andreas},
 	month = oct,
 	year = {2024},
@@ -158,7 +164,7 @@
 }
 
 @book{griffiths_introduction_1995,
-	title = {Introduction to {Quantum} {Mechanics}},
+	title = {Introduction to Quantum Mechanics},
 	isbn = {0-13-124405-1},
 	language = {en},
 	publisher = {Prentice Hall},
@@ -167,7 +173,7 @@
 }
 
 @misc{bradley_tensor_2018,
-	title = {The {Tensor} {Product}, {Demystified}},
+	title = {The Tensor Product, Demystified},
 	author = {Bradley, Tai-Danae},
 	month = nov,
 	year = {2018},
@@ -175,7 +181,7 @@
 
 @book{nielsen_quantum_2010,
 	address = {Cambridge},
-	title = {Quantum {Computation} and {Quantum} {Information}: 10th {Anniversary} {Edition}},
+	title = {Quantum Computation and Quantum Information: 10th Anniversary Edition},
 	isbn = {978-0-511-97666-7},
 	shorttitle = {Quantum {Computation} and {Quantum} {Information}},
 	doi = {10.1017/CBO9780511976667},
@@ -187,7 +193,7 @@
 }
 
 @article{geiselhart_automorphism_2021,
-	title = {Automorphism {Ensemble} {Decoding} of {Reed}–{Muller} {Codes}},
+	title = {Automorphism Ensemble Decoding of Reed–Muller Codes},
 	volume = {69},
 	issn = {1558-0857},
 	doi = {10.1109/TCOMM.2021.3098798},
@@ -199,19 +205,20 @@
 	pages = {6424--6438},
 }
 
-@article{derks_designing_2025,
+@misc{derks_designing_2025,
 	title = {Designing fault-tolerant circuits using detector error models},
 	doi = {10.48550/arXiv.2407.13826},
 	publisher = {arXiv},
 	author = {Derks, Peter-Jan H. S. and Townsend-Teague, Alex and Burchards, Ansgar G. and Eisert, Jens},
 	month = oct,
 	year = {2025},
+	howpublished = {arXiv:2407.13826},
 }
 
 @phdthesis{klinke_neural_2025,
 	address = {Karlsruhe},
 	type = {Bachelor's {Thesis}},
-	title = {Neural {Belief} {Propagation} {Ensemble} {Decoding} of {Quantum} {LDPC} {Codes}},
+	title = {Neural Belief Propagation Ensemble Decoding of Quantum {LDPC} Codes},
 	language = {English},
 	school = {KIT},
 	author = {Klinke, Jeremi},
@@ -219,14 +226,15 @@
 	year = {2025},
 }
 
-@article{camps-moreno_toward_2024,
-	title = {Toward {Quantum} {CSS}-{T} {Codes} from {Sparse} {Matrices}},
+@misc{camps-moreno_toward_2024,
+	title = {Toward Quantum {CSS}-{T} Codes from Sparse Matrices},
 	doi = {10.48550/arXiv.2406.00425},
 	abstract = {CSS-T codes were recently introduced as quantum error-correcting codes that respect a transversal gate. A CSS-T code depends on a pair \$(C\_1, C\_2)\$ of binary linear codes \$C\_1\$ and \$C\_2\$ that satisfy certain conditions. We prove that \$C\_1\$ and \$C\_2\$ form a CSS-T pair if and only if \$C\_2 {\textbackslash}subset {\textbackslash}operatorname\{Hull\}(C\_1) {\textbackslash}cap {\textbackslash}operatorname\{Hull\}(C\_1{\textasciicircum}2)\$, where the hull of a code is the intersection of the code with its dual. We show that if \$(C\_1,C\_2)\$ is a CSS-T pair, and the code \$C\_2\$ is degenerated on \${\textbackslash}\{i{\textbackslash}\}\$, meaning that the \$i{\textasciicircum}\{th\}\$-entry is zero for all the elements in \$C\_2\$, then the pair of punctured codes \$(C\_1{\textbar}\_i,C\_2{\textbar}\_i)\$ is also a CSS-T pair. Finally, we provide Magma code based on our results and quasi-cyclic codes as a step toward finding quantum LDPC or LDGM CSS-T codes computationally.},
 	publisher = {arXiv},
 	author = {Camps-Moreno, Eduardo and López, Hiram H. and Matthews, Gretchen L. and McMillon, Emily},
 	month = jun,
 	year = {2024},
+	howpublished = {arXiv:2406.00425},
 }
 
 @article{roffe_quantum_2019,
@@ -244,13 +252,14 @@
 	pages = {226--245},
 }
 
-@article{gottesman_introduction_2009,
-	title = {An {Introduction} to {Quantum} {Error} {Correction} and {Fault}-{Tolerant} {Quantum} {Computation}},
+@misc{gottesman_introduction_2009,
+	title = {An Introduction to Quantum Error Correction and Fault-Tolerant Quantum Computation},
 	doi = {10.48550/arXiv.0904.2557},
 	publisher = {arXiv},
 	author = {Gottesman, Daniel},
 	month = apr,
 	year = {2009},
+	howpublished = {arXiv:0904.2557},
 }
 
 @article{gottesman_theory_1998,
@@ -266,35 +275,38 @@
 	pages = {127--137},
 }
 
-@article{calderbank_quantum_1997,
-	title = {Quantum {Error} {Correction} via {Codes} over {GF}(4)},
+@misc{calderbank_quantum_1997,
+	title = {Quantum Error Correction via Codes over {GF}(4)},
 	doi = {10.48550/arXiv.quant-ph/9608006},
 	publisher = {arXiv},
 	author = {Calderbank, A. R. and Rains, E. M. and Shor, P. W. and Sloane, N. J. A.},
 	month = sep,
 	year = {1997},
+	howpublished = {arXiv:quant-ph/9608006},
 }
 
-@article{gottesman_stabilizer_1997,
-	title = {Stabilizer {Codes} and {Quantum} {Error} {Correction}},
+@misc{gottesman_stabilizer_1997,
+	title = {Stabilizer Codes and Quantum Error Correction},
 	doi = {10.48550/arXiv.quant-ph/9705052},
 	publisher = {arXiv},
 	author = {Gottesman, Daniel},
 	month = may,
 	year = {1997},
+	howpublished = {Ph.D. {Thesis}, arXiv:quant-ph/9705052},
 }
 
-@article{shor_fault-tolerant_1997,
+@misc{shor_fault-tolerant_1997,
 	title = {Fault-tolerant quantum computation},
 	doi = {10.48550/arXiv.quant-ph/9605011},
 	publisher = {arXiv},
 	author = {Shor, Peter W.},
 	month = mar,
 	year = {1997},
+	howpublished = {arXiv:quant-ph/9605011},
 }
 
 @article{divincenzo_fault-tolerant_1996,
-	title = {Fault-{Tolerant} {Error} {Correction} with {Efficient} {Quantum} {Codes}},
+	title = {Fault-Tolerant Error Correction with Efficient Quantum Codes},
 	volume = {77},
 	issn = {0031-9007, 1079-7114},
 	doi = {10.1103/PhysRevLett.77.3260},
@@ -335,7 +347,7 @@
 }
 
 @article{terhal_quantum_2015,
-	title = {Quantum {Error} {Correction} for {Quantum} {Memories}},
+	title = {Quantum Error Correction for Quantum Memories},
 	volume = {87},
 	issn = {0034-6861, 1539-0756},
 	doi = {10.1103/RevModPhys.87.307},
@@ -353,7 +365,7 @@
 	title = {Guidelines for snowballing in systematic literature studies and a replication in software engineering},
 	isbn = {978-1-4503-2476-2},
 	doi = {10.1145/2601248.2601268},
-	booktitle = {Proceedings of the 18th {International} {Conference} on {Evaluation} and {Assessment} in {Software} {Engineering}},
+	booktitle = {Proceedings of the 18th International Conference on Evaluation and Assessment in Software Engineering},
 	publisher = {Association for Computing Machinery},
 	author = {Wohlin, Claes},
 	month = may,
@@ -374,20 +386,21 @@
 	pages = {83--84},
 }
 
-@article{blume-kohout_estimating_2025,
+@misc{blume-kohout_estimating_2025,
 	title = {Estimating detector error models from syndrome data},
 	doi = {10.48550/arXiv.2504.14643},
 	publisher = {arXiv},
 	author = {Blume-Kohout, Robin and Young, Kevin},
 	month = apr,
 	year = {2025},
+	howpublished = {arXiv:2504.14643},
 }
 
 @inproceedings{chatterjee_quantum_2023,
-	title = {Quantum {Error} {Correction} {For} {Dummies}},
+	title = {Quantum Error Correction For Dummies},
 	volume = {01},
 	doi = {10.1109/QCE57702.2023.00017},
-	booktitle = {2023 {IEEE} {International} {Conference} on {Quantum} {Computing} and {Engineering} ({QCE})},
+	booktitle = {2023 {IEEE} International Conference on Quantum Computing and Engineering ({QCE})},
 	author = {Chatterjee, Avimita and Phalak, Koustubh and Ghosh, Swaroop},
 	month = sep,
 	year = {2023},
@@ -395,7 +408,7 @@
 }
 
 @inproceedings{petersen_systematic_2008,
-	title = {Systematic {Mapping} {Studies} in {Software} {Engineering}},
+	title = {Systematic Mapping Studies in Software Engineering},
 	doi = {10.14236/ewic/EASE2008.8},
 	language = {en},
 	publisher = {BCS Learning \& Development},
@@ -405,7 +418,7 @@
 }
 
 @article{postler_demonstration_2024,
-	title = {Demonstration of {Fault}-{Tolerant} {Steane} {Quantum} {Error} {Correction}},
+	title = {Demonstration of Fault-Tolerant Steane Quantum Error Correction},
 	volume = {5},
 	doi = {10.1103/PRXQuantum.5.030326},
 	number = {3},
@@ -418,7 +431,7 @@
 }
 
 @article{cao_exact_2025,
-	title = {Exact {Decoding} of {Quantum} {Error}-{Correcting} {Codes}},
+	title = {Exact Decoding of Quantum Error-Correcting Codes},
 	volume = {134},
 	doi = {10.1103/PhysRevLett.134.190603},
 	number = {19},
@@ -431,13 +444,14 @@
 }
 
 @misc{beni_tesseract_2025,
-	title = {Tesseract: {A} {Search}-{Based} {Decoder} for {Quantum} {Error} {Correction}},
+	title = {Tesseract: {A} Search-Based Decoder for Quantum Error Correction},
 	shorttitle = {Tesseract},
 	doi = {10.48550/arXiv.2503.10988},
 	publisher = {arXiv},
 	author = {Beni, Laleh Aghababaie and Higgott, Oscar and Shutty, Noah},
 	month = aug,
 	year = {2025},
+	howpublished = {arXiv:2503.10988},
 }
 
 @article{bausch_learning_2024,
@@ -457,12 +471,13 @@
 }
 
 @misc{bhardwaj_adaptive_2025,
-	title = {Adaptive {Estimation} of {Drifting} {Noise} in {Quantum} {Error} {Correction}},
+	title = {Adaptive Estimation of Drifting Noise in Quantum Error Correction},
 	doi = {10.48550/arXiv.2511.09491},
 	publisher = {arXiv},
 	author = {Bhardwaj, Devansh and Takou, Evangelia and Lin, Yingjia and Brown, Kenneth R.},
 	month = nov,
 	year = {2025},
+	howpublished = {arXiv:2511.09491},
 }
 
 @article{roffe_decoding_2020,
@@ -492,7 +507,7 @@
 }
 
 @article{bausch_learning_2024-1,
-	title = {Learning to {Decode} the {Surface} {Code} with a {Recurrent}, {Transformer}-{Based} {Neural} {Network}},
+	title = {Learning to Decode the Surface Code with a Recurrent, Transformer-Based Neural Network},
 	volume = {635},
 	issn = {0028-0836, 1476-4687},
 	doi = {10.1038/s41586-024-08148-8},
@@ -511,15 +526,17 @@
 	author = {Lin, Hsiang-Ku and Lim, Pak Kau and Kovalev, Alexey A. and Pryadko, Leonid P.},
 	month = aug,
 	year = {2025},
+	howpublished = {arXiv:2506.16910},
 }
 
 @misc{fan_accelerating_2025,
-	title = {Accelerating {BP}-{OSD} {Decoder} for {QLDPC} {Codes} with {Local} {Syndrome}-{Based} {Preprocessing}},
+	title = {Accelerating {BP}-{OSD} Decoder for {QLDPC} Codes with Local Syndrome-Based Preprocessing},
 	doi = {10.48550/arXiv.2509.01892},
 	publisher = {arXiv},
 	author = {Fan, Wenxuan and Suzuki, Yasunari and Ravi, Gokul Subramanian and Ueno, Yosuke and Inoue, Koji and Tanimoto, Teruo},
 	month = sep,
 	year = {2025},
+	howpublished = {arXiv:2509.01892},
 }
 
 @misc{senior_scalable_2025,
@@ -529,14 +546,16 @@
 	author = {Senior, Andrew W. and Edlich, Thomas and Heras, Francisco J. H. and Zhang, Lei M. and Higgott, Oscar and Spencer, James S. and Applebaum, Taylor and Blackwell, Sam and Ledford, Justin and Žemgulytė, Akvilė and Žídek, Augustin and Shutty, Noah and Cowie, Andrew and Li, Yin and Holland, George and Brooks, Peter and Beattie, Charlie and Newman, Michael and Davies, Alex and Jones, Cody and Boixo, Sergio and Neven, Hartmut and Kohli, Pushmeet and Bausch, Johannes},
 	month = dec,
 	year = {2025},
+	howpublished = {arXiv:2512.07737},
 }
 
 @misc{wang_fully_2025,
-	title = {Fully {Parallelized} {BP} {Decoding} for {Quantum} {LDPC} {Codes} {Can} {Outperform} {BP}-{OSD}},
+	title = {Fully Parallelized {BP} Decoding for Quantum {LDPC} Codes Can Outperform {BP}-{OSD}},
 	language = {en},
 	author = {Wang, Ming and Li, Ang and Mueller, Frank},
 	month = jun,
 	year = {2025},
+        howpublished = {arXiv:2507.00254},
 }
 
 @misc{ye_beam_2025,
@@ -565,7 +584,7 @@
 }
 
 @article{higgott_improved_2023,
-	title = {Improved {Decoding} of {Circuit} {Noise} and {Fragile} {Boundaries} of {Tailored} {Surface} {Codes}},
+	title = {Improved Decoding of Circuit Noise and Fragile Boundaries of Tailored Surface Codes},
 	volume = {13},
 	doi = {10.1103/PhysRevX.13.031007},
 	number = {3},
@@ -578,31 +597,34 @@
 }
 
 @misc{tsubouchi_degeneracy_2025,
-	title = {Degeneracy {Cutting}: {A} {Local} and {Efficient} {Post}-{Processing} for {Belief} {Propagation} {Decoding} of {Quantum} {Low}-{Density} {Parity}-{Check} {Codes}},
+	title = {Degeneracy Cutting: {A} Local and Efficient Post-Processing for Belief Propagation Decoding of Quantum Low-Density Parity-Check Codes},
 	shorttitle = {Degeneracy {Cutting}},
 	doi = {10.48550/arXiv.2510.08695},
 	publisher = {arXiv},
 	author = {Tsubouchi, Kento and Yamasaki, Hayata and Tamiya, Shiro},
 	month = oct,
 	year = {2025},
+	howpublished = {arXiv:2510.08695},
 }
 
 @misc{lee_scalable_2025,
-	title = {Scalable {Neural} {Decoders} for {Practical} {Real}-{Time} {Quantum} {Error} {Correction}},
+	title = {Scalable Neural Decoders for Practical Real-Time Quantum Error Correction},
 	doi = {10.48550/arXiv.2510.22724},
 	publisher = {arXiv},
 	author = {Lee, Changwon and Hur, Tak and Park, Daniel K.},
 	month = oct,
 	year = {2025},
+	howpublished = {arXiv:2510.22724},
 }
 
 @misc{maan_decoding_2025,
-	title = {Decoding {Correlated} {Errors} in {Quantum} {LDPC} {Codes}},
+	title = {Decoding Correlated Errors in Quantum {LDPC} Codes},
 	doi = {10.48550/arXiv.2510.14060},
 	publisher = {arXiv},
 	author = {Maan, Arshpreet Singh and Herrero, Francisco-Garcia and Paler, Alexandru and Savin, Valentin},
 	month = oct,
 	year = {2025},
+	howpublished = {arXiv:2510.14060},
 }
 
 @article{skoric_parallel_2023,
@@ -622,7 +644,7 @@
 }
 
 @article{higgott_sparse_2025,
-	title = {Sparse {Blossom}: correcting a million errors per core second with minimum-weight matching},
+	title = {Sparse Blossom: correcting a million errors per core second with minimum-weight matching},
 	volume = {9},
 	shorttitle = {Sparse {Blossom}},
 	doi = {10.22331/q-2025-01-20-1600},
@@ -636,7 +658,7 @@
 }
 
 @article{breuckmann_quantum_2021,
-	title = {Quantum {Low}-{Density} {Parity}-{Check} {Codes}},
+	title = {Quantum Low-Density Parity-Check Codes},
 	volume = {2},
 	doi = {10.1103/PRXQuantum.2.040101},
 	number = {4},
@@ -649,10 +671,10 @@
 }
 
 @inproceedings{gokduman_erasure_2024,
-	title = {Erasure {Decoding} for {Quantum} {LDPC} {Codes} via {Belief} {Propagation} with {Guided} {Decimation}},
+	title = {Erasure Decoding for Quantum {LDPC} Codes via Belief Propagation with Guided Decimation},
 	issn = {2836-4503},
 	doi = {10.1109/Allerton63246.2024.10735275},
-	booktitle = {2024 60th {Annual} {Allerton} {Conference} on {Communication}, {Control}, and {Computing}},
+	booktitle = {2024 60th Annual Allerton Conference on Communication, Control, and Computing},
 	author = {Gökduman, Mert and Yao, Hanwen and Pfister, Henry D.},
 	month = sep,
 	year = {2024},
@@ -660,13 +682,14 @@
 }
 
 @misc{swierkowska_eccentric_2025,
-	title = {{ECCentric}: {An} {Empirical} {Analysis} of {Quantum} {Error} {Correction} {Codes}},
+	title = {ECCentric: An Empirical Analysis of Quantum Error Correction Codes},
 	shorttitle = {{ECCentric}},
 	doi = {10.48550/arXiv.2511.01062},
 	publisher = {arXiv},
 	author = {{\'S}wierkowska, Aleksandra and Pflieger, Jannik and Giortamis, Emmanouil and Bhatotia, Pramod},
 	month = nov,
 	year = {2025},
+	howpublished = {arXiv:2511.01062},
 }
 
 @phdthesis{guernut_fault-tolerant_2025,
@@ -693,7 +716,7 @@
 }
 
 @article{tan_scalable_2023,
-	title = {Scalable {Surface}-{Code} {Decoders} with {Parallelization} in {Time}},
+	title = {Scalable Surface-Code Decoders with Parallelization in Time},
 	volume = {4},
 	doi = {10.1103/PRXQuantum.4.040344},
 	number = {4},
@@ -735,21 +758,23 @@
 }
 
 @misc{kuo_fault-tolerant_2024,
-	title = {Fault-{Tolerant} {Belief} {Propagation} for {Practical} {Quantum} {Memory}},
+	title = {Fault-Tolerant Belief Propagation for Practical Quantum Memory},
 	doi = {10.48550/arXiv.2409.18689},
 	publisher = {arXiv},
 	author = {Kuo, Kao-Yueh and Lai, Ching-Yi},
 	month = sep,
 	year = {2024},
+	howpublished = {arXiv:2409.18689},
 }
 
 @misc{poor_ultra_2025,
-	title = {Ultra {Low} {Overhead} {Syndrome} {Extraction} for the {Steane} code},
+	title = {Ultra Low Overhead Syndrome Extraction for the Steane code},
 	doi = {10.48550/arXiv.2511.13700},
 	publisher = {arXiv},
 	author = {Poór, Boldizsár and Rodatz, Benjamin and Kissinger, Aleks},
 	month = nov,
 	year = {2025},
+	howpublished = {arXiv:2511.13700},
 }
 
 @article{feynman_simulating_1982,
@@ -770,15 +795,16 @@
 	title = {Algorithms for quantum computation: discrete logarithms and factoring},
 	shorttitle = {Algorithms for quantum computation},
 	doi = {10.1109/SFCS.1994.365700},
-	booktitle = {Proceedings 35th {Annual} {Symposium} on {Foundations} of {Computer} {Science}},
+	booktitle = {Proc. Annual Symposium on Foundations of Computer Science},
 	author = {Shor, P.W.},
+        address = {Santa Fe},
 	month = nov,
 	year = {1994},
 	pages = {124--134},
 }
 
 @article{preskill_quantum_2018,
-	title = {Quantum {Computing} in the {NISQ} era and beyond},
+	title = {Quantum Computing in the {NISQ} era and beyond},
 	volume = {2},
 	doi = {10.22331/q-2018-08-06-79},
 	language = {en-GB},
@@ -791,7 +817,7 @@
 }
 
 @misc{google_quantum_ai_quantum_nodate,
-	title = {Quantum {Computing} {Roadmap}},
+	title = {Quantum Computing Roadmap},
 	language = {en},
 	journal = {Google Quantum AI},
 	author = {{Google Quantum AI}},
@@ -811,7 +837,7 @@
 }
 
 @article{zhang_classical_2023,
-	title = {A {Classical} {Architecture} for {Digital} {Quantum} {Computers}},
+	title = {A Classical Architecture for Digital Quantum Computers},
 	volume = {5},
 	doi = {10.1145/3626199},
 	number = {1},
@@ -829,6 +855,7 @@
 	author = {Caune, Laura and Skoric, Luka and Blunt, Nick S. and Ruban, Archibald and McDaniel, Jimmy and Valery, Joseph A. and Patterson, Andrew D. and Gramolin, Alexander V. and Majaniemi, Joonas and Barnes, Kenton M. and Bialas, Tomasz and Buğdaycı, Okan and Crawford, Ophelia and Gehér, György P. and Krovi, Hari and Matekole, Elisha and Topal, Canberk and Poletto, Stefano and Bryant, Michael and Snyder, Kalan and Gillespie, Neil I. and Jones, Glenn and Johar, Kauser and Campbell, Earl T. and Hill, Alexander D.},
 	month = oct,
 	year = {2024},
+	howpublished = {arXiv:2410.05202},
 }
 
 @misc{ye_beam_2025-1,
@@ -838,14 +865,15 @@
 	author = {Ye, Min and Wecker, Dave and Delfosse, Nicolas},
 	month = dec,
 	year = {2025},
+	howpublished = {arXiv:2512.07057},
 }
 
 @misc{noauthor_reproducing_nodate,
-	title = {Reproducing repetition and {Shor} code simulations using stim},
+	title = {Reproducing repetition and Shor code simulations using stim},
 }
 
 @misc{noauthor_tutorial_nodate,
-	title = {Tutorial - {Estimating} the {Surface} {Code} {Threshold} — {NordIQuEst} {Application} {Library}},
+	title = {Tutorial - Estimating the Surface Code Threshold — NordIQuEst Application Library},
 }
 
 @misc{noauthor_simulating_nodate,
@@ -853,7 +881,7 @@
 }
 
 @article{ryan-anderson_realization_2021,
-	title = {Realization of {Real}-{Time} {Fault}-{Tolerant} {Quantum} {Error} {Correction}},
+	title = {Realization of Real-Time Fault-Tolerant Quantum Error Correction},
 	volume = {11},
 	doi = {10.1103/PhysRevX.11.041058},
 	number = {4},
@@ -880,11 +908,11 @@
 }
 
 @misc{noauthor_tutorial_nodate-1,
-	title = {Tutorial - {Fault}-{Tolerant} {Quantum} {Computing} with {CSS} codes},
+	title = {Tutorial - Fault-Tolerant Quantum Computing with {CSS} codes},
 }
 
 @article{panteleev_degenerate_2021,
-	title = {Degenerate {Quantum} {LDPC} {Codes} {With} {Good} {Finite} {Length} {Performance}},
+	title = {Degenerate Quantum {LDPC} Codes With Good Finite Length Performance},
 	volume = {5},
 	doi = {10.22331/q-2021-11-22-585},
 	language = {en-GB},
@@ -897,27 +925,29 @@
 }
 
 @article{babar_fifteen_2015,
-	title = {Fifteen {Years} of {Quantum} {LDPC} {Coding} and {Improved} {Decoding} {Strategies}},
+	title = {Fifteen Years of Quantum {LDPC} Coding and Improved Decoding Strategies},
 	volume = {3},
 	issn = {2169-3536},
 	doi = {10.1109/ACCESS.2015.2503267},
 	journal = {IEEE Access},
 	author = {Babar, Zunaira and Botsinis, Panagiotis and Alanis, Dimitrios and Ng, Soon Xin and Hanzo, Lajos},
+        month = nov,
 	year = {2015},
 	pages = {2492--2519},
 }
 
 @misc{yao_belief_2024,
-	title = {Belief {Propagation} {Decoding} of {Quantum} {LDPC} {Codes} with {Guided} {Decimation}},
+	title = {Belief Propagation Decoding of Quantum {LDPC} Codes with Guided Decimation},
 	doi = {10.48550/arXiv.2312.10950},
 	publisher = {arXiv},
 	author = {Yao, Hanwen and Laban, Waleed Abu and Häger, Christian and Amat, Alexandre Graell i and Pfister, Henry D.},
 	month = jun,
 	year = {2024},
+	howpublished = {arXiv:2312.10950},
 }
 
 @article{sharon_efficient_2007,
-	title = {Efficient {Serial} {Message}-{Passing} {Schedules} for {LDPC} {Decoding}},
+	title = {Efficient Serial Message-Passing Schedules for {LDPC} Decoding},
 	volume = {53},
 	issn = {1557-9654},
 	doi = {10.1109/TIT.2007.907507},
@@ -943,7 +973,7 @@
 }
 
 @book{ryan_channel_2009,
-	title = {Channel {Codes}: {Classical} and {Modern}},
+	title = {Channel Codes: Classical and Modern},
 	isbn = {978-1-139-48301-8},
 	shorttitle = {Channel {Codes}},
 	language = {en},
@@ -954,7 +984,7 @@
 }
 
 @book{macwilliams_theory_1977,
-	title = {The {Theory} of {Error}-correcting {Codes}},
+	title = {The Theory of Error-correcting Codes},
 	isbn = {978-0-444-85010-2},
 	language = {en},
 	publisher = {Elsevier},
@@ -964,7 +994,7 @@
 
 @book{richardson_modern_2008,
 	address = {Cambridge},
-	title = {Modern {Coding} {Theory}},
+	title = {Modern Coding Theory},
 	isbn = {978-0-521-85229-6},
 	doi = {10.1017/CBO9780511791338},
 	publisher = {Cambridge University Press},
@@ -973,7 +1003,7 @@
 }
 
 @phdthesis{gallager_low_1960,
-	type = {Thesis},
+	type = {Ph.D. {Thesis}},
 	title = {Low density parity check codes},
 	copyright = {M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.},
 	language = {eng},
@@ -986,11 +1016,11 @@
 	title = {Fully parallel window decoder architecture for spatially-coupled {LDPC} codes},
 	issn = {1938-1883},
 	doi = {10.1109/ICC.2016.7511553},
-	booktitle = {2016 {IEEE} {International} {Conference} on {Communications} ({ICC})},
+	booktitle = {Proc. {IEEE} International Conference on Communications ({ICC})},
 	author = {Hassan, Najeeb Ul and Schlüter, Martin and Fettweis, Gerhard P.},
+        address = {Kuala Lumpur},
 	month = may,
 	year = {2016},
-	pages = {1--6},
 }
 
 @article{costello_spatially_2014,
@@ -1019,7 +1049,7 @@
 }
 
 @article{kang_quits_2025,
-	title = {{QUITS}: {A} modular {Qldpc} code {circUIT} {Simulator}},
+	title = {{QUITS}: {A} modular Qldpc code circUIT Simulator},
 	volume = {9},
 	issn = {2521-327X},
 	shorttitle = {{QUITS}},
@@ -1033,7 +1063,7 @@
 
 @book{griffiths_consistent_2001,
 	address = {Cambridge},
-	title = {Consistent {Quantum} {Theory}},
+	title = {Consistent Quantum Theory},
 	isbn = {978-0-521-53929-6},
 	doi = {10.1017/CBO9780511606052},
 	publisher = {Cambridge University Press},
@@ -1042,12 +1072,13 @@
 }
 
 @misc{gottesman_fault-tolerant_2014,
-	title = {Fault-{Tolerant} {Quantum} {Computation} with {Constant} {Overhead}},
+	title = {Fault-Tolerant Quantum Computation with Constant Overhead},
 	doi = {10.48550/arXiv.1310.2984},
 	publisher = {arXiv},
 	author = {Gottesman, Daniel},
 	month = jul,
 	year = {2014},
+	howpublished = {arXiv:1310.2984},
 }
 
 @misc{gidney_new_2023,
@@ -1057,10 +1088,11 @@
 	author = {Gidney, Craig and Jones, Cody},
 	month = dec,
 	year = {2023},
+	howpublished = {arXiv:2312.08813},
 }
 
 @article{gidney_fault-tolerant_2021,
-	title = {A {Fault}-{Tolerant} {Honeycomb} {Memory}},
+	title = {A Fault-Tolerant Honeycomb Memory},
 	volume = {5},
 	issn = {2521-327X},
 	doi = {10.22331/q-2021-12-20-605},
@@ -1070,3 +1102,65 @@
 	year = {2021},
 	pages = {605},
 }
+
+@article{chamberland_flag_2018,
+	title = {Flag fault-tolerant error correction with arbitrary distance codes},
+	volume = {2},
+	issn = {2521-327X},
+	doi = {10.22331/q-2018-02-08-53},
+	journal = {Quantum},
+	author = {Chamberland, Christopher and Beverland, Michael E.},
+	month = feb,
+	year = {2018},
+	pages = {53},
+}
+
+@article{chen_exponential_2021,
+	title = {Exponential suppression of bit or phase errors with cyclic error correction},
+	volume = {595},
+	copyright = {2021 The Author(s)},
+	issn = {1476-4687},
+	doi = {10.1038/s41586-021-03588-y},
+	language = {en},
+	number = {7867},
+	journal = {Nature},
+	publisher = {Nature Publishing Group},
+	author = {{Google Quantum AI}},
+	month = jul,
+	year = {2021},
+	pages = {383--387},
+}
+
+@article{kelly_state_2015,
+	title = {State preservation by repetitive error detection in a superconducting quantum circuit},
+	volume = {519},
+	issn = {0028-0836, 1476-4687},
+	doi = {10.1038/nature14270},
+	number = {7541},
+	journal = {Nature},
+	author = {Kelly, J. and Barends, R. and Fowler, A. G. and Megrant, A. and Jeffrey, E. and White, T. C. and Sank, D. and Mutus, J. Y. and Campbell, B. and Chen, Yu and Chen, Z. and Chiaro, B. and Dunsworth, A. and Hoi, I.-C. and Neill, C. and O'Malley, P. J. J. and Quintana, C. and Roushan, P. and Vainsencher, A. and Wenner, J. and Cleland, A. N. and Martinis, John M.},
+	month = mar,
+	year = {2015},
+	pages = {66--69},
+}
+
+@misc{bombin_modular_2023,
+	title = {Modular decoding: parallelizable real-time decoding for quantum computers},
+	shorttitle = {Modular decoding},
+	doi = {10.48550/arXiv.2303.04846},
+	publisher = {arXiv},
+	author = {Bomb{\'i}n, H{\'e}ctor and Dawson, Chris and Liu, Ye-Hua and Nickerson, Naomi and Pastawski, Fernando and Roberts, Sam},
+	month = mar,
+	year = {2023},
+	howpublished = {arXiv:2303.04846},
+}
+
+@misc{leverrier_decoding_2022,
+	title = {Decoding quantum Tanner codes},
+	doi = {10.48550/arXiv.2208.05537},
+	publisher = {arXiv},
+	author = {Leverrier, Anthony and Z{\'e}mor, Gilles},
+	month = dec,
+	year = {2022},
+	howpublished = {arXiv:2208.05537},
+}

src/thesis/chapters/1_introduction.tex

@@ -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 does not suffice 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
+consistently interact with their environment \cite[Sec.~1]{roffe_quantum_2019}.
+This interaction acts as a continuous small-scale measurement, an
+effect we call \emph{decoherence} of the stored quantum state, which
+results in errors on the qubits.
+Decoherence is the reason large systems do not 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 detect and
+correct a corrupted the quantum state.
+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 collapse 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}, achieving low latency matters more than having a 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.
+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 $1008$.
+Therefore, decoding under a \ac{dem} poses a challenge with respect to the
+latency constraint.
+
+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 for standard \ac{bp} and 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
+
+This thesis is structured as follows:
+\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.
+

src/thesis/chapters/5_conclusion_and_outlook.tex

@@ -1 +1,115 @@
 \chapter{Conclusion and Outlook}
+\label{ch:Conclusion}
+
+% Recap of motivation
+
+This thesis investigates 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 grows 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.
+This manifests as a block-diagonal structure in the detector error
+matrix when detectors are defined as the difference of consecutive
+syndrome measurement rounds.
+We draw a comparison to windowed decoding for \ac{sc}-\ac{ldpc}
+codes, but note 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 formulate the warm start for standard \ac{bp} and for
+\ac{bpgd}.
+The latter is particularly attractive as an inner decoder because it
+addresses the convergence problems caused by short cycles and
+degeneracy in \ac{qldpc} Tanner graphs.
+The decoders are evaluated by conducting Monte Carlo simulations on the
+$\llbracket 144,12,12 \rrbracket$ \ac{bb} code over $12$ syndrome
+extraction rounds under standard circuit-based depolarizing noise.
+We focus on a qualitative analysis, refraining from further
+optimizations such as introducing a normalization parameter for the
+min-sum algorithm.
+
+% Recap of experimental conclusions
+
+For standard min-sum \ac{bp}, the warm start is consistently
+beneficial to the cold start, across the considered parameter ranges.
+The size of the gain depends on the overlap between consecutive
+windows: Enlarging $W$ or shrinking $F$, both of which enlarge the
+overlap, result in larger gains of the warm-start.
+We observe 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 note 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 standard \ac{bp}: Larger overlap, achieved by larger
+$W$ or smaller $F$, yielded a larger gain, and the
+performance difference is most pronounced at low numbers of maximum iterations.
+
+% Implications from experimental results
+
+These observations imply that the warm-start modification to
+sliding-window decoding can provide 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 other inner decoders under the
+warm-start framework, such as automorphism ensemble decoding
+\cite{koutsioumpas_automorphism_2025} or neural \ac{bp}
+\cite{miao_quaternary_2025}.
+
+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.
+

src/thesis/chapters/abstract.tex

@@ -0,0 +1,58 @@
+\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.
+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.
+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 check matrix of the \ac{dem} into overlapping windows that can be
+decoded sequentially.
+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 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 subsequent window.
+
+% Our work: Warm-start
+
+% TODO: Quantify improvement. Also for conclusion
+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 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
+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.
+

src/thesis/clean_bibliography.sh

@@ -1,2 +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

src/thesis/copy_sim_results.sh

@@ -129,6 +129,24 @@ sp="/-\|"
 #     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..."
@@ -151,20 +169,20 @@ sp="/-\|"
 
 # 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++%${#sp}:1}"
-        done
-    done
-done
+# echo -e "\rCopying BPGD over max. iter. results..."
+# echo -n ' '
+# for pass_soft_info in "True" "False"; do
+#     for F in 1 2 3; do
+#         for W in 3 4 5; do
+#             SRC_PATH="${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

src/thesis/main.tex

@@ -27,6 +27,9 @@
 \usepackage[noEnd=false]{algpseudocodex}
 \usepackage{nicematrix}
 \usepackage{colortbl}
+\usepackage{cleveref}
+\usepackage{lipsum}
+\usepackage{booktabs}
 
 \usetikzlibrary{calc, positioning, arrows, fit}
 \usetikzlibrary{external}
@@ -38,6 +41,11 @@
 
 \setcounter{MaxMatrixCols}{20}
 
+\Crefname{equation}{}{}
+\Crefname{section}{Section}{Sections}
+\Crefname{subsection}{Section}{Sections}
+\Crefname{figure}{Figure}{Figures}
+
 %
 %
 % Custom commands
@@ -45,7 +53,7 @@
 %
 
 \newcommand{\red}[1]{\textcolor{red}{#1}}
-\newcommand{\content}[1]{\noindent\indent\red{[#1]}\\}
+\newcommand{\content}[1]{\noindent\indent\red{[#1]\\}}
 
 \newcommand{\figwidth}{10cm}
 \newcommand{\figheight}{7.5cm}
@@ -82,10 +90,12 @@
 % \thesisHeadOfInstitute{Prof. Dr.-Ing. Peter Rost}
 %\thesisHeadOfInstitute{Prof. Dr.-Ing. Peter Rost\\Prof. Dr.-Ing.
 % Laurent Schmalen}
-\thesisSupervisor{Jonathan Mandelbaum}
-\thesisStartDate{01.11.2025}
-\thesisEndDate{04.05.2026}
-\thesisSignatureDate{Signature date}
+\thesisSupervisor{Dr.-Ing. Hedongliang Liu\\ && M.Sc. Jonathan Mandelbaum}
+\thesisStartDate{Nov. 1st, 2025}
+\thesisEndDate{May 4th, 2026}
+\thesisSignatureDate{May 4th, 2026}
+\thesisSignature{res/Unterschrift_AT_blue.png}
+\thesisSignatureHeight{2.4cm}
 \thesisLanguage{english}
 
 \begin{document}
@@ -94,13 +104,16 @@
 \maketitle
 \newpage
 
-% \include{chapters/abstract}
+\include{chapters/abstract}
 
 \cleardoublepage
 \pagenumbering{arabic}
 
-\tableofcontents
+\newgeometry{a4paper,left=3cm,right=3cm,top=2cm,bottom=2.5cm}                               
+\addtocontents{toc}{\protect\vspace*{-9mm}}
+\tableofcontents                                                                            
 \cleardoublepage
+\restoregeometry                                                                            
 
 \input{chapters/1_introduction.tex}
 \input{chapters/2_fundamentals.tex}
@@ -113,6 +126,11 @@
 % \listoftables
 % \include{abbreviations}
 
+\cleardoublepage
+\phantomsection
+\addcontentsline{toc}{chapter}{List of Abbreviations}
+\printacronyms
+
 \bibliography{lib/cel-thesis/IEEEabrv,src/thesis/bibliography}
 
 \end{document}

src/thesis/res/sim/max_iter/SyndromeMinSumDecoder/p_0.001/LERs.csv

@@ -0,0 +1,8 @@
+max_iter,num_trials,LER,LER_per_round,num_errors
+32,10528,0.0354293313069908,0.0030015014232951387,372.99999999999915
+128,68422,0.0029230364502645,0.00024391332035389457,199.99999999999764
+256,100000,0.00184,0.00015346279666106355,184.0
+512,100000,0.00122,0.00010172355962756452,122.0
+1024,100000,0.00084,7.002696447200307e-05,84.0
+2048,100000,0.00052,4.33436645435048e-05,51.99999999999999
+4096,100000,0.00042,3.5006739308451884e-05,42.0

src/thesis/res/sim/max_iter/SyndromeMinSumDecoder/p_0.0025/LERs.csv

@@ -0,0 +1,8 @@
+max_iter,num_trials,LER,LER_per_round,num_errors
+32,5264,0.3575227963525836,0.03619728900635699,1882.0
+128,5264,0.1118920972644376,0.00983977212107956,588.9999999999995
+256,5264,0.0818768996960486,0.007093372523371166,430.99999999999983
+512,5264,0.0645896656534954,0.005548714177492475,339.9999999999998
+1024,5264,0.0524316109422492,0.004477957765848362,275.9999999999998
+2048,5264,0.0442629179331307,0.0037655941776483237,233.0
+4096,10528,0.0361892097264437,0.0030669771276242708,380.99999999999926

src/thesis/res/sim/max_iter/SyndromeMinSumDecoder/p_0.004/LERs.csv

@@ -0,0 +1,8 @@
+max_iter,num_trials,LER,LER_per_round,num_errors
+32,5264,0.8651215805471124,0.15375677320993897,4554.0
+128,5264,0.5987841945288754,0.0732807818579091,3152.0000000000005
+256,5264,0.5184270516717325,0.05907464062706547,2729.0
+512,5264,0.4591565349544073,0.04992921073125611,2417.0
+1024,5264,0.4209726443768997,0.04451268995716784,2216.0
+2048,5264,0.3865881458966565,0.03990837706831185,2035.0
+4096,5264,0.3563829787234042,0.036054914686007855,1875.9999999999995