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December 13, 2019

CATEGORY: Blog [back]
TOPIC: Quantum Dating Market [refresh]

Blogger Daniel Doro Ferrante wrote on Mar. 9, 2010 @ 18:38 GMT
It’s too late for Valentine’s Day, and too early for April Fool’s Day, so when I first saw the paper a paper titled “Quantum Dating Market, I wasn’t quite sure what to make of it. But in the spirit of William Orem’s post, “Quantum of Love,” I decided to take a look.

It turns out that the paper deals with the well-known “Stable Marriage Problem.” From Wikipedia’s entry on the topic: “Given 'n' men and 'n' women, where each person has ranked all members of the opposite sex with a unique number between '1' and 'n' in order of preference, marry the men and women off such that there are no two people of opposite sex who would both rather have each other than their current partners. If there are no such people, all the marriages are "stable".”

In the quantum dating market paper, O.G. Zabaleta and C.M. Arizmendi use a quantum algorithm to attack the problem rather than the traditional classical algorithm.

To better appreciate this result, you might want to look at some of these sources to better understand the needed ingredients.

Game theory: Wikipedia and Stanford Encyclopedia of Philosophy

Quantum Game Theory: Wikipedia, “An invitation to Quantum Game Theory” and “Quantum Game Theory (AMS Notices)

Game Theory (classical, non-quantum), roughly speaking, deals with the following problem: situations in which strategical interactions between rational players yields results with respect to the preferences chosen by said players.

Speaking a bit more mathematically, let us define a game with n people (i.e., players) through the following 2 properties,

1. 'n' sets

$S_{i}, \qquad i=1, \,\ldots\, , \, n ;$

2. 'n' real-valued functions

$P_{i}\qquad : \qquad S_{1}\times\,\dots\,\times S_{n} \rightarrow\mathbb{R}\; , \qquad i = 1,\,\ldots\, ,\, n .$

The set Si is called the “Strategy Space” of the i-th player, and the function Pi is called the “Payoff Function” of the i-th player.

This formulation is generic enough to model almost any concrete problem of strategic interactions: the Si are the available actions to player (we imagine the each player must choose an action); the actions have some consequence and Pi measures what player measures as this consequence.

Given the above, we can try and define what is a “Quantum Game”: naïvely speaking, a quantum game is one in which each player implements a _mixed_ strategy, what requires that the Strategy Space be _expanded_. Thus, in a quantum game, the player can choose a strategy that is a _linear combination_ of the classical strategies,

$S = \alpha_{1}\; S_{1} + \,\dots\, + \alpha_{n}\; S_{n}$

such that,

$\sum_{i=1}^{n} \alpha_{i} = 1 \; .$

However, this linear combination only captures one of the characteristics present in a quantum game: there is still another one which is relevant in this problem: quantum entanglement. Therefore, at the end of the day, the final result of a quantum game is different from what would be obtained through the use of a mixed strategy, once quantum entanglement could lead to very non-trivial results.

In the paper, the authors apply Grover's algorithm, which is a quantum algorithm, to the Stable Marriage Problem. The power of Grover's Algorithm is that it performs an unordered database search in

$O\bigl(\sqrt{n}\bigr)$

rather than the classical
$O(N)$

Making a loose analogy (a free interpretation of the meaning of a quantum strategy for the dating market), essentially, the paper says that a quantum strategy is more efficient to solve the SMP. Well, this implies that a certain male player would choose to date several female players (with a certain probability to each female player) at the same time, repeating this process several times, until an "equilibrium state" would be found, i.e., until the male player found its "better half".

However, one of the possible outcomes of the quantum entanglement would be that in which all female players decide, at the _same time_, not to date the male player anymore. So perhaps not such a good romantic outcome after all.

this post has been edited by the author since its original submission

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Mary Q wrote on Mar. 10, 2010 @ 12:08 GMT
In what contexts is the stable mariage problem usually applied? I'm guessing not in actual dating contexts?

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FQXi Administrator Brendan Foster replied on Mar. 10, 2010 @ 15:23 GMT
On a similar note, to what extent is the 'quantum-ness' really quantum? Can a classical dater use the quantum strategy? i.e. does 'entanglement' just mean 'dating around', or is it something wilder?

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Anonymous replied on Mar. 10, 2010 @ 18:41 GMT
"Does 'entanglement' just mean 'dating around', or is it something wilder?"

Maybe it involves dating twins, separated by a large distance.

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Member Ian Durham replied on Mar. 10, 2010 @ 21:24 GMT
Yeah, so in regards to the "quantum-ness," this is a lot like the idea of simulating quantum computers on classical computers. So, sure, the person can be "classical" but can still execute the quantum algorithm if he/she has some way to carry out parallel processes.

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paul vallettta wrote on Mar. 10, 2010 @ 20:23 GMT
The question is choice, to choose or not to choose?.

There are many probable outcomes just ask Woods, Terry or cole.

A real Quantum "gamer" would of course never get hitched in the first place, they choose to be Uncertain about all choices regarding forever Enatanglements! ;)

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Lawrence B. Crowell wrote on Mar. 11, 2010 @ 00:09 GMT
This approach to an equilibrium state sounds similar to the wave function reduction, or collapse. A quantum system will execute a Poincare recurrence, so a closed unitary system (no complicating matters of gravity included) will not permanently settle into a single state.

Cheers LC

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Jason Wolfe replied on Mar. 11, 2010 @ 01:11 GMT
Lawrence,

I've been thinking about quantum mechanics with regards to the production line that I provide technician support for. Right now, I am looking for an intermittent problem to see if it's the board that's broken or something else. I wanted to be very careful with how I document information. I started to write down

Test fixture i = 1,2...

Questioniable board i = 1,2...

Dongle i = 1,2...

I could have multiple test fixtures, multible boards, multiple dongle; if each of those has subpart, I start to get matrices of different conditions. It all started to remind me of quantum mechanics. Whatever the problem (symptom) actually is, it becomes a "particle" within this particuliar production line.

In trying to figure out what the problem is, it's like we're trying to identify what the "particle" is by how it behaves within its particular production universe.

I hope that doesn't sound too quirky.

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Blogger Daniel Doro Ferrante wrote on Mar. 11, 2010 @ 00:20 GMT
@Mary Q: there are many "real world" examples of applications of the SMP, e.g., in the US, it's used to pair medical students with hospital jobs (residence programs). However, I actually don't know how "dating websites" choose their algorithms… ;-)

@Brendan Foster: I think that, between the Anonymous and Ian Durham, you have a response. ;-) In any case, as far i know, you cannot classically simulate entanglement. My analogy was tongue-in-cheek (or tongue-in-chik, as you prefer ;-)… just meant as a teaser and not to be taken literally. 8-)

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Lawrence B. Crowell wrote on Mar. 12, 2010 @ 03:01 GMT
You can numerically integrate quantum problems. Doing this brings about its own problems to solve, such as numerical errors that cause exponential growth of wave function magnitudes. This can be solved by continually normalizing wave functions, but then digital filters may be needed to eliminate noise and ... . So in that sense you can classically simulate entanglement in the sense of a virtual world. Quantum physics has none of those annoying problems because it is already "quantal."

Quantum manufacturing would be the extreme end of nanotechnology I suppose. Who knows, maybe an atomic force microscope could rearrange atoms on a substrate in a quantum manner.

Cheers LC

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Marshall Barnes wrote on Mar. 14, 2010 @ 14:58 GMT
The comment by anonymous about dating twins at a greater distance reminds me, in part, of a series of experiments that I conducted with a private research group in the early 90s. It had to do with the actions of people who resemble each other but have not been in direct contact or even know each other. The key was that each one of them had to know one experimenter.

Long story short is that we found a greater incidence of encounters with unknown women who looked like the ones the experimenters knew, than anyone else. "Contact" was determined by the unknowns actions and not the experimenters', removing the possibility of cheating or even unintentional contamination. For example the experimenter walks into a coffee shop and happens to see a "copy". That might be worth a few points but he's not allowed to say anything to her. The real points that mattered were if she saw him and then engaged him in a conversation. That was scored much higher. The highest points were scored if, during such conversation, she remarked about something that her "original" would normally say.

The basis was to test for unusual variations of the whole spooky action at a distance model derived from the EPR paradox. I thought about it, in relation to the dating twins at a greater distance remark, because what we found was that the copies (or what we called them by various names based on how much they resembled the originals that the experimenters knew) seemed to be there to convey a message or at least serve as a reminder. It was like having the original there for a few moments, thus like seeing one twin while the other is some place else.

It was just an in-house type of experiment, kind of a "let's see what happens"...

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Converter wrote on Mar. 18, 2010 @ 09:26 GMT
Interesting posting.....

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songjoong sdfsd df wrote on Dec. 27, 2017 @ 07:18 GMT
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