Talk:Quantum finite automaton

typo?

Its been a while since my CS classes but shouldn't the state machine be listed as:

(1*01*0)*

This (1*01*01*)* expanded would become 1*01*01*1*01*01*...

1*=1*1* so it seems redundent.

Mdozturk 19:23, 16 November 2006 (UTC)

This makes my head hurt. Someone please write articles like these in... English, please.

what is the meaning of accepted

I may not read it well. How do you define the fact that a string is accepted? Is it a yes-no accept? I did not even identify where you discuss it. So I even less understand what is a language recognized by such an automaton.Teetooan (talk) 20:19, 26 February 2014 (UTC)

A string is accepted if, after measurement, the wave-function collapses to a state that is within the "accept" Hilbert space. Membership in this space is unambiguous: either it is or it isn't, so accepting is a yes/no decision.

Trying to figure out what kind of languages are accepted by these automatons is an ongoing area of research. You can't just think about it for a few minutes or an hour, and immediately know what the language is. However, I think it is fair to say that, for every QFA, there is a sequence of DFA's that approximate it arbitrarily well, and so the languages differ only on "small sets", in the limit, sets of measure-zero, if you assign a measure. But then you have to assign a measure, so that makes things complicated, again, etc (things become "markovian" when you start supplying measures...). A given QFA will of course have a much much more compact defintion that a DFA that approximates it. Kind-of-like how a non-deterministic FA is a much smaller description than a deterministic one. 67.198.37.16 (talk) 20:47, 15 August 2015 (UTC)

What is the point or this? Examples?

The article only states what QFAs are and how they are constructed. It lacks the why.

Some use cases would be cool or the description of problems, which can be solved by those. --RicardAnufriev (talk) 03:10, 16 December 2014 (UTC)

QFA's are a simplified version of quantum Turing machines, aka quantum computers. These are currently being studied because some people believe that they might be more efficient than regular computers at solving certain problems (e.g. breaking cryptography). But mostly, QFA's are studied for the same reason anything in math is studied: cause it is fun -- not because it's useful. 67.198.37.16 (talk) 20:51, 15 August 2015 (UTC)

Bad information in Informal description

" After each application of $\{U_{\alpha }\}$, though, the column vector q must be renormalized so that it only contains zeros and ones"

This is false, there is no need to normalize q. As $q_{j}\Sigma _{i}U_{\alpha _{ij}}>0\implies q_{j}>0\land \Sigma _{i}U_{\alpha _{i,j}}>0$. Note the case with negatives is not valid as we we known $U_{\alpha _{ij}}=0\lor U_{\alpha _{ij}}=1$. Hence it does not matter if q is normalized. --SelfStudyBuddy^TALK-- 00:39, 4 December 2017 (UTC)