617 lines
30 KiB
BibTeX
617 lines
30 KiB
BibTeX
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@misc{derks_designing_2025,
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title = {Designing fault-tolerant circuits using detector error models},
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url = {http://arxiv.org/abs/2407.13826},
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doi = {10.48550/arXiv.2407.13826},
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abstract = {Quantum error-correcting codes, such as subspace,
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subsystem, and Floquet codes, are typically constructed within
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the stabilizer formalism, which does not fully capture the idea
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of fault-tolerance needed for practical quantum computing
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applications. In this work, we explore the remarkably powerful
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formalism of detector error models, which fully captures
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fault-tolerance at the circuit level. We introduce the detector
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error model formalism in a pedagogical manner and provide several
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examples. Additionally, we apply the formalism to three different
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levels of abstraction in the engineering cycle of fault-tolerant
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circuit designs: finding robust syndrome extraction circuits,
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identifying efficient measurement schedules, and constructing
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fault-tolerant procedures. We enhance the surface code's
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resistance to measurement errors, devise short measurement
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schedules for color codes, and implement a more efficient
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fault-tolerant method for measuring logical operators.},
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number = {{arXiv}:2407.13826},
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publisher = {{arXiv}},
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author = {Derks, Peter-Jan H. S. and Townsend-Teague, Alex and
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Burchards, Ansgar G. and Eisert, Jens},
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urldate = {2025-10-28},
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date = {2025-10-25},
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eprinttype = {arxiv},
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eprint = {2407.13826 [quant-ph]},
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keywords = {Quantum Physics, /s1, \#{QEC}},
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file = {Preprint PDF:/home/andreas/Zotero/storage/NLEMWTH8/Derks
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et al. - 2025 - Designing fault-tolerant circuits using detector
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error
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models.pdf:application/pdf;Snapshot:/home/andreas/Zotero/storage/QEBN4FJT/2407.html:text/html},
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}
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@online{nielsen_quantum_2010,
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title = {Quantum Computation and Quantum Information: 10th
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Anniversary Edition},
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shorttitle = {Quantum Computation and Quantum Information},
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abstract = {One of the most cited books in physics of all time,
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Quantum Computation and Quantum Information remains the best
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textbook in this exciting field of science. This 10th anniversary
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edition includes an introduction from the authors setting the
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work in context. This comprehensive textbook describes such
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remarkable effects as fast quantum algorithms, quantum
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teleportation, quantum cryptography and quantum error-correction.
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Quantum mechanics and computer science are introduced before
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moving on to describe what a quantum computer is, how it can be
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used to solve problems faster than 'classical' computers and its
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real-world implementation. It concludes with an in-depth
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treatment of quantum information. Containing a wealth of figures
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and exercises, this well-known textbook is ideal for courses on
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the subject, and will interest beginning graduate students and
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researchers in physics, computer science, mathematics, and
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electrical engineering.},
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titleaddon = {Cambridge Aspire website},
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author = {Nielsen, Michael A. and Chuang, Isaac L.},
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urldate = {2025-10-28},
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date = {2010-12-09},
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langid = {english},
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doi = {10.1017/CBO9780511976667},
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note = {{ISBN}: 9780511976667
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Publisher: Cambridge University Press},
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keywords = {\#{FND}, \#{QM}, \#{QEC}},
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file = {PDF:/home/andreas/Zotero/storage/2FGWZ5CC/Nielsen and
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Chuang - 2010 - Quantum Computation and Quantum Information 10th
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Anniversary
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Edition.pdf:application/pdf;Snapshot:/home/andreas/Zotero/storage/RFPYY4AS/01E10196D0A682A6AEFFEA52D53BE9AE.html:text/html},
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}
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@thesis{klinke_neural_2025,
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location = {Karlsruhe},
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title = {Neural Belief Propagation Ensemble Decoding of Quantum
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{LDPC} Codes},
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institution = {{KIT}},
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type = {Bachelor's Thesis},
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author = {Klinke, Jeremi},
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date = {2025-09-26},
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keywords = {/s1, \#{QEC}},
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file = {PDF:/home/andreas/Zotero/storage/ENJG2F8D/Klinke - Neural
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Belief Propagation Ensemble Decoding of Quantum LDPC
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Codes.pdf:application/pdf},
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}
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@article{miao_quaternary_2025,
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title = {Quaternary Neural Belief Propagation Decoding of Quantum
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{LDPC} Codes with Overcomplete Check Matrices},
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volume = {13},
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issn = {2169-3536},
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url = {http://arxiv.org/abs/2308.08208},
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doi = {10.1109/ACCESS.2025.3539475},
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abstract = {Quantum low-density parity-check ({QLDPC}) codes are
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promising candidates for error correction in quantum computers.
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One of the major challenges in implementing {QLDPC} codes in
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quantum computers is the lack of a universal decoder. In this
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work, we first propose to decode {QLDPC} codes with a belief
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propagation ({BP}) decoder operating on overcomplete check
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matrices. Then, we extend the neural {BP} ({NBP}) decoder, which
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was originally studied for suboptimal binary {BP} decoding of
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{QLPDC} codes, to quaternary {BP} decoders. Numerical simulation
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results demonstrate that both approaches as well as their
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combination yield a low-latency, high-performance decoder for
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several short to moderate length {QLDPC} codes.},
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pages = {25637--25649},
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journaltitle = {{IEEE} Access},
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shortjournal = {{IEEE} Access},
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author = {Miao, Sisi and Schnerring, Alexander and Li, Haizheng
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and Schmalen, Laurent},
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urldate = {2025-10-28},
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date = {2025-02-05},
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eprinttype = {arxiv},
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eprint = {2308.08208 [quant-ph]},
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note = {{TLDR}: This work proposes to decode {QLDPC} codes with a
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belief propagation ({BP}) decoder operating on overcomplete check
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matrices and extends the neural {BP} decoder, which was
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originally studied for suboptimal binary {BP} decoding of {QLPDC}
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codes, to quaternary {BP} decoders.},
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keywords = {Quantum Physics, Computer Science - Information
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Theory, Mathematics - Information Theory, /unread, \#{QEC}},
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file = {Preprint PDF:/home/andreas/Zotero/storage/SJXAPQ9Z/Miao
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et al. - 2025 - Quaternary Neural Belief Propagation Decoding of
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Quantum LDPC Codes with Overcomplete Check
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Matrices.pdf:application/pdf;Snapshot:/home/andreas/Zotero/storage/ZVHBIEHR/2308.html:text/html},
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}
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@article{roffe_quantum_2019,
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title = {Quantum error correction: an introductory guide},
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volume = {60},
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issn = {0010-7514},
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url = {https://doi.org/10.1080/00107514.2019.1667078},
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doi = {10.1080/00107514.2019.1667078},
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shorttitle = {Quantum error correction},
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abstract = {Quantum error correction protocols will play a
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central role in the realisation of quantum computing; the choice
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of error correction code will influence the full quantum
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computing stack, from the layout of qubits at the physical level
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to gate compilation strategies at the software level. As such,
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familiarity with quantum coding is an essential prerequisite for
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the understanding of current and future quantum computing
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architectures. In this review, we provide an introductory guide
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to the theory and implementation of quantum error correction
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codes. Where possible, fundamental concepts are described using
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the simplest examples of detection and correction codes, the
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working of which can be verified by hand. We outline the
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construction and operation of the surface code, the most widely
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pursued error correction protocol for experiment. Finally, we
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discuss issues that arise in the practical implementation of the
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surface code and other quantum error correction codes.},
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pages = {226--245},
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number = {3},
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journaltitle = {Contemporary Physics},
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author = {Roffe, Joschka},
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urldate = {2025-11-04},
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date = {2019-07-03},
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keywords = {/s1, \#{FND}, \#{QEC}},
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file = {Full Text PDF:/home/andreas/Zotero/storage/DW4EYDQ8/Roffe
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- 2019 - Quantum error correction an introductory
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guide.pdf:application/pdf},
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}
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@misc{calderbank_quantum_1997,
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title = {Quantum Error Correction via Codes over {GF}(4)},
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url = {http://arxiv.org/abs/quant-ph/9608006},
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doi = {10.48550/arXiv.quant-ph/9608006},
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abstract = {The problem of finding quantum error-correcting codes
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is transformed into the problem of finding additive codes over
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the field {GF}(4) which are self-orthogonal with respect to a
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certain trace inner product. Many new codes and new bounds are
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presented, as well as a table of upper and lower bounds on such
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codes of length up to 30 qubits.},
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number = {{arXiv}:quant-ph/9608006},
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publisher = {{arXiv}},
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author = {Calderbank, A. R. and Rains, E. M. and Shor, P. W. and
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Sloane, N. J. A.},
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urldate = {2025-11-05},
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date = {1997-09-10},
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eprinttype = {arxiv},
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eprint = {quant-ph/9608006},
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keywords = {Quantum Physics, /s1, \#{FND}, \#{QEC}},
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file = {Preprint
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PDF:/home/andreas/Zotero/storage/5IM4A6FA/Calderbank et al. -
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1997 - Quantum Error Correction via Codes over
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GF(4).pdf:application/pdf;Snapshot:/home/andreas/Zotero/storage/LLQUFH76/9608006.html:text/html},
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}
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@article{shor_scheme_1995,
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title = {Scheme for reducing decoherence in quantum computer memory},
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volume = {52},
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rights = {http://link.aps.org/licenses/aps-default-license},
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issn = {1050-2947, 1094-1622},
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url = {https://link.aps.org/doi/10.1103/PhysRevA.52.R2493},
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doi = {10.1103/PhysRevA.52.R2493},
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pages = {R2493--R2496},
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number = {4},
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journaltitle = {Physical Review A},
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shortjournal = {Phys. Rev. A},
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author = {Shor, Peter W.},
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urldate = {2025-11-05},
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date = {1995-10-01},
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langid = {english},
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note = {{TLDR}: In the mid-1990s, theorists devised methods to
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preserve the integrity of quantum
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bits{\textbackslash}char22\{\}techniques that may become the key
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to practical quantum computing on a large scale.},
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keywords = {/s2, \#{FND}, \#{QEC}},
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file = {PDF:/home/andreas/Zotero/storage/DG6QT7UX/Shor - 1995 -
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Scheme for reducing decoherence in quantum computer
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memory.pdf:application/pdf},
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}
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@article{divincenzo_fault-tolerant_1996,
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title = {Fault-Tolerant Error Correction with Efficient Quantum Codes},
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volume = {77},
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issn = {0031-9007, 1079-7114},
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url = {http://arxiv.org/abs/quant-ph/9605031},
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doi = {10.1103/PhysRevLett.77.3260},
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abstract = {We exhibit a simple, systematic procedure for
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detecting and correcting errors using any of the recently
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reported quantum error-correcting codes. The procedure is shown
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explicitly for a code in which one qubit is mapped into five. The
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quantum networks obtained are fault tolerant, that is, they can
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function successfully even if errors occur during the error
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correction. Our construction is derived using a recently
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introduced group-theoretic framework for unifying all known quantum codes.},
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pages = {3260--3263},
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number = {15},
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journaltitle = {Physical Review Letters},
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shortjournal = {Phys. Rev. Lett.},
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author = {{DiVincenzo}, David P. and Shor, Peter W.},
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urldate = {2025-11-05},
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date = {1996-10-07},
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eprinttype = {arxiv},
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eprint = {quant-ph/9605031},
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note = {{TLDR}: This work exhibits a simple, systematic procedure
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for detecting and correcting errors using any of the recently
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reported quantum error-correcting codes, derived using a recently
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introduced group-theoretic framework for unifying all known quantum codes.},
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keywords = {Quantum Physics, /unread, \#{FND}, \#{QEC}},
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file = {Preprint
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PDF:/home/andreas/Zotero/storage/KNGHIXB3/DiVincenzo and Shor -
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1996 - Fault-Tolerant Error Correction with Efficient Quantum
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Codes.pdf:application/pdf;Snapshot:/home/andreas/Zotero/storage/6JURUG3K/9605031.html:text/html},
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}
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@misc{shor_fault-tolerant_1997,
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title = {Fault-tolerant quantum computation},
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url = {http://arxiv.org/abs/quant-ph/9605011},
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doi = {10.48550/arXiv.quant-ph/9605011},
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abstract = {Recently, it was realized that use of the properties
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of quantum mechanics might speed up certain computations
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dramatically. Interest in quantum computation has since been
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growing. One of the main difficulties of realizing quantum
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computation is that decoherence tends to destroy the information
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in a superposition of states in a quantum computer, thus making
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long computations impossible. A futher difficulty is that
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inaccuracies in quantum state transformations throughout the
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computation accumulate, rendering the output of long computations
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unreliable. It was previously known that a quantum circuit with t
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gates could tolerate O(1/t) amounts of inaccuracy and decoherence
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per gate. We show, for any quantum computation with t gates, how
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to build a polynomial size quantum circuit that can tolerate
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O(1/(log t){\textasciicircum}c) amounts of inaccuracy and
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decoherence per gate, for some constant c. We do this by showing
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how to compute using quantum error correcting codes. These codes
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were previously known to provide resistance to errors while
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storing and transmitting quantum data.},
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number = {{arXiv}:quant-ph/9605011},
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publisher = {{arXiv}},
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author = {Shor, Peter W.},
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urldate = {2025-11-05},
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date = {1997-03-05},
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eprinttype = {arxiv},
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eprint = {quant-ph/9605011},
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keywords = {Quantum Physics, /s1, \#{FND}, \#{QEC}},
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file = {Preprint PDF:/home/andreas/Zotero/storage/CSLTPZU5/Shor -
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1997 - Fault-tolerant quantum computation.pdf:application/pdf},
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}
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@misc{gottesman_stabilizer_1997,
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title = {Stabilizer Codes and Quantum Error Correction},
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url = {http://arxiv.org/abs/quant-ph/9705052},
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doi = {10.48550/arXiv.quant-ph/9705052},
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abstract = {Controlling operational errors and decoherence is one
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of the major challenges facing the field of quantum computation
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and other attempts to create specified many-particle entangled
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states. The field of quantum error correction has developed to
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meet this challenge. A group-theoretical structure and associated
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subclass of quantum codes, the stabilizer codes, has proved
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particularly fruitful in producing codes and in understanding the
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structure of both specific codes and classes of codes. I will
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give an overview of the field of quantum error correction and the
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formalism of stabilizer codes. In the context of stabilizer
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codes, I will discuss a number of known codes, the capacity of a
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quantum channel, bounds on quantum codes, and fault-tolerant
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quantum computation.},
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number = {{arXiv}:quant-ph/9705052},
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publisher = {{arXiv}},
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author = {Gottesman, Daniel},
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urldate = {2025-11-06},
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date = {1997-05-28},
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eprinttype = {arxiv},
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eprint = {quant-ph/9705052},
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keywords = {Quantum Physics, /s1, \#{FND}, \#{QEC}},
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file = {Preprint
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PDF:/home/andreas/Zotero/storage/JT582GBB/Gottesman - 1997 -
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Stabilizer Codes and Quantum Error
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Correction.pdf:application/pdf;Snapshot:/home/andreas/Zotero/storage/5GCZHHTH/9705052.html:text/html},
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}
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@article{gottesman_theory_1998,
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title = {Theory of fault-tolerant quantum computation},
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volume = {57},
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url = {https://link.aps.org/doi/10.1103/PhysRevA.57.127},
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doi = {10.1103/PhysRevA.57.127},
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abstract = {In order to use quantum error-correcting codes to
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improve the performance of a quantum computer, it is necessary to
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be able to perform operations fault-tolerantly on encoded states.
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I present a theory of fault-tolerant operations on stabilizer
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codes based on symmetries of the code stabilizer. This allows a
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straightforward determination of which operations can be
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performed fault-tolerantly on a given code. I demonstrate that
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fault-tolerant universal computation is possible for any
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stabilizer code. I discuss a number of examples in more detail,
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including the five-quantum-bit code.},
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pages = {127--137},
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number = {1},
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journaltitle = {Physical Review A},
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shortjournal = {Phys. Rev. A},
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author = {Gottesman, Daniel},
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urldate = {2025-11-06},
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date = {1998-01-01},
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note = {Publisher: American Physical Society
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{TLDR}: It is demonstrated that fault-tolerant universal
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computation is possible for any stabilizer code, including the
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five-quantum-bit code.},
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keywords = {/s1, \#{FND}, \#{QEC}},
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file = {APS
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Snapshot:/home/andreas/Zotero/storage/BP7CHBIU/PhysRevA.57.html:text/html;Full
|
||
Text PDF:/home/andreas/Zotero/storage/7E5TUIMN/Gottesman - 1998 -
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Theory of fault-tolerant quantum computation.pdf:application/pdf},
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}
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@misc{gottesman_introduction_2009,
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title = {An Introduction to Quantum Error Correction and
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Fault-Tolerant Quantum Computation},
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url = {http://arxiv.org/abs/0904.2557},
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doi = {10.48550/arXiv.0904.2557},
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abstract = {Quantum states are very delicate, so it is likely
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some sort of quantum error correction will be necessary to build
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reliable quantum computers. The theory of quantum
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error-correcting codes has some close ties to and some striking
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differences from the theory of classical error-correcting codes.
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Many quantum codes can be described in terms of the stabilizer of
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the codewords. The stabilizer is a finite Abelian group, and
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allows a straightforward characterization of the error-correcting
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properties of the code. The stabilizer formalism for quantum
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codes also illustrates the relationships to classical coding
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theory, particularly classical codes over {GF}(4), the finite
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field with four elements. To build a quantum computer which
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behaves correctly in the presence of errors, we also need a
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theory of fault-tolerant quantum computation, instructing us how
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to perform quantum gates on qubits which are encoded in a quantum
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error-correcting code. The threshold theorem states that it is
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possible to create a quantum computer to perform an arbitrary
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quantum computation provided the error rate per physical gate or
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time step is below some constant threshold value.},
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number = {{arXiv}:0904.2557},
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publisher = {{arXiv}},
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author = {Gottesman, Daniel},
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urldate = {2025-11-06},
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date = {2009-04-16},
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eprinttype = {arxiv},
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eprint = {0904.2557 [quant-ph]},
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keywords = {Quantum Physics, /s1, \#{FND}, \#{QEC}},
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file = {Preprint
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PDF:/home/andreas/Zotero/storage/AGETMT4C/Gottesman - 2009 - An
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Introduction to Quantum Error Correction and Fault-Tolerant
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Quantum
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Computation.pdf:application/pdf;Snapshot:/home/andreas/Zotero/storage/UHAPPP5S/0904.html:text/html},
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}
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@article{calderbank_good_1996,
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title = {Good quantum error-correcting codes exist},
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volume = {54},
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url = {https://link.aps.org/doi/10.1103/PhysRevA.54.1098},
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doi = {10.1103/PhysRevA.54.1098},
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abstract = {A quantum error-correcting code is defined to be a
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unitary mapping (encoding) of k qubits (two-state quantum
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systems) into a subspace of the quantum state space of n qubits
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such that if any t of the qubits undergo arbitrary decoherence,
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not necessarily independently, the resulting n qubits can be used
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to faithfully reconstruct the original quantum state of the k
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encoded qubits. Quantum error-correcting codes are shown to exist
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with asymptotic rate k/n=1-2𝐻2(2t/n) where 𝐻2(p) is the binary
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entropy function -plog2p-(1-p)log2(1-p). Upper bounds on this
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asymptotic rate are given. © 1996 The American Physical Society.},
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pages = {1098--1105},
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number = {2},
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journaltitle = {Physical Review A},
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shortjournal = {Phys. Rev. A},
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author = {Calderbank, A. R. and Shor, Peter W.},
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urldate = {2025-11-06},
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date = {1996-08-01},
|
||
note = {Publisher: American Physical Society
|
||
{TLDR}: The techniques investigated in this paper can be extended
|
||
so as to reduce the accuracy required for factorization of
|
||
numbers large enough to be difficult on conventional computers
|
||
appears to be closer to one part in billions.},
|
||
keywords = {/s1, \#{FND}, \#{QEC}},
|
||
file = {APS
|
||
Snapshot:/home/andreas/Zotero/storage/IK4DH994/PhysRevA.54.html:text/html;Full
|
||
Text PDF:/home/andreas/Zotero/storage/RLKB7SKX/Calderbank and
|
||
Shor - 1996 - Good quantum error-correcting codes
|
||
exist.pdf:application/pdf},
|
||
}
|
||
|
||
@book{griffiths_introduction_1995,
|
||
title = {Introduction to Quantum Mechanics},
|
||
isbn = {0-13-124405-1},
|
||
abstract = {Changes and additions to the new edition of this
|
||
classic textbook include a new chapter on symmetries, new
|
||
problems and examples, improved explanations, more numerical
|
||
problems to be worked on a computer, new applications to solid
|
||
state physics, and consolidated treatment of time-dependent potentials.},
|
||
publisher = {Prentice Hall},
|
||
author = {Griffiths, David J.},
|
||
date = {1995},
|
||
langid = {english},
|
||
keywords = {\#{FND}, \#{QM}, \#{MAT}},
|
||
file = {PDF:/home/andreas/Zotero/storage/ZLP4S5EB/Griffiths and
|
||
Schroeter - 2018 - Introduction to Quantum
|
||
Mechanics.pdf:application/pdf;Snapshot:/home/andreas/Zotero/storage/V7B6J8YI/990799CA07A83FC5312402AF6860311E.html:text/html},
|
||
}
|
||
|
||
@online{bradley_tensor_2018,
|
||
title = {The Tensor Product, Demystified},
|
||
url = {https://www.math3ma.com/blog/the-tensor-product-demystified},
|
||
author = {Bradley, Tai-Danae},
|
||
urldate = {2025-11-11},
|
||
date = {2018-11-18},
|
||
keywords = {\#{FND}, \#{MAT}},
|
||
file =
|
||
{Snapshot:/home/andreas/Zotero/storage/JWTQ4W7G/the-tensor-product-demystified.html:text/html},
|
||
}
|
||
|
||
@misc{camps-moreno_toward_2024,
|
||
title = {Toward Quantum {CSS}-T Codes from Sparse Matrices},
|
||
url = {http://arxiv.org/abs/2406.00425},
|
||
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.},
|
||
number = {{arXiv}:2406.00425},
|
||
publisher = {{arXiv}},
|
||
author = {Camps-Moreno, Eduardo and López, Hiram H. and Matthews,
|
||
Gretchen L. and {McMillon}, Emily},
|
||
urldate = {2025-11-13},
|
||
date = {2024-06-04},
|
||
eprinttype = {arxiv},
|
||
eprint = {2406.00425 [cs]},
|
||
keywords = {Computer Science - Information Theory, /unread, \#{QEC}},
|
||
file = {Preprint
|
||
PDF:/home/andreas/Zotero/storage/C634YE7N/Camps-Moreno et al. -
|
||
2024 - Toward Quantum CSS-T Codes from Sparse
|
||
Matrices.pdf:application/pdf;Snapshot:/home/andreas/Zotero/storage/TD3KFLFZ/2406.html:text/html},
|
||
}
|
||
|
||
@misc{koutsioumpas_colour_2025,
|
||
title = {Colour Codes Reach Surface Code Performance using Vibe Decoding},
|
||
url = {http://arxiv.org/abs/2508.15743},
|
||
doi = {10.48550/arXiv.2508.15743},
|
||
abstract = {Two-dimensional quantum colour codes hold significant
|
||
promise for quantum error correction, offering advantages such as
|
||
planar connectivity and low overhead logical gates. Despite their
|
||
theoretical appeal, the practical deployment of these codes faces
|
||
challenges due to complex decoding requirements compared to
|
||
surface codes. This paper introduces vibe decoding which, for the
|
||
first time, brings colour code performance on par with the
|
||
surface code under practical decoding. Our approach leverages an
|
||
ensemble of belief propagation decoders - each executing a
|
||
distinct serial message passing schedule - combined with
|
||
localised statistics post-processing. We refer to this combined
|
||
protocol as {VibeLSD}. The {VibeLSD} decoder is highly versatile:
|
||
our numerical results show it outperforms all practical existing
|
||
colour code decoders across various syndrome extraction schemes,
|
||
noise models, and error rates. By estimating qubit footprints
|
||
through quantum memory simulations, we show that colour codes can
|
||
operate with overhead that is comparable to, and in some cases
|
||
lower than, that of the surface code. This, combined with the
|
||
fact that localised statistics decoding is a parallel algorithm,
|
||
makes {VibeLSD} suitable for implementation on specialised
|
||
hardware for real-time decoding. Our results establish the colour
|
||
code as a practical architecture for near-term quantum hardware,
|
||
providing improved compilation efficiency for both Clifford and
|
||
non-Clifford gates without incurring additional qubit overhead
|
||
relative to the surface code.},
|
||
number = {{arXiv}:2508.15743},
|
||
publisher = {{arXiv}},
|
||
author = {Koutsioumpas, Stergios and Noszko, Tamas and Sayginel,
|
||
Hasan and Webster, Mark and Roffe, Joschka},
|
||
urldate = {2025-11-13},
|
||
date = {2025-08-22},
|
||
eprinttype = {arxiv},
|
||
eprint = {2508.15743 [quant-ph]},
|
||
note = {{TLDR}: The results establish the colour code as a
|
||
practical architecture for near-term quantum hardware, providing
|
||
improved compilation efficiency for both Clifford and
|
||
non-Clifford gates without incurring additional qubit overhead
|
||
relative to the surface code.},
|
||
keywords = {Quantum Physics, Computer Science - Information
|
||
Theory, /s1, \#{QEC}},
|
||
file = {Preprint
|
||
PDF:/home/andreas/Zotero/storage/C4K3XG2S/Koutsioumpas et al. -
|
||
2025 - Colour Codes Reach Surface Code Performance using Vibe
|
||
Decoding.pdf:application/pdf;Snapshot:/home/andreas/Zotero/storage/76EXKH3S/2508.html:text/html},
|
||
}
|
||
|
||
@article{koutsioumpas_automorphism_2025,
|
||
title = {Automorphism Ensemble Decoding of Quantum {LDPC} Codes},
|
||
author = {Koutsioumpas, Stergios and Sayginel, Hasan and Webster,
|
||
Mark and Browne, Dan E},
|
||
date = {2025-03-04},
|
||
langid = {english},
|
||
keywords = {/s1, \#{QEC}},
|
||
file = {PDF:/home/andreas/Zotero/storage/SHUGDAU8/Koutsioumpas et
|
||
al. - Automorphism Ensemble Decoding of Quantum LDPC
|
||
Codes.pdf:application/pdf},
|
||
}
|
||
|
||
@article{geiselhart_automorphism_2021,
|
||
title = {Automorphism Ensemble Decoding of Reed–Muller Codes},
|
||
volume = {69},
|
||
issn = {1558-0857},
|
||
url = {https://ieeexplore.ieee.org/document/9492151},
|
||
doi = {10.1109/TCOMM.2021.3098798},
|
||
abstract = {Reed–Muller ({RM}) codes are known for their good
|
||
maximum likelihood ({ML}) performance in the short block-length
|
||
regime. Despite being one of the oldest classes of channel codes,
|
||
finding a low complexity soft-input decoding scheme is still an
|
||
open problem. In this work, we present a versatile decoding
|
||
architecture for {RM} codes based on their rich automorphism
|
||
group. The decoding algorithm can be seen as a generalization of
|
||
multiple-bases belief propagation ({MBBP}) and may use any polar
|
||
or {RM} decoder as constituent decoders. We provide extensive
|
||
error-rate performance simulations for successive cancellation
|
||
({SC})-, {SC}-list ({SCL})- and belief propagation ({BP})-based
|
||
constituent decoders. We furthermore compare our results to
|
||
existing decoding schemes and report a near-{ML} performance for
|
||
the {RM}(3,7)-code (e.g., 0.04 {dB} away from the {ML} bound at
|
||
{BLER} of 10−3) at a competitive computational cost. Moreover, we
|
||
provide some insights into the automorphism subgroups of {RM}
|
||
codes and {SC} decoding and, thereby, prove the theoretical
|
||
limitations of this method with respect to polar codes.},
|
||
pages = {6424--6438},
|
||
number = {10},
|
||
journaltitle = {{IEEE} Transactions on Communications},
|
||
author = {Geiselhart, Marvin and Elkelesh, Ahmed and Ebada,
|
||
Moustafa and Cammerer, Sebastian and Brink, Stephan ten},
|
||
urldate = {2025-11-13},
|
||
date = {2021-07-21},
|
||
note = {{TLDR}: A versatile decoding architecture for {RM} codes
|
||
based on their rich automorphism group is presented and the
|
||
theoretical limitations of this method with respect to polar
|
||
codes are proved.},
|
||
keywords = {/unread, \#{FND}, Belief propagation, belief
|
||
propagation decoding, code automorphisms, Complexity theory,
|
||
Encoding, ensemble decoding, Generators, Iterative decoding, list
|
||
decoding, Maximum likelihood decoding, polar codes, Polar codes,
|
||
Reed-Muller Codes, successive cancellation decoding, \#{CEC}},
|
||
file = {Full Text
|
||
PDF:/home/andreas/Zotero/storage/KV3JR3MS/Geiselhart et al. -
|
||
2021 - Automorphism Ensemble Decoding of Reed–Muller
|
||
Codes.pdf:application/pdf},
|
||
}
|
||
|
||
@article{dirac_new_1939,
|
||
title = {A new notation for quantum mechanics},
|
||
volume = {35},
|
||
issn = {1469-8064, 0305-0041},
|
||
url =
|
||
{https://www.cambridge.org/core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society/article/abs/new-notation-for-quantum-mechanics/4631DB9213D680D6332BA11799D76AFB},
|
||
doi = {10.1017/S0305004100021162},
|
||
abstract = {In mathematical theories the question of notation,
|
||
while not of primary importance, is yet worthy of careful
|
||
consideration, since a good notation can be of great value in
|
||
helping the development of a theory, by making it easy to write
|
||
down those quantities or combinations of quantities that are
|
||
important, and difficult or impossible to write down those that
|
||
are unimportant. The summation convention in tensor analysis is
|
||
an example, illustrating how specially appropriate a notation can be.},
|
||
language = {en},
|
||
number = {3},
|
||
journal = {Mathematical Proceedings of the Cambridge Philosophical Society},
|
||
author = {Dirac, P. a. M.},
|
||
month = jul,
|
||
year = {1939},
|
||
keywords = {/unread},
|
||
pages = {416--418},
|
||
}
|
||
|