Bosonic coding: introduction and use cases



What is the GKP code?

AI: The GKP code is a type of bosonic stabilizer code with a discrete stabilizer group whose generators are position and momentum displacements that commute for fine-tuned values of their magnitudes. The logical subspace is a joint qudit \(+1\)-eigenvalue eigenspace spanned by codewords that are expressed as a particular lattice of position states.

What does it mean a "stabilizer code"?

AI: A "stabilizer code" is a quantum error-correcting code that uses stabilizer generators to detect and correct errors. The stabilizer group consists of commuting operators that have +1 eigenvalue on the code space. It can protect against certain types of errors in a quantum system and is designed to protect against specific types of noise, depending on the code used.

What does the acronym "GKP" stand for?

AI: The acronym "GKP" stands for "Gottesman-Kitaev-Preskill".


Victor V. Albert


Bosonic or continuous-variable coding is a field concerned with robust quantum information processing and communication with electromagnetic signals or mechanical modes. I review bosonic quantum memories, characterizing them as either bosonic stabilizer or bosonic Fock-state codes. I then enumerate various applications of bosonic encodings, four of which circumvent no-go theorems due to the intrinsic infinite-dimensionality of bosonic systems.

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Dear Dr. Albert -- Thank you for posting your review paper. One of the new services that ScienceCast offers is an independent, unbiased, and open peer-review of the papers. Below is an example of such a peer review on this exciting manuscript. This is for demonstration purposes only and you should feel free to  reply to these comment or not, or share them with any potential interested publication outlets. Thank you again for your contribution to this ScienceCast/arXiv Labs project.
ScienceCast Board

Referee Report (for information purposes only):

I have read the manuscript "A Comprehensive Overview of Bosonic Quantum Error-Correcting Codes" and found the paper to be a detailed, informative review of the current state of bosonic quantum error correction. The paper discusses the basics of bosonic error correction, the various code families, ongoing developments, and the potential future direction of the field. The author has done a commendable job in presenting the information clearly and concisely.

While the manuscript provides a strong foundation for understanding bosonic quantum error-correcting codes, there are a few areas where the author could address some questions or provide additional clarity.

  1. In the discussion of the major bosonic code families, it would be helpful if the author could provide a clearer comparison between the performance and resource requirements of each code family. This would aid readers in understanding the relative strengths and weaknesses of each code family and facilitate their choice for specific applications.
  2. The section on hardware efficiency mentions that bosonic platforms can be more resource-efficient than discrete-variable platforms in certain situations. It would be beneficial for the author to provide specific examples or case studies where this advantage has been demonstrated or is anticipated to be significant.
  3. Regarding the ongoing developments in bosonic error correction, the author briefly discusses the noise-bias preservation advantage. It would be helpful if the author could elaborate on the practical implications of this advantage and its potential impact on the performance of quantum error-correcting codes.
  4. The paper states that the future of quantum error correction likely lies in the synthesis of both bosonic and discrete-variable error correction paradigms. While this claim seems plausible, it would be helpful for the author to provide more evidence or examples to substantiate this claim. Additionally, a discussion of the challenges that need to be addressed to realize this synthesis would be beneficial.

To conclude, the manuscript provides a valuable and comprehensive overview of bosonic quantum error-correcting codes. Addressing the above questions and providing additional clarity in the mentioned areas would further strengthen the paper and make it an even more useful resource for readers interested in the field of quantum error correction.

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