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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeApr 18th 2013
    • CommentRowNumber2.
    • CommentAuthorzskoda
    • CommentTimeApr 20th 2013
    • (edited Apr 20th 2013)

    I was convinced that John had discussed this as one of the topics planned for Azimuth Project, but my search did not find any directly related entry there, maybe John wrote about it elsewhere ? To some extent it s related to

    • John C. Baez, Mike Stay, Physics, topology, logic and computation: a rosetta stone, arxiv/0903.0340

    which I will quote in the entry. The first ideas on quantum computing were due a paper of Feynman I think, but can not search for it now.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeApr 24th 2013

    I have added to the references at quantum computation and at monad (in computer science) and at functional programming a pointer to

    • Thorsten Altenkirch, Alexander Green, The quantum IO monad, in Semantic Techniques in Quantum Computation, January 2009, appeared in 2010
    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeDec 23rd 2013

    added this reference here to quantum computation

    and slightly re-arranged and briefly commented on the items in the list of references

    (all still very stubby)

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeJan 7th 2014

    added to quantum computation an explicit pointer to the article

    • Ugo Dal Lago, Claudia Faggian, On Multiplicative Linear Logic, Modality and Quantum Circuits (arXiv:1210.0613)

    which argues explicitly that linear (modal) logic is a good formalization of quantum compuation.

    But I need to stare at that article a bit more to get a better idea of what their modality does. Adding qbits? I am not sure if I got the point here.

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeFeb 7th 2020

    added this pointer:

    diff, v29, current

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeFeb 13th 2020
    • (edited Feb 14th 2020)

    added this more recent review:

    [ah, wrong entry, moved now to topological quantum computing]

    diff, v31, current

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeFeb 14th 2020

    added this more recent survey:

    • National Academies of Sciences, Engineering, and Medicine, Quantum Computing: Progress and Prospects, The National Academies Press 2019 (doi:10.17226/25196)

    diff, v32, current

    • CommentRowNumber9.
    • CommentAuthorzskoda
    • CommentTimeJan 6th 2021

    A reference on a recent experimental achievement.

    • Han-Shen Zhong et al. Quantum computational advantage using photons, Science 370, n. 6523 (2020) 1460-1463 doi

    diff, v35, current

    • CommentRowNumber10.
    • CommentAuthorUrs
    • CommentTimeMay 13th 2021

    I have added little comments on

    1. “classical control/quantum data”,

    2. quantum programming languages as linear type theory

    3. the combination: dependent linear type theory as the language for classically controlled quantum computation

    diff, v47, current

    • CommentRowNumber11.
    • CommentAuthorUrs
    • CommentTimeMay 18th 2021

    Added a bunch of very recent reviews:

    and some still fairly recent:

    • Qiang Zhang, Feihu Xu, Li Li, Nai-Le Liu, Jian-Wei Pan, Quantum information research in China, Quantum Sci. Technol. 4 040503 (doi:10.1088/2058-9565/ab4bea)

    • Farzan Jazaeri, Arnout Beckers, Armin Tajalli, Jean-Michel Sallese, A Review on Quantum Computing: Qubits, Cryogenic Electronics and Cryogenic MOSFET Physics (arXiv:1908.02656)

    diff, v49, current

    • CommentRowNumber12.
    • CommentAuthorUrs
    • CommentTimeMay 22nd 2021

    added the pointers to claims of realizing quantum supremacy:

    and some review:

    diff, v52, current

    • CommentRowNumber13.
    • CommentAuthorUrs
    • CommentTimeDec 23rd 2021
    • (edited Dec 23rd 2021)

    added pointer to:

    diff, v62, current

    • CommentRowNumber14.
    • CommentAuthorUrs
    • CommentTimeJun 16th 2022

    added pointer to today’s

    • Sophie Choe, Quantum computing overview: discrete vs. continuous variable models [[arXic:2206.07246]]

    diff, v65, current

    • CommentRowNumber15.
    • CommentAuthorUrs
    • CommentTimeJun 17th 2022
    • (edited Jun 17th 2022)

    discovered that there are all these pages:

    But I don’t see a top-level page that would link to them (?)

    diff, v66, current

    • CommentRowNumber16.
    • CommentAuthorUrs
    • CommentTimeAug 18th 2022
    • (edited Aug 18th 2022)

    added pointer to today’s

    • John Preskill, The Physics of Quantum Information, talk at The Physics of Quantum Information, 28th Solvay Conference on Physics (2022) [arXiv:2208.08064]

    (Am adding this also at quantum information)

    diff, v67, current

    • CommentRowNumber17.
    • CommentAuthorUrs
    • CommentTimeAug 28th 2022

    added pointer to

    (will also add this at Shor’s algorithm)

    diff, v69, current

    • CommentRowNumber18.
    • CommentAuthorUrs
    • CommentTimeAug 28th 2022

    also added pointer to:

    • John Preskill: Quantum computing and the entanglement frontier: pp. 63-80 in: The Theory of the Quantum World – Proceedings of the 25th Solvay Conference on Physics, World Scientific (2013) [arXiv:1203.5813, doi:10.1142/8674, slides: pdf]

    diff, v69, current

    • CommentRowNumber19.
    • CommentAuthorUrs
    • CommentTimeAug 29th 2022

    added pointer to this textbook:

    diff, v71, current

    • CommentRowNumber20.
    • CommentAuthorUrs
    • CommentTimeSep 1st 2022

    added pointer to:

    Noteworthy on p. 4:

    Categorical language is appropriate to this end.

    diff, v75, current

    • CommentRowNumber21.
    • CommentAuthorUrs
    • CommentTimeSep 1st 2022
    • (edited Sep 1st 2022)

    Can anyone help with Yuri Manin’s original 1980 article on quantum computing?

    Wikipedia references this in the weirdest way (here): via a pointer to the WaybackMachine which then points to a zip-file which finally contains a djvu-scan of Manin’s actual book.

    This seems a shame. I might make a pdf-copy of the file now and directly save it to the nLab server.

    But if anyone knows that/where Manin’s book may be hosted online (maybe on some Russian site which English Google queries won’t detect) please let me know.

    • CommentRowNumber22.
    • CommentAuthorUrs
    • CommentTimeSep 1st 2022
    • (edited Sep 1st 2022)

    Have now referenced it as follows (here):

    • Yuri I. Manin, Introduction to: Computable and Uncomputable, Sov. Radio (1980) [Russian original: pdf], Enlish translation on p. 69-77 of Mathematics as Metaphor: Selected essays of Yuri I. Manin, Collected Works 20, AMS (2007) [ISBN:978-0-8218-4331-4]

    with this quote (which, apart from the preceding paragraph on RNA copying etc., seems to be the gist of it):

    Perhaps, for a better understanding of [molecular biology], we need a mathematical theory of quantum automata.

    • CommentRowNumber23.
    • CommentAuthorUrs
    • CommentTimeOct 2nd 2022

    added pointer to:

    diff, v80, current

    • CommentRowNumber24.
    • CommentAuthorUrs
    • CommentTimeOct 27th 2022

    Starting a section (here) listing commercially available quantum computers

    diff, v83, current

    • CommentRowNumber25.
    • CommentAuthorUrs
    • CommentTimeOct 28th 2022

    added these pointers:

    diff, v85, current

    • CommentRowNumber26.
    • CommentAuthorUrs
    • CommentTimeNov 7th 2022
    • (edited Nov 7th 2022)

    In the graphics (here) showing the SQRAM model of Nagarajan, Papanikolaou & Williams (2007), Fig. 1 I have highlighted in purple the process which the Quipper community calls dynamic lifting (will give this its own little page now)

    diff, v88, current

    • CommentRowNumber27.
    • CommentAuthorUrs
    • CommentTimeNov 9th 2022

    added at least a brief mentioning of non-determinism to the first idea-praragraphs (here)

    diff, v90, current

    • CommentRowNumber28.
    • CommentAuthorUrs
    • CommentTimeFeb 19th 2023

    added pointer to:

    diff, v103, current

    • CommentRowNumber29.
    • CommentAuthorUrs
    • CommentTimeMar 15th 2023

    added pointer to:

    • Samuel J. Lomonaco (ed.), Quantum Computation: A Grand Mathematical Challenge for the Twenty-First Century and the Millennium, Proceedings of Symposia in Applied Mathematics 58, AMS (2002) [doi:10.1090/psapm/058]

    diff, v105, current

    • CommentRowNumber30.
    • CommentAuthorUrs
    • CommentTimeMay 19th 2023
    • (edited May 19th 2023)

    added pointer to this recent preprint:

    • Olivier Ezratty, Where are we heading with NISQ? [arXiv:2305.09518]

      “no one has yet successfully implemented a use case matching the original definition of the NISQ regime.”

    diff, v108, current

    • CommentRowNumber31.
    • CommentAuthorUrs
    • CommentTimeAug 16th 2023

    added pointer to:

    diff, v111, current

    • CommentRowNumber32.
    • CommentAuthorUrs
    • CommentTimeAug 16th 2023

    added pointer to:

    diff, v111, current

    • CommentRowNumber33.
    • CommentAuthorUrs
    • CommentTimeAug 18th 2023

    added pointer to:

    diff, v112, current

    • CommentRowNumber34.
    • CommentAuthorUrs
    • CommentTimeSep 22nd 2023

    added pointer to:

    diff, v116, current

    • CommentRowNumber35.
    • CommentAuthorUrs
    • CommentTimeNov 16th 2023

    added pointer to today’s

    diff, v119, current

    • CommentRowNumber36.
    • CommentAuthorUrs
    • CommentTimeJan 30th 2024

    added pointer to:

    diff, v120, current

    • CommentRowNumber37.
    • CommentAuthorUrs
    • CommentTime3 days ago

    added a few more references and quotes under References – NISQ (here)

    diff, v122, current

    • CommentRowNumber38.
    • CommentAuthorUrs
    • CommentTime1 day ago

    have expanded a little the section on classical control (here)

    diff, v125, current

    • CommentRowNumber39.
    • CommentAuthorDavid_Corfield
    • CommentTime6 hours ago

    In fact, languages for classically controlled quantum computation should be based on dependent linear type theory (Vakar 14, Vakar 15, Vakar 17, Sec. 3, Lundfall 17, Lundfall 18, following Schreiber 14) with categorical semantics in indexed monoidal categories:

    Worth adding something here on tangent \infty-toposes?

    • CommentRowNumber40.
    • CommentAuthorUrs
    • CommentTime2 hours ago

    Right now busy preparing talk notes which touch on this (but aimed at a “quantum matter”-audience far remote from topos theory): here.

  1. That’s an interesting way to put things:

    What makes this work, semantically, is a deep surprising theorem in modern algebraic topology which roughly says – echoing Bohr’s famous standpoint:

    Topological quantum logic, when parameterized, becomes a form of classical logic.

    • CommentRowNumber42.
    • CommentAuthorUrs
    • CommentTime44 minutes ago
    • (edited 44 minutes ago)

    Yes, it’s noteworthy. I had first tried to verbalize this on top of p. 5 of the Quantum Monadology, but there is room left to say it in more relatable terms.

    One of the participant type-theorists of RunningHoTT a few weeks ago quite picked up this point of how this approach allows to keep all of classical type-theorist’s tools in place and build on them in order to do quantum, instead of needing to start from scratch (cf. p. 2 of Mitchell’s slides, despite their terseness).