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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeFeb 7th 2020

stub

• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeFeb 7th 2020

still stub

• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeFeb 7th 2020

• Alexander Jahn, Marek Gluza, Fernando Pastawski, Jens Eisert, Majorana dimers and holographic quantum error-correcting codes, Phys. Rev. Research 1, 033079 (2019) (arXiv:1905.03268)
• CommentRowNumber4.
• CommentAuthorUrs
• CommentTimeFeb 11th 2020

• CommentRowNumber5.
• CommentAuthorUrs
• CommentTimeFeb 14th 2020

• Simon J. Devitt, Kae Nemoto, William J. Munro, Quantum Error Correction for Beginners, Rep. Prog. Phys. 76 (2013) 076001 (arXiv:0905.2794)
• CommentRowNumber6.
• CommentAuthorUrs
• CommentTimeFeb 12th 2021

• CommentRowNumber7.
• CommentAuthorUrs
• CommentTimeFeb 20th 2021

added these references on operator algebraic formulation of quantum error correction in the Heisenberg picture:

• Cédric Bény, Achim Kempf, David W. Kribs, Generalization of Quantum Error Correction via the Heisenberg Picture, Phys. Rev. Lett. 98, 100502 – Published 7 March 2007 (doi:10.1103/PhysRevLett.98.100502, arXiv:quant-ph/0608071)

• Cédric Bény, Achim Kempf, David W. Kribs, Quantum Error Correction of Observables, Phys. Rev. A 76, 042303 (2007) (arXiv:0705.1574)

• CommentRowNumber8.
• CommentAuthorUrs
• CommentTimeMay 2nd 2021

I have tried my hand on some first linea of an Idea-section, and then added the simple explicit example (here) of a qtrit error correcting code from CGL 99 as highlighted in ADH 14.

Still need to add a more abstract definition/characterization…

• CommentRowNumber9.
• CommentAuthorUrs
• CommentTimeMay 2nd 2021
• (edited May 2nd 2021)

• Andrew J. Ferris, David Poulin, Tensor Networks and Quantum Error Correction, Phys. Rev. Lett. 113, 030501 (2014) (arXiv:1312.4578)

• CommentRowNumber10.
• CommentAuthorUrs
• CommentTimeMay 9th 2021

• CommentRowNumber11.
• CommentAuthorUrs
• CommentTimeMay 9th 2021

• CommentRowNumber12.
• CommentAuthorUrs
• CommentTimeMay 9th 2021

• Sam Cree, Kfir Dolev, Vladimir Calvera, Dominic J. Williamson, Fault-tolerant logical gates in holographic stabilizer codes are severely restricted (arXiv:2103.13404)
• CommentRowNumber13.
• CommentAuthorUrs
• CommentTimeMay 9th 2021

that last article (CDCW 21) comments on the perspective of practical usefulness of holographic codes (finally, I kept looking for this in vain).

I have added the following quote from the article to the Idea-section of the entry:

There are a number of reasons to suspect that holographic codes may be of practical use for quantum computing.

Holographic codes can admit erasure thresholds comparable to that of the widely-studied surfacecode, and likewise for their threshold against Pauli errors. Their holographic structure also naturally leads to an organization of encoded qubits into a hierarchy of levels of protection from errors, which could be useful for applications which call for many qubits withvarying levels of protection. In particular, this is reminiscent of many schemes for magic state distillation – and indeed, the concatenated codes utilized for magic state distillation share a similar hierarchical structure to holographic codes. The layered structure of holographic codes is also reminiscent of memory architectures in classical computers, where it is useful to have different levels of short- and long-term memory. Although these codes have some notable drawbacks, in particular holographic stabilizer codes require nonlocal stabilizer generators, other codes such as concatenated codes suffer similar drawbacks and have still proven to be useful. Conversely, the stringent requirement of non-local stabilizer generators allows holographic codes to protect many more qubits than a topological code and in fact attain a finite nonzero encoding rate, which is typically not possible for topological codes. Nonetheless, many open questions remain about the usefulness of holographic codes for fault-tolerant quantum computing.

• CommentRowNumber14.
• CommentAuthorUrs
• CommentTimeMay 9th 2021

• CommentRowNumber15.
• CommentAuthorUrs
• CommentTimeMay 9th 2021

• CommentRowNumber16.
• CommentAuthorUrs
• CommentTimeMay 9th 2021
• (edited May 9th 2021)

• {#WVSB20} Paul Webster, Michael Vasmer, Thomas R. Scruby, Stephen D. Bartlett, Universal Fault-Tolerant Quantum Computing with Stabiliser Codes (arXiv:2012.05260)

with this quote:

$[$ holographic codes $]$ could be promising candidates to circumvent our results and could possibly realise a universal set of unitary implementations of logical operators.

• CommentRowNumber17.
• CommentAuthorUrs
• CommentTimeMay 19th 2021

with this quote:

Although we are currently in an era of quantum computers with tens of noisy qubits, it is likely that a decisive, practical quantum advantage can only be achieved with a scalable, fault-tolerant, error-corrected quantum computer. Therefore, development of quantum error correction is one of the central themes of the next five to ten years.

• CommentRowNumber18.
• CommentAuthorUrs
• CommentTimeMay 19th 2021

• Daniel Nigg, Markus Mueller, Esteban A. Martinez, Philipp Schindler, Markus Hennrich, Thomas Monz, Miguel A. Martin-Delgado, Rainer Blatt,

Experimental Quantum Computations on a Topologically Encoded Qubit, Science 18 Jul 2014: Vol. 345, Issue 6194, pp. 302-305 (arXiv:1403.5426, doi:10.1126/science.1253742)

and am also adding this to topological quantum computation with anyons – references

• CommentRowNumber19.
• CommentAuthorUrs
• CommentTimeMay 20th 2021

• Iulia Georgescu, Strings and qubits, Nature Reviews Physics volume 1, page 477 (2019) (doi:s42254-019-0087-6)
• CommentRowNumber20.
• CommentAuthorUrs
• CommentTimeMay 20th 2021
• (edited May 20th 2021)

added pointer to this remarkable item:

• CommentRowNumber21.
• CommentAuthorUrs
• CommentTimeMay 20th 2021

with this quote:

The codes provided by AdS/CFT often come close to saturating theoretical bounds on the performance of quantum codes. It seems AdS/CFT may be a tool for discovering better quantumcryptography?

• CommentRowNumber22.
• CommentAuthorUrs
• CommentTimeMay 22nd 2021

Even though it’s promotional, I have added this pointer, from just days ago

with the following quote, since it’s the best reference I can find, so far, on outlook/expectation on the pracrtical realizability of quantum error correction:

Within the decade, Google aims to build a useful, error-corrected quantum computer. $[\cdots]$ Our journey to build an error-corrected quantum computer within the decade includes several scientific milestones, including building an error-corrected logical qubit.

• CommentRowNumber23.
• CommentAuthorUrs
• CommentTimeMay 22nd 2021
• (edited May 22nd 2021)

on the other hand, over in China:

• Ming Gong et al. Experimental exploration of five-qubit quantum error correcting code with superconducting qubits, National Science Review, nwab011 (2021) (doi:10.1093/nsr/nwab011)

survey in:

EurekaAlert, Science China Press: Demonstration of the universal quantum error correcting code with superconducting qubits, March 2021 (2021-03/scp-dot031521)

• CommentRowNumber24.
• CommentAuthorDavid_Corfield
• CommentTimeMay 22nd 2021

The 21st century version of the Space Race.

• CommentRowNumber25.
• CommentAuthorUrs
• CommentTimeAug 16th 2021

(this would better fit in an entry “quantum cryptography”, which however we don’t have yet…)

• CommentRowNumber26.
• CommentAuthorUrs
• CommentTimeNov 23rd 2021

• Alexey Milekhin, Quantum error correction and large $N$ (arXiv:2008.12869)
• CommentRowNumber27.
• CommentAuthorUrs
• CommentTimeFeb 11th 2022

For when the editing functionality is back, to add pointer to today’s:

• Ning Bao, Charles Cao, Guanyu Zhu, Deconfinement and Error Thresholds in Holography (arXiv:2202.04710)
• CommentRowNumber28.
• CommentAuthorUrs
• CommentTimeMar 4th 2022

For when the editing functionality is back, to add pointer to today’s:

• Ning Bao, Joydeep Naskar, Code Properties of the Holographic Sierpinski Triangle (arXiv:2203.01379)