midterm: Update bib file; Add input/internal/output error diagram
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@ -1094,6 +1094,7 @@ TLDR: An end-to-end quantum error correction protocol that implements fault-tole
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author = {Kuo, Kao-Yueh and Lai, Ching-Yi},
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month = sep,
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year = {2022},
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note = {TLDR: This paper proposes a decoding algorithm for quantum codes based on quaternary BP with additional memory effects (called MBP), which is like a recursive neural network with inhibitions between neurons (edges with negative weights), which enhance the perception capability of a network.},
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keywords = {Quantum information, /s1, Computer science, Electrical and electronic engineering},
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pages = {111},
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file = {Full Text PDF:/home/andreas/workspace/work/hiwi/Zotero/storage/KTVJ5BGL/Kuo and Lai - 2022 - Exploiting degeneracy in belief propagation decoding of quantum codes.pdf:application/pdf},
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@ -1247,3 +1248,137 @@ Noisy Intermediate-Scale Quantum (NISQ) technology will be available in the near
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keywords = {/unread, Quantum Physics},
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file = {Preprint PDF:/home/andreas/workspace/work/hiwi/Zotero/storage/LGMAEBMB/Caune et al. - 2024 - Demonstrating real-time and low-latency quantum error correction with superconducting qubits.pdf:application/pdf},
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}
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@misc{ye_beam_2025-1,
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title = {Beam search decoder for quantum {LDPC} codes},
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url = {http://arxiv.org/abs/2512.07057},
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doi = {10.48550/arXiv.2512.07057},
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abstract = {We propose a decoder for quantum low density parity check (LDPC) codes based on a beam search heuristic guided by belief propagation (BP). Our beam search decoder applies to all quantum LDPC codes and achieves different speed-accuracy tradeoffs by tuning its parameters such as the beam width. We perform numerical simulations under circuit level noise for the \$[[144, 12, 12]]\$ bivariate bicycle (BB) code at noise rate \$p=10{\textasciicircum}\{-3\}\$ to estimate the logical error rate and the 99.9 percentile runtime and we compare with the BP-OSD decoder which has been the default quantum LDPC decoder for the past six years. A variant of our beam search decoder with a beam width of 64 achieves a \$17{\textbackslash}times\$ reduction in logical error rate. With a beam width of 8, we reach the same logical error rate as BP-OSD with a \$26.2{\textbackslash}times\$ reduction in the 99.9 percentile runtime. We identify the beam search decoder with beam width of 32 as a promising candidate for trapped ion architectures because it achieves a \$5.6{\textbackslash}times\$ reduction in logical error rate with a 99.9 percentile runtime per syndrome extraction round below 1ms at \$p=5 {\textbackslash}times10{\textasciicircum}\{-4\}\$. Remarkably, this is achieved in software on a single core, without any parallelization or specialized hardware (FPGA, ASIC), suggesting one might only need three 32-core CPUs to decode a trapped ion quantum computer with 1000 logical qubits.},
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urldate = {2026-01-29},
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publisher = {arXiv},
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author = {Ye, Min and Wecker, Dave and Delfosse, Nicolas},
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month = dec,
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year = {2025},
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note = {arXiv:2512.07057 [quant-ph]
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TLDR: A beam search decoder for quantum low density parity check (LDPC) codes based on a beam search heuristic guided by belief propagation (BP) is proposed, suggesting one might only need three 32-core CPUs to decode a trapped ion quantum computer with 1000 logical qubits.},
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keywords = {/unread, Computer Science - Information Theory, Quantum Physics},
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file = {Preprint PDF:/home/andreas/workspace/work/hiwi/Zotero/storage/DVFCD2FE/Ye et al. - 2025 - Beam search decoder for quantum LDPC codes.pdf:application/pdf},
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}
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@misc{noauthor_reproducing_nodate,
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title = {Reproducing repetition and {Shor} code simulations using stim},
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url = {https://textbook.riverlane.com/en/latest/notebooks/ch3-state-of-art-tools/repetition-and-shor-codes-stim.html},
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urldate = {2026-01-29},
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keywords = {/unread},
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}
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@misc{noauthor_tutorial_nodate,
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title = {Tutorial - {Estimating} the {Surface} {Code} {Threshold} — {NordIQuEst} {Application} {Library}},
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url = {https://nordiquest.net/application-library/training-material/qas2024/notebooks/surface_code_threshold.html},
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urldate = {2026-01-29},
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keywords = {/unread},
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}
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@misc{noauthor_simulating_nodate,
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title = {Simulating surface codes using stim},
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url = {https://textbook.riverlane.com/en/latest/notebooks/ch5-decoding-surfcodes/simulating-surface-codes-stim.html},
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urldate = {2026-01-29},
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keywords = {/unread},
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}
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@article{ryan-anderson_realization_2021,
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title = {Realization of {Real}-{Time} {Fault}-{Tolerant} {Quantum} {Error} {Correction}},
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volume = {11},
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url = {https://link.aps.org/doi/10.1103/PhysRevX.11.041058},
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doi = {10.1103/PhysRevX.11.041058},
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abstract = {Correcting errors in real time is essential for reliable large-scale quantum computations. Realizing this high-level function requires a system capable of several low-level primitives, including single-qubit and two-qubit operations, midcircuit measurements of subsets of qubits, real-time processing of measurement outcomes, and the ability to condition subsequent gate operations on those measurements. In this work, we use a 10-qubit quantum charge-coupled device trapped-ion quantum computer to encode a single logical qubit using the [[7,1,3]] color code, first proposed by Steane [Phys. Rev. Lett. 77, 793 (1996)]. The logical qubit is initialized into the eigenstates of three mutually unbiased bases using an encoding circuit, and we measure an average logical state preparation and measurement (SPAM) error of 1.7(2) ×10−3, compared to the average physical SPAM error 2.4(4) ×10−3 of our qubits. We then perform multiple syndrome measurements on the encoded qubit, using a real-time decoder to determine any necessary corrections that are done either as software updates to the Pauli frame or as physically applied gates. Moreover, these procedures are done repeatedly while maintaining coherence, demonstrating a dynamically protected logical qubit memory. Additionally, we demonstrate non-Clifford qubit operations by encoding a ¯𝑇{\textbar} +⟩𝐿 magic state with an error rate below the threshold required for magic state distillation. Finally, we present system-level simulations that allow us to identify key hardware upgrades that may enable the system to reach the pseudothreshold.},
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number = {4},
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urldate = {2026-01-29},
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journal = {Physical Review X},
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publisher = {American Physical Society},
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author = {Ryan-Anderson, C. and Bohnet, J. G. and Lee, K. and Gresh, D. and Hankin, A. and Gaebler, J. P. and Francois, D. and Chernoguzov, A. and Lucchetti, D. and Brown, N. C. and Gatterman, T. M. and Halit, S. K. and Gilmore, K. and Gerber, J. A. and Neyenhuis, B. and Hayes, D. and Stutz, R. P.},
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month = dec,
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year = {2021},
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note = {TLDR: This work uses a ten qubit QCCD trapped-ion quantum computer to encode a single logical qubit using the Steane 1996error color code, and demonstrates non-Clifford qubit operations by encoding a logical magic state with an error rate below the threshold required for magic state distillation.},
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keywords = {/unread},
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pages = {041058},
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file = {Full Text PDF:/home/andreas/workspace/work/hiwi/Zotero/storage/CRVKJ6VB/Ryan-Anderson et al. - 2021 - Realization of Real-Time Fault-Tolerant Quantum Error Correction.pdf:application/pdf},
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}
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@article{nigg_quantum_2014,
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title = {Quantum computations on a topologically encoded qubit},
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volume = {345},
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issn = {0036-8075, 1095-9203},
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url = {https://www.science.org/doi/10.1126/science.1253742},
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doi = {10.1126/science.1253742},
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abstract = {Fault-tolerant quantum computing
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Quantum states can be delicate. Attempts to process and manipulate quantum states can destroy the encoded information. Nigg
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et al.
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encoded the quantum state of a single qubit (in this case, a trapped ion) over the global properties of a series of trapped ions. These so-called stabilizers protected the information against noise sources that can degrade the single qubit. The protocol provides a route to fault-tolerant quantum computing.
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Science
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, this issue p.
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302
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,
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A protocol is implemented that allows for fault-tolerant quantum computing.
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,
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The construction of a quantum computer remains a fundamental scientific and technological challenge because of the influence of unavoidable noise. Quantum states and operations can be protected from errors through the use of protocols for quantum computing with faulty components. We present a quantum error-correcting code in which one qubit is encoded in entangled states distributed over seven trapped-ion qubits. The code can detect one bit flip error, one phase flip error, or a combined error of both, regardless on which of the qubits they occur. We applied sequences of gate operations on the encoded qubit to explore its computational capabilities. This seven-qubit code represents a fully functional instance of a topologically encoded qubit, or color code, and opens a route toward fault-tolerant quantum computing.},
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language = {en},
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number = {6194},
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urldate = {2026-01-29},
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journal = {Science},
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author = {Nigg, D. and Müller, M. and Martinez, E. A. and Schindler, P. and Hennrich, M. and Monz, T. and Martin-Delgado, M. A. and Blatt, R.},
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month = jul,
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year = {2014},
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note = {TLDR: A quantum error-correcting code in which one qubit is encoded in entangled states distributed over seven trapped-ion qubits, which represents a fully functional instance of a topologically encoded qubit, or color code, and opens a route toward fault-tolerant quantum computing.},
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keywords = {/unread},
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pages = {302--305},
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file = {Submitted Version:/home/andreas/workspace/work/hiwi/Zotero/storage/JK9HDSJE/Nigg et al. - 2014 - Quantum computations on a topologically encoded qubit.pdf:application/pdf},
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}
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@misc{noauthor_tutorial_nodate-1,
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title = {Tutorial - {Fault}-{Tolerant} {Quantum} {Computing} with {CSS} codes},
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url = {https://nordiquest.net/application-library/training-material/qas2024/notebooks/css_code_steane.html},
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keywords = {/unread},
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}
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@article{panteleev_degenerate_2021,
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title = {Degenerate {Quantum} {LDPC} {Codes} {With} {Good} {Finite} {Length} {Performance}},
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volume = {5},
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url = {https://quantum-journal.org/papers/q-2021-11-22-585/},
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doi = {10.22331/q-2021-11-22-585},
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abstract = {Pavel Panteleev and Gleb Kalachev,
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Quantum 5, 585 (2021).
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We study the performance of medium-length quantum LDPC (QLDPC) codes in the depolarizing channel. Only degenerate codes with the maximal stabilizer weight much smaller than their minimum dis…},
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language = {en-GB},
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urldate = {2026-01-29},
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journal = {Quantum},
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publisher = {Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften},
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author = {Panteleev, Pavel and Kalachev, Gleb},
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month = nov,
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year = {2021},
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note = {TLDR: It is shown that with the help of OSD-like post-processing the performance of the standard belief propagation (BP) decoder on many QLDPC codes can be improved by several orders of magnitude.},
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keywords = {/unread},
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pages = {585},
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file = {Full Text PDF:/home/andreas/workspace/work/hiwi/Zotero/storage/WNJDDDCI/Panteleev and Kalachev - 2021 - Degenerate Quantum LDPC Codes With Good Finite Length Performance.pdf:application/pdf},
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}
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@article{babar_fifteen_2015,
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title = {Fifteen {Years} of {Quantum} {LDPC} {Coding} and {Improved} {Decoding} {Strategies}},
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volume = {3},
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issn = {2169-3536},
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url = {https://ieeexplore.ieee.org/document/7336474},
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doi = {10.1109/ACCESS.2015.2503267},
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abstract = {The near-capacity performance of classical low-density parity check (LDPC) codes and their efficient iterative decoding makes quantum LDPC (QLPDC) codes a promising candidate for quantum error correction. In this paper, we present a comprehensive survey of QLDPC codes from the perspective of code design as well as in terms of their decoding algorithms. We also conceive a modified non-binary decoding algorithm for homogeneous Calderbank-Shor-Steane-type QLDPC codes, which is capable of alleviating the problems imposed by the unavoidable length-four cycles. Our modified decoder outperforms the state-of-the-art decoders in terms of their word error rate performance, despite imposing a reduced decoding complexity. Finally, we intricately amalgamate our modified decoder with the classic uniformly reweighted belief propagation for the sake of achieving an improved performance.},
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urldate = {2026-01-29},
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journal = {IEEE Access},
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author = {Babar, Zunaira and Botsinis, Panagiotis and Alanis, Dimitrios and Ng, Soon Xin and Hanzo, Lajos},
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year = {2015},
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note = {TLDR: This paper conceive a modified non-binary decoding algorithm for homogeneous Calderbank-Shor-Steane-type QLDPC codes, which is capable of alleviating the problems imposed by the unavoidable length-four cycles.},
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keywords = {/unread, Decoding, Complexity theory, Quantum computing, Generators, iterative decoding, Iterative decoding, Quantum error correction, Iterative Decoding, low density parity check codes, Low Density Parity Check Codes, Quantum Error Correction, quantum low density parity check codes, Quantum Low Density Parity Check Codes},
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pages = {2492--2519},
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file = {Full Text PDF:/home/andreas/workspace/work/hiwi/Zotero/storage/TRAQVN6J/Babar et al. - 2015 - Fifteen Years of Quantum LDPC Coding and Improved Decoding Strategies.pdf:application/pdf;PDF:/home/andreas/workspace/work/hiwi/Zotero/storage/K753QNFF/Babar et al. - 2015 - Fifteen Years of Quantum LDPC Coding and Improved Decoding Strategies.pdf:application/pdf},
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}
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@ -88,6 +88,21 @@
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long=Calderbank Shor Steane
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}
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\DeclareAcronym{bb}{
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short=BB,
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long=bivariate bicycle
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}
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\DeclareAcronym{dem}{
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short=DEM,
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long=detector error model
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}
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\DeclareAcronym{bp}{
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short=BP,
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long=belief propagation
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}
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%
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%
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% Document body
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@ -226,7 +241,7 @@
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\begin{frame}
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\frametitle{Peculiarities of the Quantum Setting}
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\vspace*{-5mm}
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\vspace*{-18mm}
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% Related interesting stuff
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% - No cloning theorem -> Not replication of state, protection
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@ -244,14 +259,18 @@
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% much"
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\begin{itemize}
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\item \Ac{qec} is actually able to protect the quantum state
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with all its correlations
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\item \Ac{qec} is actually able to protect the actual quantum state
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\item Similar to bits and gates, quantum systems are built on
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top of qubits and quantum gates
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\item We have to consider phase flip errors in addition to
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bit flip errors \citereference{roffe_quantum_2019}
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\vspace*{-10mm}
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\end{itemize}
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\vspace*{-3mm}
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\begin{figure}[H]
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\centering
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\begin{subfigure}{0.5\textwidth}
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\begin{subfigure}{0.32\textwidth}
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\centering
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\begin{align*}
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@ -261,7 +280,7 @@
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\caption{Bit flip (X) error}
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\end{subfigure}%
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\begin{subfigure}{0.5\textwidth}
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\begin{subfigure}{0.32\textwidth}
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\centering
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\begin{align*}
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@ -270,22 +289,37 @@
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\end{align*}
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\caption{Phase flip (Z) error}
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\end{subfigure}%
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\begin{subfigure}{0.32\textwidth}
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\centering
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\begin{align*}
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\ket{0} &\rightarrow \phantom{-j}\ket{1} \\
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\ket{1} &\rightarrow -j\ket{0}
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\end{align*}
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\caption{Y error: Combination of X and Z}
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\end{subfigure}
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\end{figure}
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\item \red{Introduce Y errors}
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\vspace*{-3mm}
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\begin{itemize}
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\item Measuring the qubits directly destroys superpositions
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and entanglement \\
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$\rightarrow$ We generally only work with the syndrome,
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which we can measure \citereference{nielsen_quantum_2010}
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\item We don't care about restoring the specific codeword,
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only finding the coset it's in
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\item Sometimes superposition permits multiple equivalent
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solutions to the decoding problem (\emph{quantum
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degeneracy}) \citereference{roffe_decoding_2020}
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\end{itemize}
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\vspace*{15mm}
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\vspace*{7mm}
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\addreferences
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{nielsen_quantum_2010}
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{roffe_quantum_2019}
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{roffe_decoding_2020}
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\stopreferences
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\end{frame}
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@ -342,10 +376,6 @@
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\begin{itemize}
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\item We entangle the state with \emph{ancilla qubits} to
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perform syndrome measurements \citereference{nielsen_quantum_2010}
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\item \red{Implicitly introduce the concept of a quantum gate
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by mentioning CNOT gates?}
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\item \red{Mention that we can perform syndrome extraction
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with just CNOTs and H? (and find citation)}
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\item \red{Do I need to show what the syndrome extraction
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circuitry for Z errors looks like?}
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\item Example: The 3-qubit repetition code%
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@ -406,15 +436,47 @@
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\begin{frame}
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\frametitle{Fault Tolerance}
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\vspace*{-10mm}
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\vspace*{-15mm}
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\begin{itemize}
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\item The quantum gates we use for syndrome extraction are
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faulty themselves \\
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$\rightarrow$ We need \emph{fault-tolerant} \ac{qec}
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\item A \ac{qec} procedure is said to be fault tolerant if it
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can account for errors that occur at any location in the
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circuit \citereference{roffe_quantum_2019}
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\item A \ac{qec} procedure is said to be fault tolerant if,
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in addition to correcting \emph{input errors}, the spread
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of \emph{internal errors} is sufficiently limited
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\citereference{derks_designing_2025}
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\end{itemize}
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\vspace*{3mm}
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\begin{figure}[H]
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\centering
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\begin{tikzpicture}
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\node[rectangle, draw, fill=orange!20, minimum
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height=3cm, minimum width=3.5cm, align=left] at (0,0)
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(internal) {Internal\\ Errors};
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\node[signal, draw, fill=blue!20, minimum height=3cm,
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minimum width=4cm, align=left, signal pointer angle=140]
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at (-3.7, 0) (input) {Input\\ Errors};
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\node at (2.5,0) {\huge =};
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\node[rectangle, draw, fill=red!20, minimum height=3cm,
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minimum width=3.5cm, align=left] at (5,0) (output)
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{Output\\ Errors};
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\node[above] at (input.north) {\small Input State};
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\node[above] at (internal.north) {\small QEC};
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\node[above] at (output.north) {\small Output State};
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\end{tikzpicture}
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\end{figure}
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\vspace*{3mm}
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\begin{itemize}
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\item We have to modify the syndrome extraction circuitry to
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be fault tolerant (e.g., by using specially prepared
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multi-qubit states for each ancilla
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@ -422,28 +484,11 @@
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\item We generally perform multiple rounds of syndrome extraction
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\end{itemize}
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% \vspace*{1mm}
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%
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% \begin{figure}[H]
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% \centering
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% % tex-fmt: off
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% \begin{quantikz}[row sep=2mm, column sep=4mm, wire types={q,q,q,q,q,n,n}]
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% & \ctrl{3} & & & & & & \ctrl{5} & & & & \\
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% \lstick{$\ket{\psi}$} & & \ctrl{2} & \ctrl{3} & & & & & \ctrl{4} & \ctrl{5} & & & \setwiretype{n}\ldots \\
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% & & & & \ctrl{2} & & & & & & \ctrl{4} & \\
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% \lstick{$\ket{0}_{\text{A}_1}$} & \targ{} & \targ{} & & & & & & & & & \meter{} \\
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% \lstick{$\ket{0}_{\text{A}_2}$} & & & \targ{} & \targ{} & & & & & & & \meter{} \\
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% & & & & & \lstick{$\ket{0}_{\text{A}_3}$} & \setwiretype{q} & \targ{} & \targ{} & & & \meter{} \\
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% & & & & & \lstick{$\ket{0}_{\text{A}_4}$} & \setwiretype{q} & & & \targ{} & \targ{} & \meter{}
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% \end{quantikz}
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% % tex-fmt: on
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% \end{figure}
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\vspace*{25mm}
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\vspace*{10mm}
|
||||
|
||||
\addreferences
|
||||
{roffe_quantum_2019}
|
||||
{shor_fault-tolerant_1997}
|
||||
{derks_designing_2025}
|
||||
\stopreferences
|
||||
\end{frame}
|
||||
|
||||
@ -586,7 +631,7 @@
|
||||
\end{frame}
|
||||
|
||||
\begin{frame}[fragile]
|
||||
\frametitle{The Measurement Syndrome Matrix II}
|
||||
\frametitle{The Measurement Syndromemani Matrix II}
|
||||
|
||||
\vspace*{-18mm}
|
||||
|
||||
@ -923,15 +968,84 @@
|
||||
\begin{frame}
|
||||
\frametitle{The Detector Error Matrix II}
|
||||
|
||||
\vspace*{-17mm}
|
||||
|
||||
\begin{itemize}
|
||||
\item \red{Highlight SC-LDPC like structure}
|
||||
\item Visualization of general process \red{Deal with 3-qubit
|
||||
state (somehow represent arbitrary qubit state)}
|
||||
\end{itemize}
|
||||
|
||||
\vspace*{5mm}
|
||||
|
||||
\begin{figure}[H]
|
||||
\centering
|
||||
|
||||
\tikzset{
|
||||
gate/.style={
|
||||
draw, %line width=1pt,
|
||||
minimum height=2cm,
|
||||
}
|
||||
}
|
||||
|
||||
% tex-fmt: off
|
||||
\begin{quantikz}[row sep=2mm, column sep=4mm, wire types={q,q,q,n,n,n}]
|
||||
& \gate[3]{SE_1} & & \gate[3]{SE_2} & & \gate[3]{SE_3} & & \gate[3]{SE_4} & \\
|
||||
\lstick{$\ket{\psi}$} & & & & & & & & & \setwiretype{n} & \ldots \\
|
||||
& \wire[d][3]{c} & & \wire[d][1]{c} & & \wire[d][1]{c} & & \wire[d][1]{c} & \\
|
||||
& \ctrl[wire=c]{0}\wire[r][1]{c} & \wire[d][1]{c} & \ctrl[vertical wire=c]{1}\wire[r][1]{c} & \wire[d][1]{c} & \ctrl[vertical wire=c]{1}\wire[r][1]{c} & \wire[d][1]{c} & \ctrl[vertical wire=c]{1}\wire[r][1]{c} & \\
|
||||
& & \wire[r][1]{c} & \targ{}\wire[d][1]{c} & \wire[r][1]{c} & \targ{}\wire[d][1]{c} & \wire[r][1]{c} & \targ{}\wire[d][1]{c} & \\
|
||||
& \gate[1]{\bm{D}_1} & & \gate[1]{\bm{D}_2} & & \gate[1]{\bm{D}_3} & & \gate[1]{\bm{D}_4} & \\
|
||||
\end{quantikz}
|
||||
% tex-fmt: on
|
||||
\end{figure}
|
||||
|
||||
\begin{itemize}
|
||||
\item E.g., for \ac{bb} codes, the resulting detector
|
||||
error matrix under circuit-level noise has the form
|
||||
\citereference{gong_toward_2024}
|
||||
\end{itemize}
|
||||
|
||||
\vspace*{-15mm}
|
||||
|
||||
\begin{align*}
|
||||
\bm{H} =
|
||||
\begin{pmatrix}
|
||||
\bm{H}_0 & \bm{H}_1 & \bm{0} & \bm{0} & \bm{0}
|
||||
& \bm{0} & \cdots \\
|
||||
\bm{0} & \bm{H}_2 & \bm{H}_0 & \bm{H}_1 & \bm{0}
|
||||
& \bm{0} & \\
|
||||
\bm{0} & \bm{0} & \bm{0} & \bm{H}_2 & \bm{H}_0
|
||||
& \bm{H}_1 & \\
|
||||
\bm{0} & \bm{0} & \bm{0} & \bm{0} & \bm{0}
|
||||
& \bm{H}_2 & \\
|
||||
\vdots & & & &
|
||||
& & \ddots
|
||||
\end{pmatrix}
|
||||
\end{align*}
|
||||
|
||||
\vspace*{3mm}
|
||||
|
||||
\addreferences
|
||||
{gong_toward_2024}
|
||||
\stopreferences
|
||||
\end{frame}
|
||||
|
||||
\begin{frame}[fragile]
|
||||
\frametitle{Noise models}
|
||||
\frametitle{Noise Model Types}
|
||||
|
||||
\vspace*{-7mm}
|
||||
% Related interesting stuff
|
||||
% - The difference between an n-qubit error and multiple
|
||||
% simultaneous single-qubit errors is that in the n-qubit case,
|
||||
% the errors can be correlated (e.g., XX more probable than XI)
|
||||
|
||||
\vspace*{-15mm}
|
||||
|
||||
\begin{itemize}
|
||||
\item The noise model assigns a likelihood to the occurrence
|
||||
of each error
|
||||
\end{itemize}
|
||||
|
||||
\vspace*{7mm}
|
||||
|
||||
\begin{minipage}{0.60\textwidth}
|
||||
\begin{itemize}
|
||||
@ -982,29 +1096,38 @@
|
||||
\end{figure}
|
||||
\end{minipage}
|
||||
|
||||
\vspace*{15mm}
|
||||
\vspace*{10mm}
|
||||
|
||||
\addreferences
|
||||
{derks_designing_2025}
|
||||
{nielsen_quantum_2010}
|
||||
{derks_designing_2025}
|
||||
\stopreferences
|
||||
\end{frame}
|
||||
|
||||
\begin{frame}
|
||||
\frametitle{Challenges}
|
||||
\frametitle{Decoding using Detector Error Models}
|
||||
|
||||
\begin{itemize}
|
||||
\item \red{Multiple different errors are summarized
|
||||
$\rightarrow$ short cycles \& degeneracy}
|
||||
\footnote{
|
||||
\texttt{
|
||||
\red{https://www.math.cit.tum.de/fileadmin/w00ccg/math/\_my\_direct\_uploads/Dan\_Browne.pdf}
|
||||
}
|
||||
}
|
||||
\\
|
||||
\red{$\rightarrow$ We generally don't use "normal BP" (BP
|
||||
+ OSD, BPGD, etc.)}
|
||||
\item A \ac{dem} combines a detector error matrix and a noise model
|
||||
\item The likelihoods of different error locations can be
|
||||
used as priors for decoding
|
||||
\vspace*{5mm}
|
||||
\item Challenges
|
||||
\begin{itemize}
|
||||
\item Repeated syndrome measurements come with
|
||||
increased decoding complexity
|
||||
\citereference{gong_toward_2024}
|
||||
\item Degeneracy and short cycles lead to degraded
|
||||
performance of \ac{bp} \citereference{babar_fifteen_2015}
|
||||
\end{itemize}
|
||||
\end{itemize}
|
||||
|
||||
\vspace*{20mm}
|
||||
|
||||
\addreferences
|
||||
{babar_fifteen_2015}
|
||||
{gong_toward_2024}
|
||||
\stopreferences{}
|
||||
\end{frame}
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
@ -1024,6 +1147,8 @@
|
||||
\item Give overview of existing research
|
||||
\item Explain exactly what they do in the main paper I am
|
||||
basing my work on
|
||||
\item \red{$\rightarrow$ We generally don't use "normal BP"
|
||||
(BP + OSD, BPGD, etc.)}
|
||||
\end{itemize}
|
||||
\end{frame}
|
||||
|
||||
|
||||
Loading…
Reference in New Issue
Block a user