Talk:Grover's algorithm

message: This article needs to flesh out the potential uses for Grover's algorithm.
There are some real challenges to scalability.
Moveovergrover (talk) 00:45, 18 March 2012 (UTC)
thread_title: Potential uses

message: from the article:
Furthermore, the probability of obtaining the wrong answer becomes O(1/N), which goes to zero for large N.
I could be way off the mark, especially because I don't understand the content of the article, but I understand O-notation is used in expressing the performance of an algorithm, not for the probability of a particular output. However, I really know nothing about quantum physics, barely more about the study of algorithms, and I haven't even read the entire article.
Moskvax 14:34, 16 November 2005 (UTC)
thread_title:  Incorrect use of O-notation? 

message: So if we search one state, then we mark this state changing this state sign. But how grovers algorithm can change sign if we are searching more than one state at once?
What will be on output? Two state at once? 212.59.24.195
:If, instead of 1 matching entry, there are k matching entries, the same algorithm works but the number of iterations must be π(N/k)1/2/4 instead of πN1/2/4
:is a quote from the article. This is the probability of getting one of the entries. If you want them all you have to run the algorithm at least k times. Don't forget to sign your posts with four tildas ~~~~ . Skippydo 01:05, 6 August 2007 (UTC)
thread_title:  How grover algorithm work if we searching more than one componenet? 

message: What do these oracle operators look like? Am I required to store for every f(x) a different oracle operator to find x? How do I have to imagine that? Can't I just find y (a number) corresponding to x (another number) by just querying f(x)?  —Preceding unsigned comment added by 84.75.137.125 (talk) 00:26, 14 January 2008 (UTC)
thread_title:  Better explanation 

message: The article often seems to use the example of N=16.  I say seems since there is no explanatory text that says for example for N = 16.  Is this intentional?  --Michael C. Price talk 12:00, 4 May 2008 (UTC)
replies: text: That is odd. I deleted the numerical examples since anyone capable of understanding the rest of the math in the article is presumably capable of plugging in numbers on their own... -- BenRG (talk) 12:39, 4 May 2008 (UTC)
thread_title: Why N=16?

message: "The optimality of Grover's algorithm suggests (but does not prove) that NP is not contained in BQP."
This statement is grossly misleading. The failure of Grover's algorithm to solve NP-complete problems efficiently does not "suggest" in any meaningful way that all of BQP also fails. Grover's algorithm is merely performing black box search -- this statement is akin to the oft-repeated "proof" that P does not equal NP, "because you have to check all the (exponentially many) possibilities".
This would be like, if I said that, if I want to find shortest paths in a graph, well if the graph has size n, then there are n! many paths, so if I go down the list crossing them off, I can't do it efficiently. Even using quantum speed up to do the black box search, I still can't do it efficiently. So I guess its impossible to do it efficiently. 
Wrong! If you are clever and think about it, it is not hard to come up with efficient algorithms for shortest path. Ruling out one naive approach, which uses none of the mathematical structure of 3SAT at all, and trying to argue from that that BQP probably doesn't contain NP, is like trying a sudoku puzzle, and when you do not get it immediately on your first guess, saying "Gee this suggests its impossible."  64.90.83.200 (talk) 06:27, 25 July 2010 (UTC)
replies: text: I also found this statement confusing, and had to do a bit of digging. My best guess at the intent of this statement is to represent the chain of reasoning described in this quantum computing stack exchange answer: NP-complete problems are solvable in exponentially many steps, Grover's algorithm provides at most a square-root speedup, the square root of an exponential function is still an exponential function. I proposed an edit to this effect. Tuzki17 (talk) 17:52, 18 August 2022 (UTC)
thread_title:  About NP vs. BQP 

message: The definition reads "Each of the eigenstates of Ω encode one of the entries in the database, in a manner that we will describe." The encoding of the entries is nowhere described (and of course is not needed). Was text removed ? The sentence needs to be changed. The way it reads now the only interpretation possible is that the lambdas encode the entries(which of course could be, but isn't described). Suggestion: retain mention of the "entries" but change this sentence so that the encoded entries are given as { C1, C2, C3...CN }. This avoids confusion.  — Preceding unsigned comment added by 79.161.24.236 (talk) 21:08, 25 October 2011 (UTC)
replies: text: I rewrote the setup section but I don't think it addresses your latest concern, other than removing the offending sentence. A function f is usually defined as a quantum map via the transformation |x>|y> to |x>|f(x)+y>. Given such a map corresponding to the database search criterion, this can be turned into the map described in the article by using an auxillary qubit intitialized to |1> and two Hadammard maps. That is, |x>|1> to |x> (|0>-|1>) to |x> (|f(x)>-|1+f(x)>) to (-1)^f(x) |x>|1>. This is what happens in the Deutsch–Jozsa algorithm as well. I'm not sure if it can/should be worked into the article. Skippydo (talk) 00:34, 28 October 2011 (UTC)
thread_title:  Text missing: Encoding of entries is NOT included... 

message: In the Algorithm description the measurement Ω and the measurement result λω are not properly defined.
— Preceding unsigned comment added by 79.161.24.236 (talk) 21:47, 16 June 2013 (UTC)
thread_title:  Measurement Ω and λω not defined 

message: In the Limitations section it may be useful to point out that the algorithm does not work if half the possible binary strings are solutions. MClerc (talk) 11:46, 1 July 2023 (UTC)
replies: text: Clarification for both this and issues with greater than half solutions in the multiple entry case has now been provided in the multiple matching entries section. Deep Gabriel (talk) 06:22, 1 September 2023 (UTC)
thread_title:  Fifty-fifty => no amplification 

message: https://www.youtube.com/watch?v=ElYwWPsPRUY Doug youvan (talk) 20:02, 13 February 2024 (UTC)
thread_title:  Simple Animation of Grover's Algorithm