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).

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.

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

]]>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?

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

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

added pointer to:

- Steven Duplij, Raimund Vogl,
*Innovative Quantum Computing*, IOP (2023) [ISBN:978-0-7503-5281-9]

added pointer to today’s

- Anton Frisk et al.,
*Lecture notes on quantum computing*[arXiv:2311.08445]

added pointer to:

- Vivien M. Kendon, Kae Nemoto, William J. Munro,
*Quantum Analogue Computing*, Phil. Trans. R. Soc. A**368**1924 (2010) 3621-3632 [arXiv:1001.2215, doi:10.1098/rsta.2010.0017]

added pointer to:

- Peter Shor,
*Quantum Computation*, Lecture notes (2022) [web]

added pointer to:

- Adriano Barenco,
*Quantum Physics and Computers*, Contemp. Phys.**37**(1996) 375-389 [arXiv:quant-ph/9612014, doi:10.1080/00107519608217543]

added pointer to:

- Richard Feynman,
*Quantum mechanical computers*, Foundations of Physics**16**(1986) 507–531 [doi:10.1007/BF01886518]

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.”

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]

added pointer to:

- David P. DiVincenzo,
*The Physical Implementation of Quantum Computation*, Fortschr. Phys.**48**9-11 (2000) 771-783 [arXiv:quant-ph/0002077, doi:10.1002/1521-3978(200009)48:9/11%3C771::AID-PROP771%3E3.0.CO;2-E]

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

]]>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)

added these pointers:

Eleanor Rieffel, Wolfgang Polak,

*Quantum Computing – A gentle introduction*, MIT Press (2011) [ISBN:9780262526678, pdf]Eleanor Rieffel, Wolfgang Polak,

*An Introduction to Quantum Computing for Non-Physicists*, ACM Comput. Surveys**32**(2000) 300-335 [arXiv:quant-ph/9809016, doi:10.1145/367701.367709]

Starting a section (here) listing commercially available quantum computers

]]>added pointer to:

- Paul Benioff,
*Quantum Mechanical Models of Turing Machines That Dissipate No Energy*, Phys. Rev. Lett.**48**1581 (1982) [doi:10.1103/PhysRevLett.48.1581]

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.

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.

]]>added pointer to:

- Yuri I. Manin,
*Classical computing, quantum computing, and Shor’s factoring algorithm*, Astérisque,**266**Séminaire Bourbaki 862 (2000) 375-404 [arXiv:quant-ph/9903008, numdam:SB_1998-1999__41__375_0]

Noteworthy on p. 4:

]]>Categorical language is appropriate to this end.

added pointer to this textbook:

- Phillip Kaye, Raymond Laflamme, Michele Mosca,
*An Introduction to Quantum Computing*Oxford University Press (2007) [pdf, ISBN:9780198570493]