“quantum mechanics is exactly true”; the framework says “the state of the world is a unit vector in a complex Hilbert space”

Nit-picky but important remark (which you are probably aware of):

We only **model** the state of the world as a unit vector in a complex Hilbert space. We make our **models** using the **framework** of quantum mechanics. It is **the best framework that we have**. The framework uses complex numbers.

But complex numbers themselves **do not exist**. Even **real numbers do not exist** [1]. So our models cannot be “exactly true”. They only work devastatingly well (and probably well enough). Until they don’t.

*[1]: e.g. this paper by Gisin (if a real number was physically real, you could store more information in it than there are atoms in the universe)*

I don’t mind skipping the chapters covering Turing machines and I wouldn’t mind a brush up on complexity classes etc but I’m looking for something where I can skip the basics of non-quantum computation without finding myself flipping back for notation every 5 minutes and doesn’t avoid covering the hard new stuff. I’ve seen a few books claimed to be aimed at mathematical audiences but they seem to think mathematical audiences mean analysts (I mean I enjoyed linear algebra in ug/grad and I’m not bad at it but I don’t yet have intuitions about diagonals and eigenvectors).

Anyone have suggestions?

]]>Yeah, I have heard of dissipative approach but cannot wrap my head around what is being claimed let alone how it works. This is over my head.

]]>no, quantum gates do not need to be reversible, as shown, for example by this proposal for efficient universal quantum computation based on dissipation: https://arxiv.org/abs/0803.1447

and by measurement-based quantum computation: PRL 86, 5188 (2001), reviewed in https://arxiv.org/abs/0910.1116

1. Google said Kasparov would lose 9-1

2. IBM said Kasparov would lose only 5.5-4.5

In 2023 IBM’s device will have 1K qubits, and nobody will give a damn anymore.

]]>1. In the Sycamore case, the researchers largely invented a new game to play

2. In the Sycamore case, the researchers themselves also played the part of Kasparov

3. In the Sycamore case, a huge leap compared to previous efforts is claimed ]]>

ppnl #70

James #71

Thank you all! Very interesting!

]]>Another clarification was: “I want to add that I do appreciate Gisin’s later work to make the connection to intuitionism, but even so I had contact to people working on dependent type theory, category theory, and all that higher order stuff, it never crossed my mind that there might be a connection to the riddle of how to avoid accidental infinite information content.”

Later I also tried to explain with a concrete example how a central paradigm of intuitionism (the concrete representation of information is important) is related to that discussion: “What I try to show with this example is that adding more words later can reduce the information content of what has been said previously. But how much information can be removed later depends on the representation of the information. So representations are important in intuitionisitic mathematics, and classical mathematics is seen as a truncation where equivalence has been replaced by equality.”

Maybe it was not the most natural example. A very canonical example is that for a computation that can fail, all failing computations are put into the same equivalence class, independent of how much output the computation produced before failing. But this means that in this representation, failing allows to remove all information given earlier. So with one last word, everything that has been said before can be invalidated!

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